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The contact state and stiffness of linear guide are affected by the complex external loads, and the vibrations in different directions are coupled with each other. However, existing dynamic models are inaccurate because they ignore displacement coupling and do not consider the position deviation of guide rail. This paper presents a five degree-of-freedom dynamic model for table system that incorporates the effects of the displacement coupling and position deviation of guide rail. The ball-to-groove contact model and position deviation model are established by using the Hertz contact theory and homogeneous coordinate transformation, respectively. Dynamic equations are solved by combining the Monte Carlo and Newmark methods to determine the displacements of table system, and the accuracy of proposed dynamic model is verified through experimental method. The results show that the vibrations of table system are coupled with each other, and the position deviation of guide rail only affects the vibration amplitudes in the region other than the resonance regions. Proposed model is thus suitable for improving the machining accuracy and stability of machine tools.

The previous studies on the vibrating system with vibrators are mainly focused on existence and stability problems for the synchronous solutions of dynamical systems from the point of view of mathematics and mechanics, whereas the Sommerfeld effect and electromechanical coupling characteristics are less considered, especially less validated by experiment. In this article, we take a dynamical model with two rigid frames driven by two vibrators, for example, where vibrators are powered by induction motors separately. The synchronous and stable states of the system are studied first. Then, the Sommerfeld effect is further revealed to study what happened around the natural frequency of the system. Based on the average method, the criteria of synchronization of two vibrators and that of the stability are discussed in theory and numeric. Under the precondition of implementing synchronization, the Sommerfeld effect is given by establishing the electromechanical coupling model, in which the jump phenomena at the resonant point for the rotational velocities and the vibration amplitude of the system are explained. The synchronization and the coupling characteristics of the considered system are examined by the experiment. Finally, a type of vibrating centrifugal dehydrator has been successfully applied in engineering according to this article.

As a continuing and intensive work of the previous literature, the synchronization and stability of a far-resonant vibrating system with three rollers and two vibrators, will be given in this paper. The criterion of implementing synchronization for two vibrators and three rollers, is obtained in theory firstly, by constructing mathematical models of the system and using the average method. The stability criterion of the synchronous states is proved to comply with the Routh–-Hurwitz principle. In numerical qualitative analyses, the coupling dynamic characteristics of the system are revealed in detail, by considering the effects of key parameters of the system, including structural parameters, friction coefficients, mass ratio and distance ratio coefficients. An experiment is carried out to further verify the validity of the theoretical and numerical results, as well as the feasibility of the theory method used. It is shown that the ideal stability effect can be reached, under the preconditions of matching reasonably a certain kind of parameters of the system. These facts can provide the theory guidance for designing some new types of vibrating crushing/grinding equipment with multiple working chambers, etc.

As a continuous work of the previous literatures, a special dynamical model with one cylindrical roller driven by a single exciter and one outer ring, is taken for example to explore the vibratory synchronization transmission (VST) of the system considering sliding dry friction in this paper. The motion differential equations of the system, are given firstly. Using the average method, the theory condition of implementing VST is obtained. The VST characteristics are qualitatively discussed in numerical, which are further quantitatively verified by simulations. It is shown that, the vibration amplitudes of the roller in the horizontal and vertical directions are basically identical, and less affected by the friction coefficient, but the stable phase difference between the exciter and the outer ring is affected too much by it. Based on the present work, some new types of vibrating equipments, such as vibrating crushers/mills, can be designed.

The dimension reduction incremental harmonic balance (DRIHB) method is developed to study the dynamic behavior of dual-rotor system with multi-frequency excitations and nonlinear rubbing faults. On the basis of consideration of an aero-engine, a dynamic model of rotor system is built and the piecewise-nonlinear model of rubbing force is used to investigate the nonlinear behavior of system. Considering the features of multi-frequency excitation, high dimension and strong nonlinearity of dual-rotor system, the dimension reduction approach combined with the incremental harmonic balance (IHB) method is derived for theoretically studying the dynamic response of system with nonlinear rubbing fault. The accuracy and efficiency of the method are proved through comparison with the numerical simulation result solved by the Newmark-[Formula: see text] method and the IHB method. Then, the influences of rubbing stiffness, contact gap, rotational speed and speed ratio on dynamic response are studied and discussed. It is shown that the dual-rotor system with nonlinear rubbing fault will cause the system to generate rich combination frequency components in addition to excitation frequency. All the works indicate that the DRIHB method is an effective tool for studying the nonlinear behavior of dual-rotor systems with multi-frequency excitation, high dimensions and strong nonlinearities.

The non-smooth nonlinear energy sink (NSNES) is used to suppress the vibration of the rotor-blade system. Firstly, the structure and working principle of the NSNES for rotor-blade system are introduced. Then, the dynamics model of the rotor-blade-NSNES system is established by Lagrangian method. And then, numerical simulations are applied to evaluate the vibration suppression ability of the NSNES on rotor and blade. The results show that the suppression rates of NSNES on the rotor and the blade can reach 81% and 74% in steady state resonance under given parameters, respectively; and for transient vibration of blade, a 1.85 times dissipating speed is obtained in rotor-blade system with NSNES than that without NSNES. In particular, NSNES has better vibration suppression capability than linear dynamic vibration absorber (LDVA) when both have the same vibration absorption mass.

