Search

• A piezoelectric combined cantilever-asymmetric-pendulum structure is proposed. • Can efficiently harvest vibratory energy from any arbitrary direction. • Numerical analysis presented as well as simulation conducted to validate theory and proposed model. • The improvement of the voltage amplitude and operational bandwidth are 128.5 % and 229.8 % over variable excitation amplitudes, respectively. This paper introduces a novel approach to address the challenges faced by traditional unidirectional cantilever-based energy harvesters in adapting to multi-directional vibration environments. The proposed solution combines a flexible cantilever with an asymmetric-conical-pendulum structure which consists of two different concentrated end masses and a rigid thin rod By investigation of energy interchange relationship between the kinetic feature of the asymmetric pendulum and beam bending vibration under horizontal and vertical excitations respectively from base movements, utilizing the Lagrange's theorem and multiple-scale method, 1:2 internal resonance can be induced for enabling the delivery of multi-directional motion of pendulums to the unidirectional bending of cantilever. On this basis, the advantages of the proposed system are revealed by comparing with traditional piezoelectric cantilever and piezoelectric cantilever-single-pendulum systems. Furthermore, the performance of the voltage amplitude and operational bandwidth was potentially improved up to 128.5 % and 229.8 % under x -direction. In addition, it is confirmed that its maximum voltage RMS value is 57.9 % and 11.4 % higher than that of the piezoelectric cantilever-single-pendulum in the x - and z -directions, owing to its multi-peak energy harvesting over variable excitation amplitudes. Therefore, the feasibility and superiorities of the proposed configuration are demonstrated theoretically and numerically in this paper. [ABSTRACT FROM AUTHOR]

The paper discusses a choice of minimal model for describing friction induced vibrations in systems with sealings between the moving and non-moving part. Two models, a classical "mass-on-belt" system and a two-mass model are compared. The parameter study shows that the two-mass model has much better agreement with the practical experiences than the mass-on-belt system. The paper includes the description of the models, the results of numerical analysis and some considerations about the restriction of friction-induced vibrations. [ABSTRACT FROM AUTHOR]

Periodic structures feature frequency band gaps in which the propagation of certain waves will be attenuated. Therefore, they are widely applied in the vibration control of structures. The premise of this theory is that the structure should be perfectly periodic. However, this must be broken more or less due to inevitable deviations, leading structures to disorder. The vibration reduction performance can be significantly altered by the disorder, as reported by various authors. Moreover, the disorder pattern plays an important role in such a performance change. In this paper, we study the influence of the disorder patterns and explore a general permutation to retune the disordered periodic structures which means to reduce the deviation of the dynamic characteristics between the nominal and disordered structures. This research is conducted through three stages. In the first stage, a diatomic lumped-mass model is used. We study the implication of the disorder and propose a sorting strategy inspired by global sensitivity analysis (GSA). In the second stage, the sorting strategy is corroborated with numerical simulations by a finite element (FE) model of beam. We use the wave finite element method (WFEM) to calculate the band gaps. A thousand samples are generated randomly to test the sorting strategy and the contrarian strategy. In the third stage, the sorting strategy is verified by an experimental structure of beam. We set up an experimental system and scheme to measure and analyze the effects of the strategy for 5 groups of experiments. We show that vibration suppression may deteriorate statistically due to disorder for periodic structures. Specifically, vibration mitigation is most sensitive to the deviation in the first unit cell from the excitation. Inspired by this finding, a retuning strategy is proposed for the first time, i.e. the unit cell with the smallest deviation should be arranged in the position nearest to the excitation. The results in all stages show that the strategy can significantly improve the similarity of the dynamic characteristics between the nominal and disordered structures. [Display omitted] • Vibration suppression may deteriorate statistically due to disorder for periodic structures. • A retuning strategy is proposed for the first time and verified experimentally. • The unit cell with minimum deviation should be arranged near the excitation. • The influence of disorder is reduced by an order of magnitude after retuning. [ABSTRACT FROM AUTHOR]

Stochastic resonance (SR) has been proven effective for weak signal detection under low signal-to-noise ratio (SNR) conditions. In this paper, a parameter matched stochastic resonance (PMSR) method is proposed to enhance the detection and extraction ability to weak signatures of moving vessels. Theoretical matched framework is established with a damped bistable SR model by optimizing the input-output signal-to-noise ratio improvement (SNRI) to nonlinear system parameters. By selecting a proper damping factor within a determinate constraint range, a weak periodic signal, background noise, and nonlinear system can be matched in generating a desired optimal output in the regime of matched parameter relationship. Then, we propose a PMSR based energy detection (ED) algorithm by taking the fully advantage of the Lorentzian characteristics. Numerical simulation analyses and application verifications are carried out to validate the effectiveness and efficiency of the proposed method, which reflects an excellent enhancement performance especially for low-frequency ship signatures. [ABSTRACT FROM AUTHOR]

In this paper, a combined numerical and experimental method, called Extended Load Confluence Algorithm, is presented to accurately predict the dynamic response of non-periodic structures when little or no information about the applied loads is available. This approach, which falls into the category of Shape Sensing methods, inputs limited experimental information acquired from sensors to a mapping algorithm that predicts the response at unmeasured locations. The proposed algorithm consists of three major cores: an experimental core for data acquisition, a numerical core based on Finite Element Method for modeling the structure, and a mapping algorithm that improves the numerical model based on a modal approach in the frequency domain. The robustness and precision of the proposed algorithm are verified through numerical and experimental examples. The results of this paper demonstrate that without a precise knowledge of the loads acting on the structure, the dynamic behavior of the system can be predicted in an effective and precise manner after just a few iterations. [ABSTRACT FROM AUTHOR]

Abstract Complex-shaped aluminium panels are adopted in many structures to make them lighter and stronger. The vibro-acoustic behaviour of these complex panels has been of interest for many years but conventional finite element and boundary element methods are not efficient in predicting their performance at higher frequencies. Where the cross-sectional properties of the panels are constant in one direction, which is the case for extruded panels, wavenumber domain numerical analysis can be applied and this becomes particularly suitable for panels with complex cross-sectional geometries. Because they are based on a two-dimensional model, these methods can reduce the computational cost compared with other numerical methods using full three-dimensional models, while nevertheless including three-dimensional effects. In this paper, a coupled waveguide finite element and boundary element method is applied to predict the radiation efficiency and sound transmission of a double-layered aluminium extruded panel from a train carriage floor. The results are interpreted in the wavenumber domain from which the contributions of different types of waves can be identified. In the calculations, the air cavities between top and bottom panels are considered to examine their contributions to the vibro-acoustic behaviour of the panel. The predicted results are compared with measured ones obtained using a finite length panel. To reflect the finite length of the actual panel used in the measurement, spatial window functions are applied to the sound transmission through the infinitely long panel, giving improved agreement with the measurements. [ABSTRACT FROM AUTHOR]

