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The dynamic instability of electroconductive cylindrical shells interacting with an external magnetic fields is considered in the paper. Two cases of applied external dynamic loads are discussed, namely (i) a harmonic mechanical force, and (ii) a harmonic magnetic field force. Analytical descriptions of the two-dimensional equations and associate conditions of dynamic instability are presented. On the basis of the formulated problems, specific issues related to the dynamic instability of electroconductive cylindrical shells in a magnetic field are offered. The study illustrated the effect of magnetoelastic interaction. Specifically it is shown that there exist a minimum value of the given magnetic field intensity, above which the parametric resonance due to external harmonic force is eliminated; furthermore, in a presence of time-harmonic magnetic field the parametric resonance with a resonance frequency can be generated not only near the first frequency of the external magnetic field (which is equal to the natural frequency of vibrations), but near the double frequency of natural vibrations. When the forced vibrations of conductive shells caused by external forces of non-electromagnetic origin is considered, including the effect of a time-harmonic magnetic field, resonance can occur in the presence of a non-stationary harmonic magnetic field. Results reveal that the rapid increase of the amplitude of vibrations occurs when the frequency of the external magnetic field is in close proximity to the first natural frequency of the magnetoelastic vibrations of the plate, as well as when the frequency of the magnetic field, is equal to half of the shell natural frequency.

The identification of nonlinear systems in aeroelasticity poses a significant challenge for practitioners, often hampered by the complex nature of aeroelastic response data which may contain multiple forms of nonlinearity. Characterizing and quantifying nonlinearities is further hampered when the response is obtained at a location which is away from the nonlinear source and/or the response is contaminated by noise. In the present paper, a three-degree-of-freedom airfoil with a freeplay nonlinearity located in the control surface and exposed to transonic flow is investigated. In this Part I paper the main form of analysis is via higher-order spectra techniques to unveil features of the nonlinear mechanism which result from i) structural nonlinearities (freeplay) in isolation and ii) freeplay with Euler derived nonlinear inviscid aerodynamic phenomena (transition between Tijdeman Type-A and Type-B shock motion). It is shown that the control surface structural freeplay nonlinearity is characterized by strong cubic phase-coupling between linear and nonlinear modes. On the other hand, nonlinear inviscid flow phenomena are shown to be characterized by quadratic phase-coupling between linear and nonlinear modular modes, the strength of which is related to the strength of the aerodynamic nonlinearity (amplitude of the shock motion). The nonlinear inviscid flow phenomena do not appear to affect the identification of the freeplay nonlinearity. Conjectures are made which address the transition between aperiodic, quasi-periodic and periodic behavior (pre-flutter), further physical support towards these conjectures is provided in Part II [1] . The limitations of the higher-order spectra approach are assessed, in particular, the analysis demonstrates the difficulty in extracting natural frequencies with this approach.

The Hilbert–Huang Transform is used to analyze the nonlinear aeroelastic response of a 2D 3DOF aeroelastic airfoil system with control surface freeplay under transonic flow conditions. Both static and dynamic aerodynamic conditions, i . e . , for accelerating freestream speed, are considered using a linearized aerodynamic model. The main aim of this paper is to provide an in-depth physical understanding of the observed transition between periodic and aperiodic behavior, and the presence of a stable periodic region well below the domain characterized by stable limit cycles. Physical insights towards the forward and backward abrupt transition between aperiodic/chaotic and periodic behavior types appear to be the result of an internal resonance (IR) phenomenon between linear modes followed by a lock-in between linear and nonlinear modes. More specifically, initially a 2:1 IR between linear modes leads to a shift in the frequency composition and dynamic behavior of the system. A secondary effect of the IR can be observed immediately after the exact point of 2:1 IR such that a nonlinear mode locks into a subharmonic of the linear mode which in-turn drives a finite stable periodic region.

