Static/Dynamic Characteristics And Resonance Behaviors Of The Magneto-Electro-Elastic Laminated Beams

The dynamic characteristics,nonlinear post-buckling and resonance behaviors of magneto-electro-elastic beams are investigated in this thesis.The effects of the variable cross-section parameter,material lay-up mode,temperature and magneto-electric field on the magneto-electro-mechanical responses are discussed in detail.On the basis of magneto-electro-elastic constitutive relationship,two kinds of dynamical models are established: one is for transversely isotropic variable cross-section beam,and the other is for laminated beam considering thermal environment.The forced vibrations are studied for a magneto-electro-elastic beam with constant thickness and exponentially varying width,and corresponding solutions are given by means of Green's functions.The effects of cross-section parameters on the dynamical characteristics and magneto-electro-mechanical responses are discussed.It is found that the variations of the cross-section parameter significantly affect not only the natural frequencies but also the mode shapes.When the beams are undergoing the external excitation,the resonance peaks shift with the variations of the cross-section parameter and the material properties of the beam.In addition,Appearances of the antiresonance peaks on the frequency response curve depend on many factors such as the location of the external excitation,the selected response position in the beam and the cross-section parameter,which likewise affect the magnitude and curve configuration of the magnet-elctro-displacement response.The nonlinear bending and vibration of the magneto-electro-elastic laminated beams are investigated.The analytical solutions of the corresponding issues,derived by a two-step perturbation technique,are used to discuss the effects of material lay-up mode,temperature load and magneto-electric boundary condition(i.e,external magneto-electric field)on the nonlinear bending paths and frequencies.It is revealed that the material lay-up mode and temperature load type have remarkable influences on the bending paths and frequencies,and determine whether or not the bending moments exist in the beam.The natural frequencies are increased or decreased by the magneto-electric fields,which is concerned with the loaded directions of the corresponding fields.For the magneto-electric potentials,their distribution magnitudes and shapes through the beam's thickness change greatly with the degree of bending deformation.Furthermore,magneto-electric boundaries also have significant influences on the magneto-electric potential distributions.The thermal post-buckling and post-buckling vibration analyses are carried out for magneto-electro-elastic laminated beams.The solutions of post-buckling paths are obtained by the generalized differential quadrature method in conjunction with pseudo-arc length continuation algorithm,and the free vibrations on the buckled beam are analyzed by solving the associated linear eigenvalue problems.Special attentions are focused on the effects of the material lay-up mode,temperature load type and magneto-electric fields on the post-buckling paths and post-buckling vibration frequencies.The numerical results show that:(1)the thermal post-buckling path curves of the magneto-electro-elastic laminated beams have two types,bifurcation and non-bifurcation;(2)the post-buckling vibration frequencies decrease first and then increase with the developments of the post-buckling paths;(3)the magneto-electric potential boundary loads play a role in regulating and controlling the trend of the post-buckling path development.Studies of nonlinear resonance behaviors are performed for the magneto-electro-elastic laminated beams with two elastic foundations.The continuous systems are transformed into a reduced-order model using a two-step perturbation technique,and the obtained equation is discretized on time domain based on highly precise differentiation matrix operators.Subsequently,the periodic solutions of the forced vibration are analyzed,and the frequencyand force-response curves are constructed by pseudo-arc length continuation algorithm.Numerical studies are conducted to account for the influences of the material lay-up mode,temperature and foundations on the frequency-and force-responses.The results indicate that:the primary resonant response curves of the magneto-electro-elastic laminated beams present hardening-type spring characteristic;The occurrences of the cyclic-fold bifurcation are concerned with the parameters such as the amplitude of the external excitation,damping value and material lay-up mode;The periodic motions of the laminated beams with respect to their equilibrium positions are symmetric or not that is determined by material lay-up mode and temperature load type;Two foundations have hardening effects on the beams' stiffnesses,and regulating and controlling functions for the primary resonance behaviors of the beams in thermal environment;The higher the temperature is,the easier super harmonic resonance appear;The force-responses are also affected by the material lay-up mode,temperature load,and magnitudes of external excitation frequency and force.Finally,the research results concerning this work are summarized briefly,and some plans are listed for the related studies further improved.