In this paper, a newly composite synchronization scheme is proposed to ensure the straight line vibration form of a linear vibration system driven by four exciters. Composite synchronization is a combination of self-synchronization and controlled synchronization. Firstly, controlled synchronization of two pairs of homodromous coupling exciters with zero phase differences is implemented by using the master–slave control structure and the adaptive sliding mode control algorithm. On basis of controlled synchronization, self-synchronization of two coupling exciters rotating in the opposite directions is studied. Based on the perturbation method, the synchronization and stability conditions of composite synchronization are obtained. The theoretical results indicate that composite synchronization of four exciters with zero phase differences can be implemented with different supply frequencies and the straight line vibration form of the linear vibration system also can be obtained. Some simulations are conducted to verify the feasibility of the proposed composite synchronization scheme. The effects of some structural parameters on composite synchronization of four exciters are discussed. Finally, some experiments are operated to validate the effectiveness of the proposed composite synchronization scheme.

The synchronization and stability of two or more vibrators in vibrating systems with double rigid frames are rarely investigated in previous studies. To make up this drawback, we take a dynamical model with double rigid frames driven by two homodromy vibrators, for example the synchronous and stable states of the corresponding system, as well as the relative motion characteristics between the two rigid frames, are analyzed in detail. First, the mathematical modeling of the system is given; the absolute motion and relative motion differential equations of the system are deduced. After that, the theory conditions of implementing synchronization and those of stability are obtained, by using the average method and Hamilton’s principle, respectively. Based on the theoretical results, some numerical qualitative analyses are provided to reveal the coupling dynamical characteristics of the system, and the corresponding ideal working regions are suggested. Finally, experiments are carried out to further examine the validity of the theoretical and numerical results. The present work can offer a reference to design some new vibrating machines such as the considered model.

Through the combination of theory and experiment, the natural characteristics of the fiber metal laminates thin plates under cantilever boundary are analyzed and verified. Based on the mechanics of composites and classical laminated plate theory, the theoretical model is established. The orthogonal polynomial method and the energy method are used to solve the natural characteristics. Meanwhile the calculation process is proposed. And then, the natural characteristics of a TA2/TC500 fiber metal laminates thin plate are tested. It is found that comparing the calculation results of the frequencies with the test ones, the errors are within the range of 3.4 % to 4.5 %, the trends of modal shapes are consistent as well, thus the effectiveness of above method has been verified.

In the existing literature, most studies investigated the free vibrations of a rotating pre-twisted cantilever beam; however, few considered the effect of the elasticsupport boundary and the quantification of modal coupling degree among different vibration directions. In addition, Coriolis, spin softening, and centrifugal stiffening effects are not fully included in the derived equations of motion of a rotating beam in most literature, especially the centrifugal stiffening effect in torsional direction. Considering these deficiencies, this study established a coupled flapwise–chordwise–axial–torsional dynamic model of a rotating double-tapered, pre-twisted, and inclined Timoshenko beam with elastic supports based on the semi-analytic method. Then, the proposed model was verified with experiments and ANSYS models using Beam188 and Shell181 elements. Finally, the effects of setting and pretwisted angles on the degree of coupling among flapwise, chordwise, and torsional directions were quantified via modal strain energy ratios. Results showed that 1) the appearance of torsional vibration originates from the combined effect of flapwise–torsional and chordwise–torsional couplings dependent on the Coriolis effect, and that 2) the flapwise–chordwise coupling caused by the pure pre-twisted angle is stronger than that caused by the pure setting angle.

A simplified computational model of a twisted shrouded blade with impact and friction is established. In this model, the shrouded blade is simulated by a flexible Timoshenko beam with a tip-mass, and the effects of centrifugal stiffening, spin softening, and Coriolis force are considered. Impact force is simulated using a linear spring model, and friction force is generated by a tangential spring model under sticking state and a Coulomb friction model under sliding state. The proposed model is validated by a finite element model. Then, the effects of initial gap and normal preload, coefficient of friction, and contact stiffness ratio (the ratio of tangential contact stiffness to normal contact stiffness) on system vibration responses are analyzed. Results show that resonant peaks become inconspicuous and impact plays a dominant role when initial gaps are large between adjacent shrouds. By contrast, in small initial gaps or initial normal preloads condition, resonant speed increases sharply, and the optimal initial normal preloads that can minimize resonant amplitude becomes apparent. Coefficient of friction affects the optimal initial normal preload, but it does not affect vibration responses when the contact between shrouds is under full stick. System resonant amplitude decreases with the increase of contact stiffness ratio, but the optimal initial normal preload is unaffected.

