考虑几何非线性的正交各向异性层合板随机振动响应数值解

In order to improve the analysis accuracy of random vibration response of satellite composite structures, a numerical solution method for nonlinear random vibration response of orthotropic medium plates is proposed by fully considering the geometric nonlinear characteristics of structures. Firstly, the motion equation of rectangular plate is established based on the first-order shear deformation theory. Then, the nonlinear natural frequency of the laminated plate structure is obtained by Galerkin’s method and Perturbation method. Last, on this basis, the numerical solutions of nonlinear random vibration response of orthotropic medium plates under three boundary conditions are derived by combining the equivalent linearization method and the virtual excitation method. Using the proposed nonlinear random vibration numerical method, the random response characteristics of medium composite plates for satellites are analyzed with specific examples. The results show that there are great differences between the results of solving the random vibration response of medium plates by linearization method and nonlinear method. The nonlinear method can significantly improve the accuracy of the numerical solutions of random vibration response. When the small excitation is applied on the plate, under the same bending boundary condition, the difference of plane boundary conditions has little effect on the power spectral density and root mean square of the random vibration response; while when the applied excitation is large, it has significant effect on the random vibration response. The nonlinear random vibration response solution method proposed provides a new research idea and method for the dynamic analysis of satellite structure, which has important theoretical research and engineering application value.