Analytical modeling on the vibration response of a beam-stiffened Mindlin thick plate with free boundary conditions

IF 3.4 Q1 ENGINEERING, MECHANICAL 国际机械系统动力学学报(英文) Pub Date : 2023-06-26 DOI:10.1002/msd2.12078
Hui Guo, Kai Zhang
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Abstract

This paper presents a new analytical solution for the vibration response of a beam-stiffened Mindlin plate having a completely free boundary condition by utilizing a finite cosine integral transform. In the solution, the unknown coupling force and moments at the beam/plate interface and the unknown modal constants from the integral transform are determined by the continuity and compatibility conditions at the interface as well as the boundary conditions. It provides an easily implemented tool for exploring complex edge value problems for a class of higher-order partial differential equations represented by fully free-stiffened Mindlin thick plates. The validity of the model is evaluated by comparing the calculated free and forced vibration responses of the beam-stiffened plate with those calculated using a beam-stiffened thin plate and those from finite element analysis.

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具有自由边界条件的梁加筋Mindlin厚板振动响应的分析建模
本文利用有限余弦积分变换,给出了具有完全自由边界条件的梁加肋Mindlin板振动响应的新解析解。在该解中,梁/板界面处的未知耦合力和力矩以及来自积分变换的未知模态常数由界面处的连续性和相容性条件以及边界条件确定。它为探索一类由完全自由加肋Mindlin厚板表示的高阶偏微分方程的复杂边值问题提供了一个易于实现的工具。通过比较计算的梁加筋板的自由和受力振动响应、使用梁加筋薄板计算的振动响应和有限元分析的振动响应,评估了该模型的有效性。
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