Nonlinear Dynamic Behavior Analysis For Functionally Graded Material/Fiber Metal Laminated Plates With Interfacial Damage

In this dissertation, considering fiber metal laminated(FML) plates under piezoelectric-thermal-mechanical loadings, the analysis of temperature distribution within the plate subjected to transient thermal field, elasto-plastic buckling and post-buckling path, nonlinear dynamic response and active control, nonlinear stability as well as the bifurcation and chaos behavior of FML plates with interfacial damage are systematically studied. The research results have important effect on the enrichment and development of fiber metal materials in theory and on its engineering application. The main results contain as follows.Based on the elasto-plastic theory, considering the effect of spherical stress tensor on the elasto-plastic deformation and using the slicing treatment to deal with the plasticity of functionally graded coatings, the elasto-plastic increment constitutive equations of the sandwich plates with functionally graded metal-metal face sheets can be derived. Applying the weak bonded theory to the interfacial constitutive relation and taking into account geometric nonlinearity, the nonlinear increment differential equilibrium equations of the sandwich plates with functionally graded metal-metal face sheets are obtained by using the minimum potential energy principle. The finite difference method and the iterative method are used to obtain the post-buckling path. When the effect of geometrical nonlinearity of plate is ignored, the elasto-plastic critical buckling load of the sandwich plates with functionally graded metal-metal face sheets can be solved by using the Galerkin method and the iterative method. In the numerical examples, effects of the interface damages, the induced load ratio, the functionally graded index, and geometry parameters on the elasto-plastic post-buckling path and the elasto-plastic critical buckling load are investigated.Considering temperature effect, high-order shear deformation and geometrical nonlinearity, the nonlinear governing equations of FMLs under stationary temperature field are obtained by the Hamilton variational principle. Based on the assumption of focal adhesion during low oblique velocity contact process, the interaction between the impactor and the plate is determined by modified Hertz contact law at the normal direction and Mindlin friction contact force model at the tangential direction. To solve the problem, firstly, the Galerkin method and Newmark- ? method are used to discrete the variations in time and space domain, then, nonlinear terms in the governing equations are linearized, finally, the whole problem is solved by the iterative method. In numerical examples, effects of the velocity and the angle of the oblique impact on the normal and tangential contact force history are analyzed. Meanwhile, effects of the temperature field, the mass and the velocity of impactor and the geometrical parameters of plate on the nonlinear dynamic response of the FMLs are presented.Based on the higher order shear deformation theory and the geometric nonlinear theory, the nonlinear motion equations, to which the effects of the positive and negative piezoelectric and the thermal are introduced by piezoelectric FML plates in an unsteady temperature, are established by Hamilton’s variational principle. Then, the control algorithm of negative-velocity feedback is applied to realize the vibration control of the piezoelectric FML plates. During the solving process, firstly, the formal functions of the displacements that fulfilled the boundary conditions are proposed. Then, heat conduction equations and nonlinear differential equations are dealt with using the differential quadrature(DQ) and Galerkin methods, respectively. On the basis of the previous processing, the time domain is dispersed by the Newmark- ? method. Finally, the whole problem can be investigated by the iterative method. In the numerical examples, the influence of the applied voltage, the temperature loading and geometric parameters on the nonlinear dynamic response of the piezoelectric FML plates is analyzed. Meanwhile, the effect of feedback control gain and the position of the piezoelectric layer, the initial deflection and the external temperature on the active control of the piezoelectric layers have been studied. The model development and the research results can serve as a basis for nonlinear vibration analysis of the FML structures.For the nonlinear dynamic stability analysis of FML plate with interfacial damage under thermal-piezoelectric-mechanical loadings, the semi-analytical method is adopted. Firstly, by introducing Heaviside step function, the global displacement field of the plate is established, then some parameters can be determined by the boundary conditions of the top and bottom surface and continuity conditions of the interfaces, and then, based on the weak bonded theory to the interfacial constitutive relation, a higher order displacement field for FML plates with interfacial damage is obtained. Based on the geometric nonlinear theory, and considering the thermal and piezoelectric effect, nonlinear motion control equations are set up. The nonlinear Mathieu equations of the plates are derived by using Galerkin method. And by comprehensively application of the incremental harmonic balance(HIB) method and the Newton-Raphson method, the nonlinear dynamic stability of piezoelectric FML plate with interfacial damage is analyzed. In numerical examples, effects of interfacial damage, geometrical nonlinearity, thermal and piezoelectric loads on the main regions of nonlinear dynamic instability are researched in detail.And for further analysis of the bifurcation and chaos characteristics of FML plate with interfacial damage in steady temperature field considering damping effect of the plate, some new variables is introduced and the problem is qualitatively investigated by forth order Runge-Kutta method. Bifurcation diagram, phase plane portrait, Poincare map, time history and spectrum for the FML plate are given out. Which reveal the abundant mechanical property of the plate and vividly show effects of interfacial damage, temperature on these dynamic behaviors.