Abstract Several vibro-acoustic models for either single wall or multi-layer constructions are based on classical plate and first order shear deformation theories. The equivalent or condensed plate models employ the thin plate model to extract the dynamic mechanical properties of the multi-layer system considering only flexural and shear motions for the structure under investigation. Since these plate models do not account for the compressional or symmetric motion of the structure, both thin and thick plate theories encounter limitations for mid to high frequency predictions depending on the structures considered. In this work, analytical expressions for the frequency limit of thin and thick plate theories are derived for an elastic layer of isotropic material from the analyses of wavenumbers and admittances. Additionally, refined expressions for coincidence and critical frequencies are presented. Validation of these frequency limits are made by comparing the transmission loss (TL) obtained from both plate theories with the TL computed through the theory of elasticity for a range of thin/thick and soft/stiff materials.

中文翻译：

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关于振动声学预测板块理论的精度限制

摘要 用于单壁或多层结构的几种振动声学模型基于经典板和一阶剪切变形理论。等效或凝聚板模型采用薄板模型来提取多层系统的动态力学特性，仅考虑所研究结构的弯曲和剪切运动。由于这些板模型没有考虑结构的压缩或对称运动，因此根据所考虑的结构，薄板和厚板理论在中高频预测方面都遇到了限制。在这项工作中，根据波数和导纳的分析，推导出了各向同性材料弹性层的薄板和厚板理论频率极限的解析表达式。此外，呈现了对巧合和临界频率的精炼表达。这些频率限制的验证是通过比较从两种板理论获得的传输损耗 (TL) 与通过弹性理论计算的 TL 来进行的，这些损耗是针对一系列薄/厚和软/硬材料。