Understanding the effect of mechanical uncertainties can play a significant role in design of the nanocomposites. The uncertain natural frequencies of moderately thick doubly-curved functionally graded composite panels reinforced by carbon nanotube (CNT) are investigated. Specifically, doubly-curved shell panels, including spherical, cylindrical and hyperbolic paraboloid panels are examined. To evaluate uncertainty propagation, uncertainty resources including distribution of the CNT through the thickness as well as the mechanical properties of the CNT and polymer matrix are taken into consideration. To assess the propagated uncertainties in the vibrational characteristics of nanocomposite panels, the interval analysis method is employed while the mechanical properties of nanocomposite panels are predicted using the modified rule of mixture method. Based on the comparison between the results of the present study and those reported in the literature, the accuracy of the results is validated. The sensitivity analysis is performed to distinguish the most prominent uncertain variables. Furthermore, numerical results reveal the influences of various uncertainty resources on the upper and lower bounds of uncertain frequencies and uncertainty propagation percent.

Environmental vibrations often exist in a broadband form. To have a robust performance over a wide frequency range, vibration energy harvesters need to be designed to be insensitive to excitation frequencies. In this paper, we propose a novel two-degree-of-freedom (DOF) piezoelectric energy harvester (PEH) with stoppers that introduce nonlinear dynamic interaction between the two DOFs. First, the mechanical model of the 2DOF system with stoppers is developed by emulating the impact behavior as a piecewise linear stiffness and the working principle is explained. Subsequently, the analytical solution of the system with piecewise linear stiffness is derived using the averaging method and the dynamic response of the system is obtained and confirms its wide bandwidth property. Finally, by integrating the mechanical system with a piezoelectric transducer, the energy harvesting performance of the proposed 2DOF PEH with stoppers is numerically evaluated. The open circuit voltage response of the proposed system is compared with that of the conventional linear 2DOF and 1DOF PEHs. A parametric study reveals the effect of the stopper distance on the energy harvesting performance in terms of both the bandwidth and open circuit voltage output. The superiority of the proposed system in terms of both power output and operation bandwidth is demonstrated.

Structural freeplay due to loosened mechanical linkages is a discrete nonlinear event which occurs pseudo-routinely in modern aircraft, causing severe airframe vibration. This impacts fatigue life, and has serious implications for fleet management and Structural Health Monitoring (SHM). While the concepts which drive SHM for aircraft are traditionally based on reactive procedures, we are currently observing a major shift towards actionable and pro-active condition-based maintenance, known as Prognostics and Health Management (PHM), to significantly reduce fleet sustainment costs. Given this current paradigm shift, there is a demand for the development of novel strategies to address decades old SHM problems, where the adaptation of existing methods or the development of new and innovative techniques both play critical roles. In this paper a signal processing framework is presented, based upon well-established nonlinear system identification methods, to rapidly diagnose structural freeplay in aircraft systems with a focus on the requirements of PHM technology. The framework exploits the nonlinear dynamical characteristics of the structural freeplay anomaly in a transonic aeroelastic system by specifically targeting rich bilinear signatures that are encoded in time-domain sensory outputs, via the Higher-Order Spectra (HOS) and the Empirical Mode Decomposition (EMD). The characteristic freeplay signatures which were initially extracted from computational transonic aeroelastic models are shown to be analogous in a transonic flight-test case-study (an all-movable horizontal tail with actuator freeplay), presenting a rare and important opportunity to verify the practical freeplay identification research. Once verified, a comprehensive understanding of the fundamental bilinear signatures allows the HOS and EMD to be adapted and refined towards a structured freeplay diagnosis framework. Using the extensive flight-test dataset as a case study, it is shown that the freeplay location and magnitude information can be extracted with a high level of robustness, verified by making consistent predictions over a period of three years and several maintenance cycles, with a large variation in Mach number and angle-of-attack (predominantly high angle maneuvers). The paper is intended to communicate the fundamental principles and significance of the data-driven framework, highlighting revisiting and adapting existing well-established nonlinear identification tools, it is possible to address the requirements of contemporary SHM, although practical implementation requires ongoing research. Limitations of the data-driven approach are discussed, predominantly related to data acquisition requirements.

