基于梁模态的复合板表观弯曲刚度识别及其隔声量预测方法研究

A Method for Identifying Apparent Bending Stiffness and Predicting Sound Transmission Loss of Composite Panels Using Beam Modes

摘要: 轻质复合板因兼具轻量化与高强度的优异静态力学性能，在工程领域具有广泛应用，但其“高静低动”的动态力学特性导致吻合频率向低频偏移，使其隔声性能低于同面密度的均质板。针对复杂复合结构声学特性解析与数值预测中存在的理论建模困难及高频计算难题，本文提出一种基于自由边界条件下复合梁弯曲模态的方法，确定对应复合板的表观弯曲刚度，进而结合模态叠加法计算简支条件下矩形复合板的隔声量。该方法不依赖于复合结构的几何对称性或规则性，预测结果与实验结果吻合良好，可为高性能声学复合板的设计提供理论指导。

Abstract: Lightweight composite panels are widely used in engineering fields due to their excellent static mechanical properties, combining light weight with high strength. However, their dynamic mechanical characteristic of “high static stiffness but low dynamic stiffness” causes the coincidence frequency to shift toward lower frequencies, resulting in sound insulation performance inferior to that of homogeneous panels with the same surface density. To address the challenges of theoretical modeling difficulties and high-frequency computational complexities in the analytical and numerical prediction of acoustic characteristics of complex composite structures, this paper proposes a method based on the flexural modes of composite beams under free boundary conditions to determine the apparent bending stiffness of the corresponding composite panels. The sound transmission loss simply-supported rectangular composite plates is then calculated using the modal superposition method. This approach effectively circumvents the dependence of analytical methods on the geometric symmetry or regularity of composite structures. The predicted results are in good agreement with experimental data, providing theoretical guidance for the design of high-performance acoustic composite panels.