Research On Energy Transfer In Nonlinear Systems And Its Applications To Structural Vibration Suppression

Reducing the unwanted vibrations of spacecraft structures,and ensuring the normal functioning of spacecraft equipments under complex and changeable dynamic environments,has been one of the most important topics in aerospace engineering.The transfer of energy plays an important role for passive vibration damping.Focusing on the passive control of structural vibrations in aerospace engineering,this thesis investigated the applications of nonlinear energy transfer theory in spacecraft structures characterized as concentrated mass,beams and plates for vibration suppression.For structures characterized with a concentrated mass,one simple and efficient alternative that developed recently is attaching a light nonlinear device for passive energy localization to itself,termed as Nonlinear Energy Sink(NES).Considering the effect of nonlinear damping,the dynamics of discrete systems with a 1-dof or 2-dof NES are investigated.For 1-dof NES,an analytical treatment for the bifurcations is developed by presenting a slow/fast decomposition leading to slow flows,where a truncation damping and failure frequency are reported.Existence of Strongly Modulated Response(SMR)is also determined.The procedures are then partly paralleled to the investigation of 2-dof NES for the bifurcation analysis,with particular attention paid to the effect of mass distribution between the NES.To study the frequency response for 2-dof NES,the periodic solutions and their Stability are obtained by Incremental Harmonic Balance(IHB)method and Floquet theory,respectively.Poincare map and energy spectrum are specially introduced for comparing the efficiency of the NESs to the application of vibration suppression.The efficiency of the 1-dof NES with nonlinear damping,together with its the superiority on the 2-dof case are thus proved.Taking the beam structures on spacecraft as an example,the vibration suppression of continuous systems is then studied.Considering several typical linear and nonlinear vibration control techniques,three systems including a uniform with an attached tuned mass damper,a beam with an attached NES,and a beam in contact with a rigid contact point are thus investigated.A numerical scheme based on the finite difference method is first established for the analysis of each system.Thanks to the high convergence and energy conservation property of the derived numerical scheme,the vibration response and energy transfer of each vibration system are well described.Then the energy transfer,response mechanism and vibration reduction performance of each system are compared and evaluated.Investigated a specific type of beam with variable thickness: Acoustic Black Hole(ABH),which refers to a passive vibration damping technique without added mass based on flexural waves properties in thin structures with variable thickness.Focusing on the problem that a classical ABH can only be efficient at high frequency but less than desirable at low frequency band,a vibro-impact acoustic black hole(VI-ABH)is introduced,using the contact nonlinearity as a mean to transfer energy from low to high frequencies.A numerical model of a VI-ABH is derived from an Euler-Bernoulli beam,the Hertzian contact law and a Ross-Kerwin-Ungard damping model.The problem is solved with a modal approach combined with an energy-conserving time integration scheme.Numerical results show that the VI-ABH brings about a strong nonlinear regime,changing the nature of more traditional black holes by redistributing all the vibrational energy.It can lead to a effective transfer of the energy from the low frequencies to the high frequencies,and hence to a large extent improves the low frequency performance of the ABH.Established the VI-ABH to the case of plate structures,where the flexural vibration of plate is described by von-karman equation with variable thickness,in order to take into consideration the effect of geometric nonlinearity,the contact force is handled by Hertzian contact law.The linear performance of the ABH plate is analyzed at first with special attention paid to the effect of 2D plate modes,and discovered the structures of eigenvalues on the complex plane.Then,considering the effect of contact nonlinearity,the main conclusion related to the VI-ABH beam is thus paralled to the 2D case,with a demonstration on the effect of energy transfer that brought by contact nonlinearity.Based on the characteristics of the ABH plate,the steps for the optimal design of the contact points configuration are also given.Finally,taking into consideration the coupling effect of geometric and contact nonlinearity,the energy transfer regimes of the VI-ABH plate is analyzed together with the application to vibration suppression.