This study has two primary objectives; they are to investigate the nonlinear interactions (or quadratic phase-coupling) in a chaotic Rossler system under periodic closed-loop control via wavelet bispectral analysis; and to further identify the component mechanisms of synchronization. It is observed that a fixed-gain, fixed-frequency controller produces quadratic phase-coupling and decoupling along lines of constant frequency and that are perpendicular to the diagonal of the bicoherence matrix. Further, it was also observed that for synchronization to occur, both frequency entrainment and quadratic phase-coupling must be present. It was found that forcing the Rossler system with a constant frequency did not reduce the amplitude of the resulting period-1 orbit at sufficiently high gains. For the controller with a fixed gain and time-varying error signal, it was found that the time varying forcing frequency (adjusted by an extremum seeking feedback loop) linearizes the Rossler system and in doing so, suppresses the phase coherence completely. The time-varying forcing frequency removes the conditions for frequency entrainment by providing broadband attenuation; the result is suppression without synchronization.

Flutter of sail mounted hydroplanes system is a self-excited dynamic hydroelastic phenomenon due to an undesirable coupling occurring between the elastic structure and hydrodynamic flows. The flutter behavior depends on both structure parameters and free-play nonlinearities in the hydroplanes system. The free-play nonlinearity introduces persistent limit cycle oscillations (LCO) which can cause water noise, and it will have an undesirable effect on the concealment capability of marine vehicles. The impact of structure parameters and free-play of the hydroplanes systems on the hydroelastic stability is not fully understood and is an active area of research. In order to explore the fundamental nature of the hydroplanes system, the present paper, Part II of this work, focus on two aspects: (i) the analysis of the full-scale hydroplanes system hydroelastic response based on Computational Fluid Dynamics/Computational Structure Dynamics (CFD/CSD) two-way coupling method which verified by the AGARD 445.6 wing standard flutter model. Results show that the hydroplanes system hydroelastic response is completely symmetrical, and it proves Part I work, that is the full-scale system can be simplified as one hydroplane with a torsional spring. Additionally, (ii) the 2-DOF structural model and the Theodorsen's theory of hydroplanes system are used to get a better understanding of the structure parameters and free-play effect on linear/nonlinear flutter of the hydroplanes system. To validate the accuracy of the modeling predictions, the linear/nonlinear simulation in-home codes are compared with those theoretical and experimental reported in the existing literature, and good results within engineering error margins are obtained. Results show that structural parameters might effect on the classical flutter speed and LCO only occurred in low flow speed due to free-play.

The recent development of the Structural Health Monitoring (SHM) framework has required the simultaneous development of the tools fundamentals for its realization. The shape sensing methods and the loads identification ones have established themselves as crucial tools for the monitoring of aerospace structures. The two families of methods have been developed separately, although the possibility to achieve the knowledge of the displacement field and of the external loads together can enable a further progress in the SHM. In this paper, an integrated approach to simultaneously preform loads identification and shape sensing from discrete strain measurements is proposed. The methods is based on a two-steps process. The first step involves the identification of continuously distributed and concentrated external loads from discrete strain measurements. This step is achieved by discretizing the loads with Finite Elements (FE) and by computing the coefficients of influence between the nodal values of the loads and the discrete strain measurements. The second step reduces the shape sensing inverse problem to a simple direct Finite Element Analysis. The loads identified in the previous step are applied to a refined FE model of the structure and the displacement field is easily obtained through a direct FE analysis. This investigation proves that the two-steps method can accurately identify the loads and the displacement field of a wing box subject to an aerodynamic pressure distribution and a set of concentrated forces, when a sufficient number of strain information is available. When the number of discrete strain measurements decreases or the strains are affected by measurement error, the loads are poorly predicted but the method is still capable of an extremely accurate displacements reconstruction.

Hydroelastic stability and vibration analysis of full-scale fairwater planes system/or bow planes system mounted on the sail (bridge)/or main body can be quite complex. With the aim of addressing these problems, the present paper, Part I of a two part work, focuses on two aspects: (i) modeling and computation of the natural vibration characteristics of the entire assembly system utilizing and comparing two approaches, based on a finite element commercial software ANSYS and a recently developed Transfer Matrix Method of Multibody systems (MSTMM). Results show the latter technique is computationally accurate and efficient. It is also shown that an equivalent model consisting of one hydroplane with a torsional spring under specified boundary conditions may capture the dynamics behavior of the whole system; and (ii) implementing an equivalent model and MSTMM to obtain in-vacuum uncoupled pure bending and torsional frequencies. Such a treatment of the problem enables one to get a better understanding of the various parameters involved in the linear/nonlinear hydroelastic problem from a two degrees-of-freedom (2-DOF) reduced order model.

