采用高斯展开法分析组合式开口矩形Mindlin板的弯曲自振特性

Gaussian expansion method is introduced into the study of flexural vibration of rectangular plates with combined openings based on the Mindlin plate theory. The localization characteristic of the Gaussian wavelet function can accurately capture the characteristics of the local opening and improve the computational efficiency by selecting the Gaussian wavelet function as the displacement shape function. The expansion factor and shift factor of the Gaussian function are defined, and the basis functions used to fit the displacement field of the plate with opening are generated by a series of expansion and shift transformations. The larger the expansion factor is, the higher the resolution of the shape function will be. It can accurately simulate higher-frequency vibration field. The Lagrangian energy functional of the plate with opening is established by taking the energy method as the basic framework. The artificial spring model is introduced into simulate various boundary conditions, and the influence of boundary conditions on vibration of plates is transformed into the influence of increased elastic potential energy on stiffness matrix. The accuracy and applicability of the method is verified by comparing the results of the research example with that of the finite element software, which provides a reference for practical engineering problems.