Abstract In this paper we proposed a hierarchical structure with tetrad elliptical patterns in perforated plates. It is discovered that the introduction of structural hierarchy can enhance wave energy localization and introduce additional band gaps in 3d plates, in which elastic wave cannot propagate. However, if the hierarchical level increases further, extra vibration modes will be introduced, which may lead to the narrowing or vanishing of the band gaps. Parametric studies have been carried out to illustrate the possibility of tuning band gaps with geometric variation, and the results also demonstrate that the effect of structural hierarchy is not only limited to one specific geometric configuration. In this study, the finite element analysis and band diagram analysis are used for investigation. Moreover, experimental tests have been conducted for level-1 and level-2 perforated plates for comparison, and excellent agreement between numerical analysis and experimental tests has been achieved, which also shows the feasibility of applying this strategy in structural design and other vibration mitigation applications. [ABSTRACT FROM AUTHOR]

Abstract Research on nonlinear isolation has always focused on the vibration of discrete systems. The elastic vibration of the main structure itself is always ignored. In order to study the influence of the multimodal elastic vibration of the main structure on the nonlinear isolation effect, nonlinear isolation of the transverse vibration of a pre-pressure elastic beam is studied in this paper. Three linear springs are utilized to build a nonlinear isolation system, in which horizontal springs are utilized to provide non-linearity and to achieve quasi-zero stiffness. The transverse vibration of the beam is isolated by the elastic support at the two ends. The Galerkin truncation method (GTM) is used to solve the response of the forced vibration. The isolation effect of the primary resonance of the pre-pressure beam is presented. The effects of the axial pre-pressure and nonlinear isolation system on vibration transmission are explored. Results of the GTM are confirmed by utilizing the finite difference method (FDM). It also illustrates the effectiveness of the proposed difference method for nonlinear support structures. The numerical results demonstrate that under certain conditions, the quasi-zero stiffness isolation system may increase the transmission of high-order modal vibration of the elastic continuum. Furthermore, this work finds that the initial axial pre-pressure could be beneficial to vibration isolation of elastic structures. [ABSTRACT FROM AUTHOR]

Abstract Recently, a wavenumber approach was proposed to analyse the active control of plane waves with arrays of secondary sources (J. Sound Vib. 419, 405–419, 2018) for improving the sound transmission loss of open windows by distributing an array of loudspeakers evenly on the opening. This paper investigates the feasibility of the boundary control for sound transmission through an opening, which only installs the secondary sources on its frame and thus has advantages of better ventilation and easier access. An analytical model is developed first to obtain the sound field transmitted into a cavity with a baffled opening by using the modal expansion method, and then the performances of the boundary control systems are investigated for different primary source and secondary source configurations numerically based on the model. The wavelength corresponding to the upper limit effective frequency of the proposed boundary control system with more than 10 dB noise reduction is found to be equal to the length of the short sides of the opening. Finally, experimental results are presented to verify the discoveries. [ABSTRACT FROM AUTHOR]

Abstract Predicting the response of gas turbine blades with underplatform friction dampers is challenging due to the combination of frictional nonlinearity and system uncertainty: a traditional Monte Carlo approach to predicting response distributions requires a large number of nonlinear simulations which is computationally expensive. This paper presents a new approach based on the principle of Maximum Entropy that provides an estimate of the response distribution that is approximately two orders of magnitude faster than Monte Carlo Harmonic Balance Method simulations. The premise is to include the concept of 'computational uncertainty': incorporating lack of knowledge of the solution as part of the uncertainty, on the basis that there are diminishing returns in computing precise solutions to an uncertain system. To achieve this, the method uses a describing function approximation of the friction-damped part of the system; chooses an ignorance prior probability density function for the complex value of the describing function based on Coulombs friction law; updates the distribution using an estimate of the mean solution, the admissible domain of solutions, and the principle of Maximum Entropy; then carries out a linear Monte Carlo simulation to estimate the response distribution. The approach is validated by comparison with HBM simulations and experimental tests, using an idealised academic system consisting of a periodic array of beams (with controllable uncertainty) coupled by single-point friction dampers. Comparisons with two- and eight-blade systems show generally good agreement. Predicting the response statistics of the maximum blade amplitude reveals specific well-understood circumstances when the method is less effective. Predictions of the overall blade response statistics agree with Monte Carlo HBM extremely well across a wide range of excitation amplitudes and uncertainty levels. Critically, experimental comparisons reveal the care that is needed in accurately characterising uncertainty in order to obtain agreement of response percentiles. The new method allowed fast iteration of uncertainty parameters and correlations to achieve good agreement, which would not have been possible using traditional methods. Highlights • A new approach to predict variability of friction-damped turbine blades is presented. • The method uses Maximum Entropy to estimate a PDF of the friction describing function. • Computationally expensive Monte Carlo simulations of the nonlinear system are avoided. • Comparisons with numerical and experimental tests show generally good agreement. • The method enables rapid estimates of the response distribution. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we provide a variational derivation of modified Bresse-Timoshenko equations. This process leads to the additional term to so called truncated set of Bresse-Timoshenko equations; this new term is associated with the modified slope inertia. The two sets of truncated versions of the Bresse-Timoshenko equations are contrasted with each other, as well as with the original Bresse-Timoshenko equations on the example of the (a) beam that is simply supported at its both ends, and (b) the cantilever beam with end mass. It is concluded that application of either truncated sets of equations is advantageous over the original Bresse-Timoshenko equations. As far as two truncated sets of equations are concerned, the variationally derived set appears to be preferable. [ABSTRACT FROM AUTHOR]

This paper presents the calculation of Lyapunov exponents in a beam subjected to distributed impact. In this case, discontinuity sporadically occurs over the contacted area. The impact area is spatially discretized and the transition condition at impact instance is applied to all impact nodes in the finite element manner. The solution of the continuous vibration in the impacted beam is expressed in the modal expansion form. Then, the spectra of Lyapunov exponents in the periodic and chaotic motion are estimated for the truncated number of modes. Numerical results show that the calculated largest Lyapunov exponent agrees with the bifurcation plot. [ABSTRACT FROM AUTHOR]

