Abstract:This paper studies the damping vibration properties of the big damping bar by the generalized multisymplectic method based on the Bridges’s multisymplectic method and the Hamilton variation principle. Introducing orthogonal momenta, a firstorder approximate symplectic form, named generalized multisymplectic form is derived from the control equation of the big damping bar vibration firstly. And then a midpoint Box generalized multisymplectic scheme is constructed by the midpoint method; Finally, the dissipation effect of the big damping bar vibration is studied. From the results of the numerical experiment, the good properties of the generalized multisymplectic method are verified: satisfying the conservative properties of the system and reproducing the dissipation effect of the system.

Abstract:There is an increasing number of discontinuous dynamics problems, such as contact and impact, in the engineering field. The known modelling theories and methods, which are used to solve the continuous dynamics of flexible multibody systems, are not able to solve those problems or to solve those problems perfectly. In this paper, an appending constraint method was proposed to solve the contact/impact dynamics of flexible multibody system based on the idea of topology variable. The impact experiment of flexible bars was designed to verify the validity of the proposed method. At last, a multi-variable method was proposed to solve the multi-scale problems of time and space when the global simulation of the discontinuous dynamics of flexible multibody systems was carried out, and the computational efficiency of the global simulation of the discontinuous dynamics of flexible multibody systems was improved by using this method.

Abstract:The dynamics of the whole aero-engine system has always been the important part that cannot be neglected in the research and design of the engine, as the framework of the engine, the vibration of the casing directly reflects the level of the whole aeroengine vibration. In this paper, an analysis was made on the research of the problems and fault classification of aero-engine casing dynamics, and an overview was made on the research of present situation, development trend, problems and solutions of the domestic and foreign of casing dynamics, which expanded the present situation of the Inclusiveness problems of aero-engine casing dynamics. Finally, some proposals were put forward for the development of the casing dynamics suitable for our country aero-engine technology level.

Abstract:This paper summarized the advances in two transverse models for nonlinear vibration of axially moving beams. Based on a nonlinear model for planar vibration of axially moving beams with coupled transverse and longitudinal motion, the derivation of two nonlinear models of transverse vibration was reviewed. The comparisons between approximate analytical results based on the two models for free, forced and parametric vibration of axially moving beams were surveyed. The deviations of the numerical solutions to the two transverse models from the solution to the coupled equation for different vibrations were also summarized. Some problems for further investigations were discussed.

Abstract:We studied the existence of homoclinic orbits and the homoclinic bifurcations in planar piecewiselinear system. The existence of homoclinic orbit in this system can be divided into two cases, one is a system formed by a visible saddle point and a visible focus (or a center), the other is a system formed by the coincidence of the original point and two nodes with inverse stability. In this paper, we provided the necessary and sufficient condition for the existence of homoclinic orbit, and then analyzed the homoclinic bifurcation.

Abstract:The vibration suppression of torsional vibrating system is investigated by using the delayed vibration absorber. The stability switch method was applied to analyze the stability of the delayed vibration absorber and the combined system, and their stable and unstable regions were obtained respectively. The results show that the vibration of the primary system could be suppressed absolutely when the delay is chosen as the critical stable value of the delayed vibration absorber. The vibration of the primary system could be suppressed partly when the delay is chosen in the stable region of the delayed vibration absorber. As the value of the delay increases, the vibration suppression ability is improved. If the value of the delay is larger than the critical value of the combined system, the structure of the combined system could be destroyed. The analytical results agree with the numerical simulation well.

Abstract:The differential quadrature method (DQM) was developed to solve numerically the nonlinear partialdifferential equation of the nonlinear transverse vibration of an axially accelerating viscoelastic beam. Based on the numerical solutions, the nonlinear dynamical behaviors, such as bifurcations and chaotic motions of the nonlinear system, were investigated by use of Poincare map, phase portrait.

Abstract:Spikefrequency adaptation is a prominent property of neuronal dynamics in neural information processing. The external electric field has effect on the generation and conduction of neural information, and the dynamic behaviors of the neural system. Based on the leaky integrateandfire (LIF) model, a modified LIF model under the external electric field is established. From the membrane potential curve and the spikefrequency curve along with the time evolution process, the onset spikefrequency curve and the steady state spikefrequency curve along with the external electric field changes, and the correlation between successive interspike intervals (ISIs), the effect of external electrical field with different strength or frequency on the adaptability of the proposed model is discussed.