Transfer Matrix Method for Multibody Systems (MSTMM) has high precision and it is easy to formulate, systematic to apply, simple to code and the matrices are low order which contributes to higher computational efficiency than ordinary dynamics methods. It is applied widely in the field of engineering, and the significant effects gained. Based on the MSTMM advantages, the linear and nonlinear hydroelastic models of a full-scale sail mounted hydroplanes system, using rigid-flexible coupling multibody system, coupled with a Theodorsen fluid theory are presented in this paper. The model is validated using data available from literature and simulation results from commercial software. This work provides an engineering reference for an efficient linear and nonlinear fluid-structure interaction (FSI) modeling and simulation of other rigid-flexible coupling multibody system.

The vortex induced vibration (VIV) mitigation on a circular cylinder with low mass ratio (i.e. the ratio of structural to displaced fluid mass) parameter and moderate Reynolds numbers through a nonlinear energy sink (NES) is investigated numerically as basis for applications on dynamics of spar platform, marine tunnel or risers used in the ocean engineering industry. The Reynolds-Averaged-Navier–Stokes (RANS) equations and shear Stress transport (SST) k – ω turbulence model are used to calculate the flow field, while a fourth-order Runge–Kutta method is employed for evaluating the nonlinear structure dynamics of flow–cylinder–NES coupled system. The computational model includes an overset mesh solution which can avoid the negative volume grid problem as a dynamic mesh method is involved to deform the domain according to the motion of the fluid–structure interface. The numerical model is validated against experimental data of VIV of an isolated cylinder in uniform current. The study is aimed to investigate the effect of NES parameters, including mass, damping and nonlinear cubic stiffness, and various reduced velocities on the VIV response of the cylinder. The VIV amplitudes’ distribution along the various reduced velocities, trajectories of cylinder motion, hydrodynamic response, and temporal evolution of vortex shedding, are obtained by conducting numerical simulations. Subsequently, it is found that placing a NES with appropriate parameters inside the cylinder, can affect the distribution of the three-branch response and narrows the lock-in range. A good VIV amplitudes’ suppression can be achieved with a large NES mass, small nonlinear cubic stiffness, and the NES damping is higher in the critical range for this kind low mass ratio cylinder structures.

This paper presents the development of indicial functions (IFs) for two-dimensional bridge deck sections. A new set of IFs predicted for the cross section of the Great Belt Bridge (GBB) are discussed. Two approaches, based on the time- and frequency-domain descriptions, are applied. In time domain, IFs are determined by imposing an instantaneous change to a system state variable, e.g., the angle of attack (AOA) of air flow to the bridge section. In frequency domain, indicial representation is derived from the aeroelastic (or flutter) derivatives typically used to define the self-excited harmonic forces in an eigenvalue problem and generated by imposing a sinusoidal motion to the bridge section and performing a sweep in the frequency range of oscillations of the section. IFs are thus evaluated by exploiting the reciprocal relations that exist between them and the aerodynamic derivatives. To determine the aerodynamic response of a bridge cross section due to a step change in the AOA and to calculate the flutter derivatives from sinusoidal oscillations, the meshless discrete vortex method implemented in DVMFLOW ® is adopted. The results from the proposed work can be applied in the development of reduced-order models (ROM) of aerodynamic loads suitable to investigate fluid–structure interaction (FSI) problems associated with practical analysis of wind effects on long-span bridges, including phenomena such as flutter, vortex-induced vibration, buffeting and galloping. The IFs reported in this paper illustrate the importance of flow separation and vortex shedding and their dependence on the magnitude of the change in a state variable such as, in particular, the AOA for the cases reported herein.