We present a new formulation to calculate the response of a system containing rolling-element bearings operating under a radial clearance and a dominant radial load. The nonlinear bearing force- and stiffness-displacement characteristics in combination with the bearing clearance necessitate an advanced numerical analysis. The response of a shaft-bearing-housing assembly can be unstable in the transient regions, e.g., at the start of a system run-up or when passing the critical speed of a system. This can lead to long computational times or even to non-converged solutions. In this paper, a new analytical bearing-stiffness model is presented that is capable of overcoming these problems by smoothing the nonlinear bearing force- and stiffness-displacement characteristics in the discontinuous regions. The smoothing is implemented on the deformation scale. The proposed model is modular, allowing us to define a specific value of the smoothing to each rolling element that comes into contact. A simple case study that involves two bearings of different types (ball and cylindrical roller) is presented. They support an unbalanced rotor, subjected to a constant angular acceleration. We show that a small smoothing value can significantly enhance the numerical calculation of the chosen system in terms of speed and stability. [ABSTRACT FROM AUTHOR]

This paper presents a 2-D semi-analytical model for the vibration analyses of a plate with a power-law-profiled thickness variation, referred to as an Acoustic Black Hole (ABH) plate. The proposed model, along with the associated wavelet-based solution procedure, is intended to overcome major technical difficulties which are specific to ABH structures: the non-uniform wavelength distribution and ABH-induced wave compressions at the high frequency range in a realistic structure of finite size. Under the general Rayleigh-Ritz framework, Daubechies wavelet (DW) scaling functions are chosen as the admissible functions to decompose the transverse displacement of the plate with ABH indentations featuring a thickness variation along one direction of the panel. Modal and forced vibration analyses are carried out with results compared with those obtained by the FEM. It is shown that the model allows an accurate prediction of various vibration parameters and a realistic description of the typical ABH phenomena. Meanwhile, the use of Daubechies wavelet functions allows enhancing the effectiveness of the Rayleigh-Ritz method to reach the high frequency range, where systematic Acoustic Black Hole (ABH) effects are expected. Numerical analyses also reveal the potential of using strip ABH indentations in a plate to achieve a light-weight design with appealing vibration reduction properties. Analyses on the ABH-induced damping enhancement demonstrate the dominant effect of the local structural modes within indented area, which exhibit lower-order deformations (containing typically half and one wave along the direction in which the thickness is tailored). [ABSTRACT FROM AUTHOR]

This paper is concerned with the development of a simplified model for noise control treatments to speed up finite element analysis in vibroacoustic applications. The methodology relies on the assumption that the acoustic treatment is flat and homogeneous. Moreover, its finite lateral extent is neglected. This hypothesis is justified by short wavelength and large dissipation, which suggest that the reflected field emanating from the acoustic treatment lateral boundaries does not substantially affect its dynamic response. Under these circumstances, the response of the noise control treatment can be formally obtained by means of convolution integrals involving simple analytical kernels (i.e. Green functions). Such fundamental solutions can be computed efficiently by the transfer matrix method. However, some arbitrariness arises in the formulation of the mathematical model, resulting in different baffling conditions at the two ends of the treatment to be considered. Thus, the paper investigates the possibility of different formulations (i.e. baffling conditions) within the same hybrid finite element-transfer matrix framework, seeking for the best strategy in terms of tradeoff between efficiency and accuracy. Numerical examples are provided to show strengths and limitations of the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper investigates a coupled computational analysis framework that uses reduced-order models and the generalized finite element method to model vibratory induced stress near local defects. The application area of interest is the life prediction of thin gauge structural components exhibiting nonlinear, path-dependent dynamic response. Full-order finite element models of these structural components can require prohibitively large amounts of processor time. Recent developments in nonlinear reduced-order models have demonstrated efficient computation of the dynamic response. These models are relatively insensitive to small imperfections. Conversely, the generalized finite element method provides the ability to model local defects without geometric dependency on the mesh. A more robust version of the method, with numerically built enrichment functions, provides a multiple-scale modeling capability through direct coupling of global and local finite element models. Replacing the component finite element model with a reduced-order model allows for efficient computation of dynamic response while providing the necessary information to drive local, solid analyses which can zoom in on regions containing stress risers or cracks. This paper describes the coupling of these approaches to enable fatigue and crack propagation predictions. Numerical/experimental examples are provided. [ABSTRACT FROM AUTHOR]

Abstract: The present paper considers the problem of realizing an effective targeted energy pumping from a linear oscillator to a set of ungrounded linear resonators attached to it. Theoretical as well as numerical results demonstrate the efficacy of using a complex attachment as a passive absorber of broadband energy injected into the primary structure. The paper unveils also the existence of an instantaneous frequency associated with the master response characterized by intermittency: a rather surprising result for a linear autonomous system. Comparison with nonlinear energy sinks demonstrates that the two systems have some analogies in this respect and that the linear complex attachment is a very efficient energy trap. [Copyright &y& Elsevier]

Abstract: Train–track interaction has been extensively studied in the last 40 years at least, leading to modelling approaches that can deal satisfactorily with many dynamic problems arising at the wheel/rail interface. However, the available models are usually not considering specifically the running dynamics of the vehicle in a curve, whereas a number of train–track interaction phenomena are specific to curve negotiation. The aim of this paper is to define a model for a flexible wheelset running on a flexible curved track. The main novelty of this work is to combine a trajectory coordinate set with Eulerian modal coordinates; the former permits to consider curved tracks, and the latter models the small relative displacements between the trajectory frame and the solid. In order to reduce the computational complexity of the problem, one single flexible wheelset is considered instead of one complete bogie, and suitable forces are prescribed at the primary suspension seats so that the mean values of the creepages and contact forces are consistent with the low frequency curving dynamics of the complete vehicle. The wheelset model is coupled to a cyclic track model having constant curvature by means of a wheel/rail contact model which accounts for the actual geometry of the contacting profiles and for the nonlinear relationship between creepages and creep forces. The proposed model can be used to analyse a variety of dynamic problems for railway vehicles, including rail corrugation and wheel polygonalisation, squeal noise, numerical estimation of the wheelset service loads. In this paper, simulation results are presented for some selected running conditions to exemplify the application of the model to the study of realistic train–track interaction cases and to point out the importance of curve negotiation effects specifically addressed in the work. [Copyright &y& Elsevier]

