以变厚度薄板理论模型及振动特性求解方法为研究基础，对不同类型变厚度薄板的振动特性进行仿真分析，总结其随厚度改变的变化规律，并在此发现上，提出一种新型变厚度薄板。通过对线性和非线性变厚度薄板的建模仿真，验证了变厚度薄板建模过程和仿真结果的准确性；基于同种建模方法，赋予薄板不同的厚度变化规律，包括单向线性、单向非线性、双向线性和双向非线性变厚度薄板四种，研究其在经典边界条件下与对应的等质量等厚度薄板之间的振动特性差异及自身随厚度变化参数改变的变化规律；最后，提出一种新型变厚度薄板，发现并验证其较前面四种变厚度薄板在经典边界条件下更能有效提升薄板低阶固有频率，并将研究范围扩充至任意弹性边界条件。
Abstract
Based on the theoretical model of the variable-thickness thin plate and the method of solving vibration characteristics, the vibration characteristics of different types of variable-thickness thin plates are simulated and analyzed, and the change rule with the thickness change is summarized. Through the modeling and simulation of linear and non-linear variable thickness thin plates, the accuracy of the variable thickness thin plate modeling process and simulation results is verified; based on the same modeling method, the thin plate is given different thickness variation rules, including unidirectional linear, single There are four kinds of nonlinear thickness, bidirectional linear and bidirectional nonlinear variable thickness thin plates. The vibration characteristics of the thin plates with equal thickness and equal thickness under the classic boundary conditions and their own changes with the thickness change parameters are changed. Finally, A new type of variable-thickness thin plate is proposed, and it is found and verified that it can effectively improve the low-order natural frequency of the thin plate under the classical boundary conditions compared to the previous four variable-thickness thin plates.
关键词
变厚度薄板 /
振动特性 /
新型厚度分布 /
弹性边界
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Key words
thin plate with variable thickness /
vibration characteristics /
new thickness distribution /
elastic boundary
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参考文献
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