From the mixed variational principle, by the selection of the state variables and its dual variables, the Hamiltonian canonical equation for the dynamic analysis of shear deformable antisymmetric angle-ply laminated p...From the mixed variational principle, by the selection of the state variables and its dual variables, the Hamiltonian canonical equation for the dynamic analysis of shear deformable antisymmetric angle-ply laminated plates is derived, leading to the mathematical frame of symplectic geometry and algorithms, and the exact solution for the arbitrary boundary conditions is also derived by the adjoint orthonormalized symplectic expansion method. Numerical results are presented with the emphasis on the effects of length/thickness ratio, arbitrary boundary conditions, degrees of anisotropy, number of layers, ply-angles and the corrected coefficients of transverse shear.展开更多
An asymptotic perturbation method is presented based on the Fourier expansion and temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported angle-ply composite laminated r...An asymptotic perturbation method is presented based on the Fourier expansion and temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported angle-ply composite laminated rectangular thin plate with parametric and external excitations.According to the Reddy's third-order plate theory,the governing equations of motion for the angle-ply composite laminated rectangular thin plate are derived by using the Hamilton's principle.Then,the Galerkin procedure is applied to the partial differential governing equation to obtain a two-degrees-of-freedom nonlinear system including the quadratic and cubic nonlinear terms.Such equations are utilized to deal with the resonant case of 1:1 internal resonance and primary parametric resonance-1/2 subharmonic resonance.Furthermore,the stability analysis is given for the steady-state solutions of the averaged equation.Based on the averaged equation obtained by the asymptotic perturbation method,the phase portrait and power spectrum are used to analyze the multi-pulse chaotic motions of the angle-ply composite laminated rectangular thin plate.Under certain conditions the various chaotic motions of the angle-ply composite laminated rectangular thin plate are found.展开更多
文摘From the mixed variational principle, by the selection of the state variables and its dual variables, the Hamiltonian canonical equation for the dynamic analysis of shear deformable antisymmetric angle-ply laminated plates is derived, leading to the mathematical frame of symplectic geometry and algorithms, and the exact solution for the arbitrary boundary conditions is also derived by the adjoint orthonormalized symplectic expansion method. Numerical results are presented with the emphasis on the effects of length/thickness ratio, arbitrary boundary conditions, degrees of anisotropy, number of layers, ply-angles and the corrected coefficients of transverse shear.
基金supported by the National Natural Science Foundation of China (Grant Nos.10732020,10872010)the National Science Fund for Distinguished Young Scholars (Grant No.10425209)
文摘An asymptotic perturbation method is presented based on the Fourier expansion and temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported angle-ply composite laminated rectangular thin plate with parametric and external excitations.According to the Reddy's third-order plate theory,the governing equations of motion for the angle-ply composite laminated rectangular thin plate are derived by using the Hamilton's principle.Then,the Galerkin procedure is applied to the partial differential governing equation to obtain a two-degrees-of-freedom nonlinear system including the quadratic and cubic nonlinear terms.Such equations are utilized to deal with the resonant case of 1:1 internal resonance and primary parametric resonance-1/2 subharmonic resonance.Furthermore,the stability analysis is given for the steady-state solutions of the averaged equation.Based on the averaged equation obtained by the asymptotic perturbation method,the phase portrait and power spectrum are used to analyze the multi-pulse chaotic motions of the angle-ply composite laminated rectangular thin plate.Under certain conditions the various chaotic motions of the angle-ply composite laminated rectangular thin plate are found.