In the context of aeronautics, automotive and construction applications, the design of light multilayer plates with optimized vibroacoustical damping and isolation performances remains a major industrial challenge and a hot topic of research. This paper focuses on the vibrational behavior of three-layered sandwich composite plates in a broad-band frequency range. Several aspects are studied through measurement techniques and analytical modelling of a steel/polymer/steel plate sandwich system. A contactless measurement of the velocity field of plates using a scanning laser vibrometer is performed, from which the equivalent single layer complex rigidity (apparent bending stiffness and apparent damping) in the mid/high frequency ranges is estimated. The results are combined with low/mid frequency estimations obtained with a high-resolution modal analysis method so that the frequency dependent equivalent Young's modulus and equivalent loss factor of the composite plate are identified for the whole [40 Hz-20 kHz] frequency band. The results are in very good agreement with an equivalent single layer analytical modelling based on wave propagation analysis (model of Guyader). The comparison with this model allows identifying the frequency dependent complex modulus of the polymer core layer through inverse resolution. Dynamical mechanical analysis measurements are also performed on the polymer layer alone and compared with the values obtained through the inverse method. Again, a good agreement between these two estimations over the broad-band frequency range demonstrates the validity of the approach. [ABSTRACT FROM AUTHOR]

As the number of degrees of freedom (DOFs) in structural dynamic problems becomes larger, the analyzing complexity and CPU usage of computers increase drastically. Condensation (or reduction) method is an efficient technique to reduce the size of the full model or the dimension of the structural matrices by eliminating the unimportant DOFs. After the first presentation of condensation method by Guyan in 1965 for undamped structures, which ignores the dynamic effects of the mass term, various forms of dynamic condensation methods were presented to overcome this issue. Moreover, researchers have tried to expand the dynamic condensation method to non-classically damped structures. Dynamic reduction of such systems is far more complicated than undamped systems. The proposed non-iterative method in this paper is introduced as 'Maclaurin Expansion of the frequency response function in Laplace Domain' (MELD) applied for dynamic reduction of non-classically damped structures. The present approach is implemented in four numerical examples of 2D bending-shear-axial frames with various numbers of stories and spans and also a floating raft isolation system. The results of natural frequencies and dynamic responses of models are compared with each other before and after the dynamic reduction. It is shown that the result accuracy has acceptable convergence in both cases. In addition, it is indicated that the result of the proposed method is more accurate than the results of some other existing condensation methods. [ABSTRACT FROM AUTHOR]

Optical interferometry has been successfully applied in measuring acoustic pressures in plane-wave fields and spherical-wave fields. In this paper, the “effective” refractive index for focused acoustic fields was developed, through numerical simulation and experiments, the feasibility of the optical method in measuring acoustic fields of focused transducers was proved. Compared with the results from a membrane hydrophone, it was concluded that the optical method has good spatial resolution and is suitable for detecting focused fields with fluctuant distributions. The influences of a few factors (the generated lamb wave, laser beam directivity, etc.) were analyzed, and corresponding suggestions were proposed for effective application of this technology. [ABSTRACT FROM AUTHOR]

Brush seals are an efficient alternative for labyrinth seals in turbomachinery. Brush seals show on the one hand a better leakage reduction in relation to their axial length and hence allow a shorter design of the machinery. On the other hand, the particularly small gap between bristles and the engine shaft increases the risk of rotor-stator-contact. The flexible brush seals induces basically light-rubs that in some cases might lead to spiral vibrations and thermal mechanical instabilities. Spiral vibrations are caused by a thermal deflection of the rotor induced by a heat flow into the shaft. To predict areas of instabilites during the design process a tool was developed at the Berlin Institute of Technology. The model combines a rotor dynamic model and a thermal model. The thermal system is reduced using a stationary solution, so that the final system, on which the stability analysis is performed, is comparable to the established Kellenberger model. The paper presents the numerical model for the predictions of unstable regions depending on rotational speed. This is illustrated by means of an example of an axial compressor manufactured by MAN Diesel & Turbo. [ABSTRACT FROM AUTHOR]

A strong-form boundary collocation method, the singular boundary method (SBM), is developed in this paper for the wave propagation analysis at low and moderate wavenumbers in periodic structures. The SBM is of several advantages including mathematically simple, easy-to-program, meshless with the application of the concept of origin intensity factors in order to eliminate the singularity of the fundamental solutions and avoid the numerical evaluation of the singular integrals in the boundary element method. Due to the periodic behaviors of the structures, the SBM coefficient matrix can be represented as a block Toeplitz matrix. By employing three different fast Toeplitz-matrix solvers, the computational time and storage requirements are significantly reduced in the proposed SBM analysis. To demonstrate the effectiveness of the proposed SBM formulation for wave propagation analysis in periodic structures, several benchmark examples are presented and discussed The proposed SBM results are compared with the analytical solutions, the reference results and the COMSOL software. [ABSTRACT FROM AUTHOR]

The free vibration analysis of functionally graded beams (FGBs) and frameworks containing FGBs is carried out by applying the dynamic stiffness method and deriving the elements of the dynamic stiffness matrix in explicit algebraic form. The usually adopted rule that the material properties of the FGB vary continuously through the thickness according to a power law forms the fundamental basis of the governing differential equations of motion in free vibration. The differential equations are solved in closed analytical form when the free vibratory motion is harmonic. The dynamic stiffness matrix is then formulated by relating the amplitudes of forces to those of the displacements at the two ends of the beam. Next, the explicit algebraic expressions for the dynamic stiffness elements are derived with the help of symbolic computation. Finally the Wittrick-Williams algorithm is applied as solution technique to solve the free vibration problems of FGBs with uniform cross-section, stepped FGBs and frameworks consisting of FGBs. Some numerical results are validated against published results, but in the absence of published results for frameworks containing FGBs, consistency checks on the reliability of results are performed. The paper closes with discussion of results and conclusions. [ABSTRACT FROM AUTHOR]

This paper presents a numerical analysis for the stick-slip vibration of a transversely moving beam, considering both stick-slip transition and friction force discontinuity. The dynamic state of the beam was separated into the stick state and the slip state, and boundary conditions were defined for both. By applying the finite element method, two matrix-vector equations were derived: one for stick state and the other for slip state. However, the equations have different degrees of freedom depending on whether the end of a beam sticks or slips, so we encountered difficulties in time integration. To overcome the difficulties, we proposed a new numerical technique to alternatively use the matrix-vector equations with different matrix sizes. In addition, to eliminate spurious high-frequency responses, we applied the generalized- α time integration method with appropriate value of high-frequency numerical dissipation. Finally, the dynamic responses of stick-slip vibration were analyzed in time and frequency domains: the dynamic behavior of the beam was explained to facilitate understanding of the stick-slip motion, and frequency characteristics of the stick-slip vibration were investigated in relation to the natural frequencies of the beam. The effects of the axial load and the moving speed upon the dynamic response were also examined. [ABSTRACT FROM AUTHOR]

