The global governing vibration equation of an unconstrained damped plate was deduced based on the Kirchhoff theory and the analysis of the complex stiffness.The methodology for predicting the vibration of the unconstrained damped plate and the acoustics of the coupled 3D vibro-acoustic system was proposed by virtue of the wave based method (WBM).Taking a four edges clamped rectangular plate coupled with a box like vibro-acoustic system as a numerical example,the out-plane displacement of the unconstrained damped plate was analysed.The responses at a selected reference point was calculated in the 50-500 Hz frequency band by using the WBM and FEM respectively.The results of the two method validate that the WBM is capable for predicting the vibration and acoustic responses of the unconstrained damped system effectively,and the WBM is more efficient to deal with vibro-acoustic problems compared with the FEM.%对敷设自由阻尼薄板振动响应进行了分析,以复刚度为基础得到了在Kirchhoff理论下复合薄板振动控制方程.基于波函数法理论,推导了自由阻尼薄板振动分析模型以及包含自由阻尼结构与声腔的三维耦合模型的建模方法;以四边固支自由阻尼矩形板及耦合的结构声学系统为例,分别以波函数法与有限元法计算了其50 ～500 Hz频段内的结构与声学响应.结果表明:波函数法能有效的应用于添加自由阻尼的薄板振动以及结构声耦合系统响应的预测与分析;相比于有限元法,其高精度、高收敛率的特点使波函数能有效解决更高频率的声振问题.
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