Research On Nonlinear Statics And Dynamics For Viscoelastic/Piezoelectric Laminated Structures Including Damage Effect

In this dissertation, considering fibre-reinforced composite laminated plates and piezoelectric laminated structures composed by the piezoelectric membranes and fibre-reinforced composite laminated plates as the subjects investigated, the nonlinear dynamic response, nonlinear vibration, creep postbuckling, bifurcation and chaos behaviors of viscoelastic laminated plates including damage effect, as well as the nonlinear dynamic stability of piezoelectric laminated plates with damage are systematically studied. The research results have an important meaning not only in the academic but also in the practical engineering. The main results contain as follows:Based on the viscoelastic theory and the continuum damage mechanics, and according to the Boltzmann superposition principle and strain energy equivalence, a constitutive model is established for viscoelastic composites with orthotropic damage. Suppose the damage variables remain constant throughout the thickness in each layer, then, the damage/viscoelastic constitutive model suited for the global analysis of the laminated plates is obtained. By using the composite mechanics and Von Karman's nonlinear theory, the nonlinear governing equations of motion for the viscoelastic laminated plates with damage are derived. The damage evolution law is characterized by the Kachanov damage evolution equations. Through applying the finite difference method, Newmark method, Newton-Cotes method and iterative procedure, the governing equations are solved. The comparative studies are carried out to validate the validity of the present method. The influences of damage effect, load parameters, geometric and material parameters as well as ply orientations on the critical time of failure initiation and nonlinear dynamic responses for the damage/viscoelastic laminated plates are discussed in detail.According to Timoshenko-Mindlin theory of thick plates, strain energy equivalence hypotheses and Boltzmann superposition principle, the nonlinear dynamic equations of viscoelastic laminated plates including the effects of damage and transverse shear deformation are given. By employing the Galerkin method, the original integro-partial-differential equations are transformed into a set of integro-ordinary equations. In the numerical calculations, the viscoelastic material is taken as a standard linear solid and the damage evolution model proposed by Kachanov is adopted. Firstly, the present result is compared with available data. Then, the influences of different span-thickness and aspect ratio as well as boundary condition on the nonlinear amplitude-frequency responses of the damage/viscoelastic...