This paper introduces a novel semi-analytical representation of a displacement-based finite element model reduced via nested polynomials obtained through fitting of modal data. This method, termed Poly-SAFE (Polynomial Semi-Analytical Finite Element), is particularly suitable for modelling thin-walled composite structures subject to recursive analyses under varying loads, a common scenario in fluid–structure interaction (FSI) and Progressive Failure Assessment (PFA). The resulting functionals, i.e. polynomials inside polynomials, can be evaluated in an analytical fashion to yield displacements at arbitrary positions not limited to typical finite element grid nodes. These functionals remain virtually load-independent, allowing a Poly-SAFE model to be constructed without previous knowledge of magnitude, direction and location of applied loads, either static or dynamic. In this paper the theoretical framework of the Poly-SAFE method is presented in some detail, followed by an application of the theory to an extruded airfoil-shaped, laminated thin-walled beam subject to static loads. The displacement field captured by the new method is compared to the predictions of its associated finite element model, showing an excellent overall agreement. Finally, the advantages of Poly-SAFE against FE models in specific analyses and contexts are emphasised.

Hybrid systems consisting of a single or multiple primary sources along with a storage component are used in renewable energy production due to the wide disparity between the intermittent power generated and the power demand. Finding the optimal size of a hybrid system with no loss of power supply (LPS) is of utmost concern when considering the levelized cost of energy (LCE) of the project over its lifecycle. In this study, an optimization routine employing a search algorithm is developed to find the minimum LCE that meets zero LPS in the context of data center application. To this end, a system model is developed by integrating basic models of the subsystems. The system model is then used to investigate two different loading cases, 1) a case where the demand cannot be controlled as in the case of power demand in a residential network, and 2) a case where the demand can be controlled up to certain limits, as in the case of power demand in a data center or a data center network. Various types of controllable power demand scenarios are studied. The results demonstrate a significant reduction in the life cycle costs of the system when controllable power demand is considered, especially in regions where wind and solar resources are relatively low.

The fouling effect of seawater samples collected from three New Hampshire beaches on a 90/10 Cu/Ni commercial heat exchanger tube was investigated. A fouling monitoring device, designed on the basis of fouling thermal resistance, was used for this experimental study. The filtered seawater samples were circulated through the closed loop experimental setup for durations of seven and 14 days and the fouling thermal resistance was measured continuously. Analytical microscopy was performed on the tube surface before and after the experiments to see the effect of seawater fouling on the tube surface. The results show different fouling behavior for the seawater samples. This different behavior is confirmed by the different composition of the samples. Fouling monitoring experiments reveal a higher fouling thermal resistance for one of the seawater samples, Hampton seawater, contrary to the results of SEM analysis which show a lower crystallization rate for Hampton sample. Water decomposition analysis shows the lowest sodium content for Hampton seawater compared to the other samples. Accordingly, corrosion of the tube surface occurs with a higher rate for Hampton seawater due to the presence of chlorine ions and a lower concentration of sodium. The high fouling resistance of Hampton seawater can be explained as the result of several simultaneous fouling mechanisms, corrosion and crystallization indicating composite fouling behavior. The results of the current study are critical for the industries which use seawater as the cooling water source.

Higher-order spectra have become a useful tool in spectral analysis, particularly for identifying the presence and type of system non-linearity. Two such spectra that have figured prominently in signal processing are the bispectrum and trispectrum. In a previous work, the authors developed an analytical solution for the bispectrum for multi-degree-of-freedom systems. Here this analysis is extended to the trispectrum. Specifically, an expression is developed for the trispectrum of a multi-degree-of-freedom system subject to Gaussian excitation applied at an arbitrary location. The analytical expression is compared to those obtained via estimation using the direct method.

Higher-order spectral analysis techniques are often used to identify nonlinearities in complex dynamical systems. More specifically, the auto- and cross-bispectrum have proven to be useful tools in testing for the presence of quadratic nonlinearities based on knowledge of a system's input and output. In this paper, analytical expressions for the auto- and cross-bispectrum are developed using a Volterra functional approach under the assumption of a zero-mean, stationary Gaussian input; proper simplifications are presented when the whiteness of the input signal is also imposed. These formulae show the contributions of the bispectrum in terms of the system frequency response function and elementary physical properties of the system. Simulations based on a stochastic numerical integration technique accompany the analytical solutions for a mechanical mass–spring–damper system possessing quadratic damping and stiffness coefficients and subjected to Gaussian white noise excitation. Subsequent estimates of the bispectrum based on the simulated signals show excellent agreement with theory. These results show how modes may interact nonlinearly producing intermodulation components at the sum and/or difference frequency of the fundamental modes of oscillation. The presence and extent of nonlinear interactions between frequency components are identified. Advantages of using higher-order spectra techniques will be revealed and pertinent conclusions will be outlined.