Abstract:Based on Euler-Bernoulli beam theory, Hamilton’s principle and Galerkin method, the second-order nonlinear ordinary differential dynamical equation was derived for the cantilever metal foam sandwich beam under transverse loading. The effect of damping on the vibration response of the metal foam sandwich beam was investigated for the cases of different frequencies and amplitudes of the transverse loading. It is shown that the chaotic vibration of the sandwich beam can be suppressed effectively by the damping performance of metal foam.

Abstract:A honeycomb sandwich plate with hexagonal honeycomb core was investigated to reveal the dynamic behavior near a critical point characterized by initial resonance. Based on the averaged equations, the transition boundaries were obtained to divide the parameter space into a set of regions, which correspond to different types of solutions. By applying the stability criteria to determine the stable conditions of respective equilibrium points, the conditions of the occurrence of double Hopf bifurcations were found. Two types of periodic solutions may bifurcate from the initial equilibrium. And the periodic solutions may lose their stabilities via a generalized static bifurcation, which leads to stable quasi-periodic solutions, or via a generalized Hopf bifurcation, which leads to stable 3D tori.

Abstract:The approximately analytical solution for a semiactive suspension system under relative control with timedelay is investigated in this paper. At first, the quartercar model is established and dimensionless analysis is done. Then a system of four nonlinear algebra equations for the approximate solution is obtained by the averaging method, which could be easily treated by numerical methods for algebra equations. At last, the numerical solution of the semiactive relativecontrol suspension system is also obtained through the simulation in MATLAB software. The comparison of the two methods shows the approximately analytical solution is correct and has satisfactory precision.

Abstract:This paper studied the nonstationary stochastic response and the optimal control of a half car dynamical model with nonlinear active suspension under the excitation of random road surface. Using the method of equivalent linearization, the response statistics and stochastic optimal control of the nonlinear suspension were obtained. The comparison and analysis of the nonstationary response of active and passive suspension show that the nonlinear active suspension is better than the passive suspension. Finally, the accuracy of the equivalent linearization technique was verified by Monte Carlo simulation.

Abstract:In order to avoid the magnetic influence of satellite to the measurement information in the space detection missions, lightweight flexible booms are required to support various types of payload on their tip away from the satellite platform. While the elastic vibration of flexible booms will affect the attitude control accuracy of the satellite. Considering the complexity of appendages vibration and its effect on the satellite, an optimal input shaping(OIS) is applied to the flexible booms to suppress its loworder mode vibration, and then an adaptive disturbance rejection filter(ADRF) is designed to reject the disturbance caused by the residual vibration of booms further. Simulation results show that the proposed composite vibration control method can improve the satellite attitude control accuracy greatly.

Abstract:A self-powered active control system was designed. First, a kind of drive mode of motor actuator for self-powered active control was given, so that the actuator can work in three modes and switch functions. Second, the relationship between proportion of working hours and energy balance was analyzed, and the basic conditions to achieve energy balance were given, then the conditions of the system energy balance were obtained. Finally, the feasibility of the method was verified by a designed self-powered active control system. The simulation indicates that the active control system can effectively reduce the interference of vibrational excitation, and the energy balance of the system is achieved, which means that the control system does not require an external energy supply.

Abstract:The nonlinear output frequency response functions(NOFRF) which is derived from the Volterra series can facilitate the analysis of nonlinear systems in frequency domain, it is a one dimensional function of frequency. The paper introduces the structural damage detection method which is based on NARMAX model and NOFRF. An experimental study demonstrates the feasibility of the structural damage detection method. Because the nonlinear characteristics of system can be used for the detection of structural damage, and is sensitive about the state of system, in addition, the structural damage detection method which is based on NARMAX model and NOFRF is a nonlinear method for analyzing the state of system, the characteristics extracting from system is a nonlinear characteristics, so the damage detection method can be used for the detection of structural damage, and has the advantage which is sensitive to the state of system.