The theoretical analysis of thick plate vibration behavior has been investigated in the literature, but most of the studies were focused on flexural dynamic characteristics and lack experimental verification. In this study, the analytical solutions based on the superposition method for both the flexural and extensional vibrations are presented to obtain resonant frequencies and associated mode shapes for a transversely isotropic thick rectangular plate. The displacement equilibrium equations and boundary conditions of the modified first-order shear deformation theory (FSDT) are derived by utilizing Hamilton’s principle and the variation method. To verify the validity of the theoretical model, the finite-element method (FEM) and impact experiment results for thick plates are employed in this work. Excellent agreement of resonant frequencies and associated mode shapes is obtained for FEM calculation and theoretical analysis. To excite vibrations of a thick rectangular plate, a steel ball controlled by an electromagnet is utilized. A steel ball is dropped freely from a height of 231 mm on the top of the plate surface, and a transient wave will be generated after the ball impact on the specimen. The frequency spectrum of the thick rectangular plate is constructed by using the fast Fourier transform of the time-domain transient response. The excited resonant frequencies obtained from experimental measurement are compared with theoretical results. The comparisons show that the modified FSDT provides an excellent prediction of the resonant frequencies and mode shapes for the dynamic characteristics of thick rectangular plates.

中文翻译：

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基于修正FSDT假设的横向各向同性矩形板耦合动力特性理论分析与实验测量

厚板振动行为的理论分析已在文献中进行了研究，但大多数研究都集中在弯曲动力学特性上，缺乏实验验证。在这项研究中，提出了基于叠加方法的弯曲和拉伸振动的解析解，以获得横向各向同性厚矩形板的共振频率和相关的模式形状。利用哈密顿原理和变分法推导出修正一阶剪切变形理论(FSDT)的位移平衡方程和边界条件。为了验证理论模型的有效性，本文采用有限元法（FEM）和厚板冲击实验结果。对于 FEM 计算和理论分析，共振频率和相关模态形状非常一致。为了激发厚矩形板的振动，使用了由电磁铁控制的钢球。钢球从板面顶部231mm高度自由落下，钢球撞击试件后会产生瞬态波。利用时域瞬态响应的快速傅立叶变换构建厚矩形板的频谱。从实验测量中获得的激发共振频率与理论结果进行了比较。比较表明，改进的 FSDT 为厚矩形板的动态特性提供了谐振频率和模式形状的极好预测。