Higher-order spectra appear often in the analysis and identification of nonlinear systems. The auto-bispectral density is one example of a higher-order spectrum and may be used in the analysis of stationary structural response data to detect the presence of certain types of structural nonlinearities. In this work a closed-form expression for the auto-bispectral density, derived previously by the authors, is used to find the bispectral frequency most sensitive to the nonlinearity. The properties of nonlinearity detectors based on estimates of the magnitude of the auto-bispectral density at this frequency are then explored. Estimates of the auto-bispectral density are obtained using the direct method based on the discrete Fourier transform. The bias associated with this estimator is derived here and combined with previously derived expressions for the estimator variance to give both Type-I and Type-II errors for the detector. Detector performance is quantified using a receiver operating characteristic (ROC) curve illustrating the trade-off between false positives (Type-I error) and power of detection (1.0-Type-II error). Theoretically derived ROC curves are compared to those obtained via numerical simulation and show excellent agreement. Results are presented for different levels of nonlinearity in both the stiffness and damping terms for a spring–mass system. Possible consequences are discussed with regard to the detection of damage-induced nonlinearities in structures.

The flutter and post flutter of a two-dimensional double-wedge lifting surface with combined freeplay and cubic stiffness nonlinearities in both plunging and pitching degrees-of-freedom operating in supersonic/hypersonic flight speed regimes have been analyzed. In addition to the structural nonlinearities, the third-order piston theory aerodynamics is used to evaluate the unsteady non-linear aerodynamic force and moment. Such model accounts for stiffness and damping contributions produced by the aerodynamic loads. Responses involving limit cycle oscillation and chaotic motion are observed over a large number of parameters that characterizes the aeroelastic system. Results of the present study show that the freeplay in the pitching degree-of-freedom and soft/hard cubic stiffness in the pitching and plunging degrees-of-freedom have significant effects on the LCOs exhibited by the aeroelastic system in the supersonic/hypersonic flight speed regimes. The simulations also show that the aeroelastic system behavior is greatly affected by physical structural parameters, such as the radius of gyration and the frequency ratio, especially in post-flutter regimes, when accounting for all system nonlinearities. It has been shown that at high Mach numbers the non-linear aerodynamic stiffness yields detrimental effects from the aeroelastic point of view, while the damping one do not.

This paper concerns the flutter, post-flutter and adaptive control of a non-linear 2-D wing-flap system operating in supersonic/hypersonic flight speed regimes. An output feedback control law is implemented and its performance toward suppressing flutter and limit cycle oscillations (LCOs) as well as reducing the vibrational level in the subcritical flight speed range is demonstrated. This control law is applicable to minimum phase systems and we provide conditions for stability of the zero dynamics. The control objective is to design a control strategy to stabilize the pitch angle while adaptively compensating for uncertainties in all the aeroelastic model parameters. It is shown that all the states of the closed-loop system are asymptotically stable.

The performance of a robust control strategy applied to a three-degrees-of-freedom (3-DOF) flap-wing aeroelastic system impacted by a pressure pulse in the subcritical flight speed regime is investigated. The goal of its implementation is to suppress flutter instability and reduce the vibrational level in the subcritical flight speed range. To this end, the linear quadratic Gaussian (LQG) control methodology in conjunction with a sliding mode observer (SMO) are used. Comparisons with the counterpart results obtained via implementation of LQG controller with conventional Kalman filter (KF) are also provided and pertinent conclusions are outlined.

Two basic issues related to the open/closed-loop aeroelasticity of 2-D lifting surfaces in an incompressible flow field are considered. These concern the subcritical aeroelastic response to external time-dependent excitations, and the flutter instability of actively controlled airfoils involving a time-delayed feedback control. Results and comparisons regarding the flutter instability obtained via the first Volterra kernel in conjunction with a frequency eigenvalue analysis are presented. In the same context, the implications on the instability boundary and aeroelastic response of the presence of time-delays in the feedback control are investigated and pertinent conclusions are supplied.