In the present work, a new dynamical model with a single rigid frame driven by two pairs of vibrators, of which each pair of vibrators is engaged with each other by gear mechanism, is proposed to explore the composite synchronization of the system. The motion differential equations and vibration responses of the system are given first. The theory condition for achieving composite synchronization of the system is obtained, by using the average method to deduce the average torque balance equations of the two pairs of vibrators. According to the Hamilton’s theory, the system stability condition is presented, and it is mainly determined by the structural parameters of the system. The synchronous stable regions and stability ability versus the key parameters of the system are qualitatively discussed in numeric, and further quantitatively verified by simulations. It is shown that, in engineering, the reasonable working points of the system, should be selected in the region where the stable phase difference of the two pairs of vibrators is stabilized in the vicinity of zero. Only in this way, can the exciting forces of the two pairs of vibrators be positively superposed, and the linear motion of the system in the vertical direction be realized.

In this paper, an inverse method to identify the mechanical parameters of fiber metal laminates is proposed on the basis of the measured and calculated frequency response functions. The classical laminates theory, orthogonal polynomial method, and energy method are employed to characterize the theoretical modal of a fiber metal-laminated thin plate under pulse excitation. And, an iterative solution on the basis of frequency response functions and least square method is proposed to identify the mechanical parameters of fiber metal laminates, which conclude the elastic modulus, Poisson's ratios, and loss factors. As an example to demonstrate the feasibility of the developed inverse method, the experimental test of a TA2/TC 300 fiber metal-laminated thin plate is implemented to identify the mechanical parameters. Moreover, the influences of approximation points and calculation step sizes on the identification accuracy and efficiency are discussed.

This study focuses on vibration characteristics analysis of fiber metal laminated thin plate (FMLTP) with partial constraint layer damping (CLD) patches treatment. Firstly, the overall stress–strain relationships of the viscoelastic layer, the constraint layer and the covered FMLTP are deduced to establish the theoretical model. Then, the classical laminates theory, orthogonal polynomial method, complex modulus method and energy method are employed to solve the natural frequencies, modal shapes, vibration responses and modal damping ratios. As an example to demonstrate the feasibility of the developed model, the experimental test of TA2/TC500 laminated thin plate treated with different sizes and shapes of stainless steel/Zn-33 CLD patches is implemented. The calculated and measured results show a good consistency. Moreover, the influences of different CLD treating positions and shapes on the vibration characteristics of FMLTP are investigated here.

This study derived a novel computation algorithm for a mechanical system with multiple friction contact interfaces that is well-suited to the investigation of nonlinear mode characteristic of a coupling system. The procedure uses the incremental harmonic balance method to obtain the nonlinear parameters of the contact interface. Thereafter, the computed nonlinear parameters are applied to rebuild the matrices of the coupling system, which can be easily solved to calculate the nonlinear mode characteristics by standard iterative solvers. Lastly, the derived method is applied to a cycle symmetry system, which represents a shaft-disk-blade system subjected to dry friction. Moreover, this study analyzed the effects of the tuned and mistuned contact features on the nonlinear mode characteristics. Numerical results prove that the proposed method is particularly suitable for the study of nonlinear characteristics in such nonlinear systems.

In this paper, the forming mechanism of the 2-D shape and position error for turning workpiece was discussed and an on-line detecting and analyzing method was designed. Firstly, two laser displacement sensors were orthogonally distributed on both sides of the workpiece to obtain the distance data from each measuring point of the rotating workpiece to the sensor. Then, according to the geometric position relationship, the synchronous error, asynchronous error and surface roughness were solved by the method of stepwise error separation, and the inverse calculation was carried out. The simulation results under different parameters were analyzed. The results show that the shape and position error obtained by the simulation method are consistent with the verification results of inverse calculation. The results of this method are relatively stable. Therefore, the simulation analysis method has good practicability and maneuverability. Finally, the feasibility and correctness of the algorithm were verified by experiments.

Rub-impact fault is one of the most common and severe failure modes for rotating machinery. Disclosing the changing dynamic in rub-impact fault signal could provide a basic foundation for rub-impact detection of rotor systems. In this study, a dynamic model of a flexible rotor system is established to simulate the rub-impact fault signal to help us understand the dynamic characteristics of rub-impact fault signal. Meanwhile, considering that an advanced time-frequency analysis method is of vital importance in an effective rub-impact fault detection method. A new time-frequency analysis algorithm termed as second order multi-synchrosqueezing transform is also proposed in this study, in which a second order two-dimensional instantaneous frequency estimation is embedded into a multi-synchrosqueezing framework. It is shown that the proposed method could produce a time-frequency representation result with a high time-frequency resolution. Assisted by the proposed method, the impulse shaped amplitude modulated phenomenon in high frequency band and the fast varying frequency modulated phenomenon around the rotation frequency and its fractional or super harmonics are clearly revealed through the analysis of rub-impact fault signals from both dynamical simulation and experimental cases.