In this paper, a new structural identification method is proposed to identify the modal properties of engineering structures based on dynamic response decomposition using the variational mode decomposition (VMD). The VMD approach is a decomposition algorithm that has been developed as a means to overcome some of the drawbacks and limitations of the empirical mode decomposition method. The VMD-based modal identification algorithm decomposes the acceleration signal into a series of distinct modal responses and their respective center frequencies, such that when combined their cumulative modal responses reproduce the original acceleration response. The decaying amplitude of the extracted modal responses is then used to identify the modal damping ratios using a linear fitting function on modal response data. Finally, after extracting modal responses from available sensors, the mode shape vector for each of the decomposed modes in the system is identified from all obtained modal response data. To demonstrate the efficiency of the algorithm, a series of numerical, laboratory, and field case studies were evaluated. The laboratory case study utilized the vibration response of a three-story shear frame, whereas the field study leveraged the ambient vibration response of a pedestrian bridge to characterize the modal properties of the structure. The modal properties of the shear frame were computed using analytical approach for a comparison with the experimental modal frequencies. Results from these case studies demonstrated that the proposed method is efficient and accurate in identifying modal data of the structures. [ABSTRACT FROM AUTHOR]

This paper presents the results of an investigation on the dynamics of unforced and vertically forced rocking elliptical and semi-elliptical disks. The full equation of motion for both rocking disks is derived from first principles. For unforced behavior, Lamb's method is used to derive the linear natural frequency of both disks, and harmonic balance is used to determine their amplitude-dependent rocking frequencies. A stability analysis then reveals that the equilibria and stability of the two disks are considerably different, as the semi-elliptical disk has a super-critical pitchfork bifurcation that enables it to exhibit bistable rocking behavior. Experimental studies were conducted to verify the trends. For vertically forced behavior, numerical investigations show the disk's responses to forward and reverse frequency sweeps. Three modes of periodicity were observed for the steady state behavior. Experiments were performed to verify the frequency responses and the presence of the three rocking modes. Comparisons between the experiments and numerical investigations show good agreement. [ABSTRACT FROM AUTHOR]

This paper presents the application of the spectral-Tchebychev (ST) technique for solution of three-dimensional dynamics of curved beams/structures having variable and arbitrary cross-section under mixed boundary conditions. To accurately capture the vibrational behavior of curved structures, a three-dimensional (3D) solution approach is required since these structures generally exhibit coupled motions. In this study, the integral boundary value problem (IBVP) governing the dynamics of the curved structures is found using extended Hamilton's principle where the strain energy is expressed using 3D linear elasticity equation. To solve the IBVP numerically, the 3D spectral Tchebychev (3D-ST) approach is used. To evaluate the integral and derivative operations defined by the IBVP and to render the complex geometry into an equivalent straight beam with rectangular cross-section, a series of coordinate transformations are applied. To validate and assess the performance of the presented solution approach, two case studies are performed: (i) curved beam with rectangular cross-section, (ii) curved and pretwisted beam with airfoil cross-section. In both cases, the results (natural frequencies and mode shapes) are also found using a finite element (FE) solution approach. It is shown that the difference in predicted natural frequencies are less than 1%, and the mode shapes are in excellent agreement based on the modal assurance criteria (MAC) analyses; however, the presented spectral-Tchebychev solution approach significantly reduces the computational burden. Therefore, it can be concluded that the presented solution approach can capture the 3D vibrational behavior of curved beams as accurately as an FE solution, but for a fraction of the computational cost. [ABSTRACT FROM AUTHOR]

Empirical models such as the Eldred standard model are commonly used for rocket noise prediction. Such models directly provide a definition of the Sound Pressure Level through the quadratic pressure term by uncorrelated sources. In this paper, an improvement of the Eldred Standard model has been formulated. This new formulation contains an explicit expression for the acoustic pressure of each noise source, in terms of amplitude and phase, in order to investigate the sources correlation effects and to propagate them through a wave equation. In particular, the correlation effects between adjacent and not-adjacent sources have been modeled and analyzed. The noise prediction obtained with the revised Eldred-based model has then been used for formulating an empirical/BEM (Boundary Element Method) hybrid approach that allows an evaluation of the scattering effects. In the framework of the European Space Agency funded program VECEP (VEga Consolidation and Evolution Programme), these models have been applied for the prediction of the aeroacoustics loads of the VEGA (Vettore Europeo di Generazione Avanzata – Advanced Generation European Carrier Rocket) launch vehicle at lift-off and the results have been compared with experimental data. [ABSTRACT FROM AUTHOR]

• The measurement data is used to validate the pantograph-catenary model in overlap sections. • Strong dependence on interaction performance of the speed with crossing point height is observed. • Steady arm damper improves the trailing pantograph's performance but sacrifice the leading one's. The overlap section is a railway catenary arrangement where the pantograph transfers from one section to another. In the overlap section, the unsynchronised vibration of two contact wires, contact wire height variation, and elasticity unevenness destabilise the pantograph-interaction performance. This paper presents a systematic investigation of the dynamic behaviours of the pantograph-catenary in an overlap section, including the mathematical modeling, model validation and numerical analysis. In combination with the traditional shape-finding method, an initialization procedure is proposed to accurately describe the crossing point height in an overlap section of a catenary. The measurement data of the maximum uplift of the crossing point collected from the field test in the Gardemobanen line is utilised to validate the pantograph-catenary model in the overlap section. The numerical analysis mainly focuses on the effect of the crossing point height and the inclusion of steady arm damping on the interaction performance at different speeds. The results indicate a strong dependence of the dynamic behaviour in an overlap section on the train speed. A good performance can be achieved with a low crossing point when the speed is much lower than the design speed, while a high crossing point can benefit the transition distance and maximum contact force at high speed. The inclusion of a steady arm damper can improve the pantographs' performance at a low speed. However, the effectiveness degrades with the increase of the train speed, especially for the leading pantograph. [ABSTRACT FROM AUTHOR]

This paper describes a floating-frame-of-reference-based (FFRF-based) recursive formulation for flexible bodies. A new definition of the joint coordinate system is introduced that makes it simpler to formulate more concise velocity transformation matrices. A path matrix, which defines the connectivity of the mechanism for the open loop system, simplifies introducing the topology of the rigid and/or flexible spanning tree. The flexible multibody system is often subjected to large reference motion but small deformations. Both Euler–Bernoulli-based beam (EBB) and continuum-mechanics-based beam (CMB) elements are implemented to validate the proposed approach. The reference conditions mentioned here are used to eliminate the rigid body motion from the deformation field, i.e., removal of the coordinate redundancy, in the FFRF. Thus, different reference conditions, such as simply supported, single-cantilever, and double-cantilever are used. Finally, it is demonstrated that the proposed approach is not limited by the choice of reference conditions, which helps the modeler to apply the approach to different multibody applications. In the numerical analysis, the results of the total energy variation and constraint violations of the close loop systems are fulfilled with good accuracy by using both penalty formulation with augmented Lagrangian method and coordinate partitioning approach for constraint stabilization. Furthermore, the proposed semi-recursive method produces dynamic analysis results comparable to the ANCF with better computational efficiency. In the end, compared to fully recursive approach, the proposed semi-recursive approach shows better efficiency and easier implementation. [ABSTRACT FROM AUTHOR]

