热载荷下板模态间耦合对声功率的影响分析

Analysis of The Influence of Plate Modal Coupling on Sound Power Under Thermal Load

板结构辐射声功率的传统理论模型通常采用数值积分法计算,许多模型不考虑模态间的耦合作用以缩短计算时间。研究模态间耦合对声功率的影响能为精确地预测和控制板结构声辐射特性提供重要的参考。为了高效地计算模态间的耦合项,基于模态辐射效率的幂级数形式解析解模型,提出并建立了矩阵形式解析解模型。数值算例验证了该模型的正确性。研究了板结构在均匀热环境下的声振特性,分析了定点激励和随机位置激励下结构振动模态间的耦合对声功率的影响在不同温度环境中的变化。计算结果表明,结构内温变产生的热应力导致结构等效刚度降低,各阶固有频率变小,声功率曲线各峰值向低频漂移;在计算声功率时必须考虑板模态间的耦合作用,尤其在中低频时,尽管结构某些工况下耦合项对声功率的影响很小,但是当环境温度或外激励作用的位置发生改变后耦合项的影响会变大。

The traditional theoretical model of the radiated sound power of plate structure is usually calculated by numerical integration method. Many models don’t consider the coupling between modes to shorten the calculation time. The study of the influence of the coupling between modes on the sound power can provide an important reference for accurately predicting and controlling the sound radiation characteristics of the plate structure. In order to efficiently calculate the coupling terms between modes,a matrix form analytic solution model based on the power series form analytic solution model of mode radiation efficiency is proposed and established. Numerical examples show that the model is correct. The acoustic vibration characteristics of plate structure under uniform thermal environment are studied and the influence of the coupling of vibration modes on the acoustic power under fixed-point excitation and random excitation in different temperatures is analyzed. The results show that the thermal stress caused by the internal temperature change reduces the equivalent stiffness of the structure, the natural frequency of each order decreases, and the peak value of the sound power curve shifts to the low frequency. The coupling between modes must be considered in the calculation of sound power, especially at low and medium frequencies, although the coupling term has little influence on the sound power of the structure under some conditions, the influence of the coupling terms will increase when the ambient temperature or the position of external excitation changes.