Abstract: For conservative systems instability can occur only by divergence and the presence of damage can produce both a reduction of the buckling loads and modification of the corresponding mode shapes, depending on the positions and intensities of the damage distribution. For nonconservative systems instability is found to occur by divergence, flutter, or both, characterised by multiple stable and unstable ranges of the loads whose boundary can be altered by the damage distribution. This paper focuses on the stability behaviour of multi-cracked cantilever Euler beam-column subjected to conservative or nonconservative axial loads. The exact flutter and divergence critical loads are obtained by means of the exact closed form solution of the multi-cracked beam-column, derived by the authors in a previous paper. The extensive numerical applications, reported in the paper, aimed at evaluating the influence of several damage scenarios for different values of the degree of nonconservativeness. It is shown how the presence of damage can strongly modify the ranges of divergence and flutter critical loads of the corresponding undamaged cantilever column, which has been the subject of several papers starting from the Pflüger paradoxical results. [Copyright &y& Elsevier]

Abstract: In the present paper we outline the basic theory of assembling substructures for which the dynamics are described as Impulse Response Functions. The assembly procedure computes the time response of a system by evaluating per substructure the convolution product between the Impulse Response Functions and the applied forces, including the interface forces that are computed to satisfy the interface compatibility. We call this approach the Impulse Based Substructuring method since it transposes to the time domain the Frequency Based Substructuring approach. In the Impulse Based Substructuring technique the Impulse Response Functions of the substructures can be gathered either from experimental tests using a hammer impact or from time-integration of numerical submodels. In this paper the implementation of the method is outlined for the case when the impulse responses of the substructures are computed numerically. A simple bar example is shown in order to illustrate the concept. The Impulse Based Substructuring allows fast evaluation of impact response of a structure when the impulse response of its components is known. It can thus be used to efficiently optimize designs of consumer products by including impact behavior at the early stage of the design, but also for performing substructured simulations of complex structures such as offshore wind turbines. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the analysis of the dependence of low frequency impact sound transmission through floating floor systems on in situ matched resonances. The evidence for the floating floor matched resonances has been found previously considering laboratory and numerical tests for one concrete slab and floating floor with varying resilient layers. In the present paper, considering laboratory and field tests for concrete slabs and floating floors with different plan configurations, this evidence is strengthened as differences between laboratory and field measurements of the impact sound level were negligible for the bare concrete slab but not with the floating floor installed. These results were also confirmed numerically. The analysis indicates that the dependence of low frequency impact sound transmission through floating floor systems on in situ matched resonances should be considered in addition to the conventional single degree of freedom models in order to improve accuracy. [Copyright &y& Elsevier]

Abstract: A numerical approach for predicting tonal aerodynamic noise from “open rotors” is presented. “Open rotor” refers to an engine architecture with a pair of counter-rotating propellers. Typical noise spectra from an open rotor consist of dominant tones, which arise due to both the steady loading/thickness and the aerodynamic interaction between the two bladerows. The proposed prediction approach utilizes Reynolds Averaged Navier–Stokes (RANS) Computational Fluid Dynamics (CFD) simulations to obtain near-field description of the noise sources. The near-to-far-field propagation is then carried out by solving the Ffowcs Williams–Hawkings equation. Since the interest of this paper is limited to tone noise, a linearized, frequency domain approach is adopted to solve the wake/vortex–blade interaction problem. This paper focuses primarily on the speed scaling of the aerodynamic tonal noise from open rotors. Even though there is no theoretical mode cut-off due to the absence of nacelle in open rotors, the far-field noise is a strong function of the azimuthal mode order. While the steady loading/thickness noise has circumferential modes of high order, due to the relatively large number of blades ( ), the interaction noise typically has modes of small orders. The high mode orders have very low radiation efficiency and exhibit very strong scaling with Mach number, while the low mode orders show a relatively weaker scaling. The prediction approach is able to capture the speed scaling (observed in experiment) of the overall aerodynamic noise very well. [Copyright &y& Elsevier]

Abstract: Self-sustained musical instruments (bowed string, woodwind and brass instruments) can be modelled by nonlinear lumped dynamical systems. Among these instruments, flutes and flue organ pipes present the particularity to be modelled as a delay dynamical system. In this paper, such a system, a toy model of flute-like instruments, is studied using numerical continuation. Equilibrium and periodic solutions are explored with respect to the blowing pressure, with focus on amplitude and frequency evolutions along the different solution branches, as well as “jumps” between periodic solution branches. The influence of a second model parameter (namely the inharmonicity) on the behaviour of the system is addressed. It is shown that harmonicity plays a key role in the presence of hysteresis or quasiperiodic regime. Throughout the paper, experimental results on a real instrument are presented to illustrate various phenomena, and allow some qualitative comparisons with numerical results. [Copyright &y& Elsevier]

Abstract: This paper proposes the identification of vibration excitations by an inverse method. The use of the local operator of a structure, for which the vibration field is obtained by measurements, is investigated. This method has already been developed on analytically known structures, but there are as yet few applications. The goal of this paper is to adapt the same technique by using an operator obtained with the Finite Element Method rather than a discretised differential motion equation. The first difficulty is the measurement of rotational degrees of freedom. A concept analogous to an observation matrix enabling only the measurement of displacements is then proposed. The method of extracting the operator on a part of the structure is also discussed. Two variants are proposed: an operator with free boundary conditions and a truncated operator without boundary conditions. The first permits identifying internal forces at the boundaries of the subdomain, whereas the second ignores them. In order to regularise the inverse method, a Tikhonov approach is used. An important point of this paper is the discussion of the effect of this regularisation which implies ambiguities between reconstructed forces and moments in the results. The possibility of an a priori “force only” assumption is then demonstrated and recommended. After illustrations obtained from numerical simulations on beams, an experimental validation is provided for a beam excited by a shaker where several signals are used, giving several signal to noise ratios. The results are discussed and compared to the force measured directly by a piezoelectric sensor. [Copyright &y& Elsevier]

Abstract: In this paper, the integrated optimization of actuator placement and vibration control for piezoelectric adaptive truss is studied. Based on the dynamic finite element (FE) model and a linear-quadratic-Gaussian (LQG) model of vibration control for an adaptive truss, an integrated optimization model is built in which an improved quadratic performance index is adopted as the objective function and the mode closed-loop damping ratio, modal controllability and actuator number are selected as the constraints. A layered optimization strategy is implemented to address this optimization problem with discrete-continuous design variable. To prevent the optimization process from converging to the local optimal solution, the genetic algorithm (GA) for outside-layer optimization is extended with an improved penalty function. Numerical examples and the vibration control experiments for piezoelectric adaptive truss were used to validate the efficiency of the proposed method. The following conclusions were drawn from the results. (1) The improved penalty function can orient the optimization process to the global optimal solution. (2) Although the number of struts on the truss is large, the optimization computation time is short because of the high efficiency of the proposed method. (3) In the experiment, the quadratic performance index, modal response and sensor signals for the present paper''s optimal actuator placement scheme are better than those described in the literature, but the placement requires more energy, which is consistent with the numerical results. [Copyright &y& Elsevier]

In a conventional railway track, the rails are laid on sleepers, usually made of concrete, which are supported by a layer of coarse stones known as ballast. This paper focuses on quantifying the influence that the ballast has on the noise produced by the vibration of the track, particularly on the rail and sleeper radiation ratios. A one-fifth scale model of a railway track has been used to conduct acoustic and vibration measurements. This includes reduced-scale ballast that has been produced with stone sizes in the correct proportions. Two different scaling factors (1:√5 and 1:5) have been adopted for the stone sizes in an attempt to reproduce approximately the acoustic properties of full-scale ballast. It is shown that, although a scale factor of 1:√5 gives a better scaling of the acoustic properties, the stones scaled at 1:5 also give acceptable results. The flow resistivity and porosity of this ballast sample have been measured. These have been used in a local reaction model based on the Johnson-Allard formulation to predict the ballast absorption, showing good agreement with measurements of the absorption coefficient. The effects of the presence of the ballast on the noise radiation from a reduced-scale steel rail and concrete sleeper have been investigated experimentally with the ballast located on a rigid foundation. Comparisons are made with the corresponding numerical predictions obtained by using the boundary element method, in which the ballast is represented by a surface impedance. Additionally the finite element method has been used in which the porous medium is considered as an equivalent fluid. From these results it is shown that the extended reaction model gives better agreement with the measurements. Finally, the effects of the ballast vibration on the sleeper radiation have also been investigated for a case of three sleepers embedded in ballast. The ballast vibration is shown to increase the sound radiation by between 1 and 4.5 dB for frequencies between 20 and 300 Hz at full scale whereas at higher frequencies the effect is negligible. [ABSTRACT FROM AUTHOR]

Certain nonlinear vibrating systems have frequency response curves (FRCs), in which isolated detached curves exist inside the main continuous FRC. The behavior of these systems has hitherto been studied analytically and numerically, but to the authors’ knowledge, there is no record of an inner detached FRC being detected experimentally. These curves may be hidden by numerical or experimental analysis, particularly when a system is subject to swept or stepped-sine excitation. Their existence may thus lead to unexpected dramatic changes in the amplitude of the system response. This paper presents an experimental study that involves the design, construction and testing of a specific system that has an isolated detached FRC inside the main continuous FRC. The experimental design of the test rig is supported by multibody dynamic simulations, and in the experimental tests the existence of a detached FRC was verified. [ABSTRACT FROM AUTHOR]

Understanding the occurrence of bearing defects in electrical current signals using Motor Current Signal Analysis (MCSA) requires the implementation of numerical models. In this paper, an electro-magnetic-mechanical model is proposed to describe the dynamic behavior of a squirrel cage induction motor coupled to a rotating shaft supported by elastic foundations. The aim of this research work is to gain understanding of the interaction between multiphysics subsystems, mainly in faulty cases, to decipher the transfer path from the defect to its manifestation in stator currents. A new method of writing dynamic equations for simplified simulations of an induction motor is developed using an angular approach. In addition to its capacity to extend the modeling to non-stationary operating conditions, the model proposed highlights the angular periodicity of the rotating motor’s geometry. The electromagnetic field of the motor is redistributed periodically when a geometric defect occurs on a rotating part of the global system. In this case, the electromagnetic torque of the induction motor may present angularly-periodic variations. After having presented the electromagnetic-mechanical coupling methodology, the influence of torque variations is investigated and the importance of the angle-time function is highlighted. [ABSTRACT FROM AUTHOR]

This investigation aims at assessing the fluid-structure interaction (FSI) occurring during hydraulic transients in straight pipeline systems fixed to anchor blocks. A two mode 4-equation model is implemented incorporating the main interacting mechanisms: Poisson, friction and junction coupling. The resistance to movement due to inertia and dry friction of the anchor blocks is treated as junction coupling. Unsteady skin friction is taken into account in friction coupling. Experimental waterhammer tests collected from a straight copper pipe-rig are used for model validation in terms of wave shape, timing and damping. Numerical results successfully reproduce laboratory measurements for realistic values of calibration parameters. The novelty of this paper is the presentation of a 1D FSI solver capable of describing the resistance to movement of anchor blocks and its effect on the transient pressure wave propagation in straight pipelines. [ABSTRACT FROM AUTHOR]

Previous studies have shown that numerical models of tapered thin-walled C-section beams based on a stepped or piecewise prismatic beam approximation are inaccurate regardless of the number of elements assumed in the discretization. Andrade recently addressed this problem by extending Vlasov beam theory to a tapered geometry resulting in new terms that vanish for the uniform beam. (See One-Dimensional Models for the Spatial Behaviour of Tapered Thin-Walled Bars with Open Cross-Sections: Static, Dynamic and Buckling Analyses, PhD Thesis, University of Coimbra, Portugal, 2012, https://estudogeral.sib.uc.pt ) In this paper, we model the coupled bending-twisting vibration of a cantilevered tapered thin-walled C-section using a Galerkin approximation of Andrade's beam equations resulting in an 8-degree-of-freedom beam element. Experimental natural frequencies and mode shapes for 3 prismatic and 2 tapered channel beams are compared to model predictions. In addition, comparisons are made to detailed shell finite element models and exact solutions for the uniform beams to confirm the validity of the approach. Comparisons to the incorrect stepped model are also presented. [ABSTRACT FROM AUTHOR]

In this paper, the well-established problem of self-excited vibrations in machining is revisited to include the nonlinearity of process damping at the tool and workpiece interface. Machining dynamics is modeled using a time-delayed system with nonlinear damping, and the method of averaging is used to obtain the amplitude of the resulting limit cycles. As a result, an analytical relationship is presented to establish the stability charts corresponding with arbitrary limit cycles in machining systems. The presented analytical solutions are verified using experiments and numerical solutions. [ABSTRACT FROM AUTHOR]

While a piezoelectric-based vibration-driven system is an excellent candidate for actuating small-size crawling-type locomotion robots, it has the major drawback of limited stroke output that would severely constraint the system's locomotion performance. In this paper, to advance the state of the art, we propose two novel designs of piezoelectric vibration-driven locomotion systems. The first utilizes the resonant amplification concept, and the second explores the design of a bistable device. While these two ideas have been explored for piezoelectric actuation amplification in general, they have never been exploited for crawling-type robotic locomotion. Numerical analyses on both systems reveal that resonance and bistability can substantially increase the systems’ average locomotion speed. Moreover, this research shows that with bistability, the system is able to output high average locomotion speed in a wider frequency band, possess multiple locomotion modes, and achieve fast switches among them. Through proof-of-concept prototypes, the predicted locomotion performance improvements brought by resonance and bistability are verified. Finally, the basin stability is evaluated to systematically describe the occurring probability of certain locomotion behavior of the bistable system, which would provide useful guideline to the design and control of bistable vibration-driven locomotion systems. [ABSTRACT FROM AUTHOR]

Periodic solutions of systems with friction are difficult to investigate because of the non-smooth nature of friction laws. This paper examines periodic solutions and most notably stick–slip, on a simple one-degree-of-freedom system (mass, spring, damper, and belt), with Coulomb's friction law, and with a regularized friction law (i.e. the friction coefficient becomes a function of relative speed, with a stiffness parameter). With Coulomb's law, the stick–slip solution is constructed step by step, which gives a usable existence condition. With the regularized law, the Asymptotic Numerical Method and the Harmonic Balance Method provide bifurcation diagrams with respect to the belt speed or normal force, and for several values of the regularization parameter. Formulations from the Coulomb case give the means of a comparison between regularized solutions and a standard reference. With an appropriate definition, regularized stick–slip motion exists, its amplitude increases with respect to the belt speed and its pulsation decreases with respect to the normal force. [ABSTRACT FROM AUTHOR]

A closed-form semi-analytical solution for the vibrations due to a moving point load in a tunnel embedded in a half-space is given in this paper. The tunnel is modelled as an elastic hollow cylinder and the ground surrounding the tunnel as a linear viscoelastic material. The total wave field in the half-space with a cylindrical hole is represented by outgoing cylindrical waves and down-going plane waves. To apply the boundary conditions on the ground surface and at the tunnel–soil interface, the transformation properties between the plane and cylindrical wave functions are employed. The proposed solution can predict the ground vibration from an underground railway tunnel of circular cross-section with a reasonable computational effort and can serve as a benchmark solution for other computational methods. Numerical results for the ground vibrations on the free surface due to a moving constant load and a moving harmonic load applied at the tunnel invert are presented for different load velocities and excitation frequencies. It is found that Rayleigh waves play an important role in the ground vibrations from a shallow tunnel. [ABSTRACT FROM AUTHOR]

The present paper proposes a new strategy for selecting representative points in the probability density evolution method (PDEM) to conduct stochastic seismic response analysis of nonlinear structures with uncertain parameters. In PDEM, the strategy for selecting representative points in random-variate space is of critical importance to the efficiency and accuracy. The proposed strategy is established based on the marginal fractional moments of input random variables, which can be evaluated both analytically and numerically without difficulty before performing stochastic analysis. In this strategy, an optimization problem is actually involved. First, the initial points are generated by a low discrepancy sequence and the corresponding assigned probabilities can be computed accordingly. Then, the initial points are rearranged to minimize the index, which is adopted as the maximum relative error between the estimated marginal moments and the exact ones. The rearranged points are accepted as the representative points in PDEM when the index reaches the prescribed tolerance. Numerical example is investigated, showing that the proposed strategy can achieve the good tradeoff of efficiency and accuracy in PDEM for seismic response analysis of structures with uncertain parameters. [ABSTRACT FROM AUTHOR]

An imprecise probability approach based on evidence theory is proposed for squeal instability analysis of uncertain disc brakes in this paper. First, the squeal instability of the finite element (FE) model of a disc brake is investigated and its dominant unstable eigenvalue is detected by running two typical numerical simulations, i.e., complex eigenvalue analysis (CEA) and transient dynamical analysis. Next, the uncertainty mainly caused by contact and friction is taken into account and some key parameters of the brake are described as uncertain parameters. All these uncertain parameters are usually involved with imprecise data such as incomplete information and conflict information. Finally, a squeal instability analysis model considering imprecise uncertainty is established by integrating evidence theory, Taylor expansion, subinterval analysis and surrogate model. In the proposed analysis model, the uncertain parameters with imprecise data are treated as evidence variables, and the belief measure and plausibility measure are employed to evaluate system squeal instability. The effectiveness of the proposed approach is demonstrated by numerical examples and some interesting observations and conclusions are summarized from the analyses and discussions. The proposed approach is generally limited to the squeal problems without too many investigated parameters. It can be considered as a potential method for squeal instability analysis, which will act as the first step to reduce squeal noise of uncertain brakes with imprecise information. [ABSTRACT FROM AUTHOR]

Abstract: The magnetic properties of carbon nanotubes and their mechanical behaviour in a magnetic field have attracted considerable attention among the scientific and engineering communities. This paper reports an analytical approach to study the effect of a longitudinal magnetic field on the transverse vibration of a magnetically sensitive double-walled carbon nanotube (DWCNT). The study is based on nonlocal elasticity theory. Equivalent analytical nonlocal double-beam theory is utilised. Governing equations for nonlocal transverse vibration of the DWCNT under a longitudinal magnetic field are derived considering the Lorentz magnetic force obtained from Maxwell''s relation. Numerical results from the model show that the longitudinal magnetic field increases the natural frequencies of the DWCNT. Both synchronous and asynchronous vibration phases of the tubes are studied in detail. Synchronous vibration phases of DWCNT are more affected by nonlocal effects than asynchronous vibration phases. The effects of a longitudinal magnetic field on higher natural frequencies are also presented. Vibration response of DWCNT with outer-wall stationary and single-walled carbon nanotube under the effect of longitudinal magnetic field are also discussed in the paper. [Copyright &y& Elsevier]