基于分片传递函数法的声振耦合

Vibro-Acoustic Coupling Research Based on Patch Transfer Function Method

强耦合条件下,复杂系统的有限元分析受到自由度的影响计算成本高昂。虽然模态叠加技术能减少耦合系统的自由度,但基于忽略不同子系统间高阶模态和低阶模态耦合作用的假设,若使用非耦合模态可能导致收敛性差。基于无阻尼声振耦合方程,本文采用分片传递函数法(Patch transfer function method,PTFM)将耦合面处理成一系列独立的分片,每个分片上所属单元节点值的平均值定义为分片传递函数,通过使用连续性关系计算耦合系统的分片传递函数。将耦合矩阵的求逆简化为源点到响应点的传递函数,可以快速计算耦合系统响应值。分别利用直接耦合法(Direct coupling method,DCM)和分片传递函数法计算板和空气声腔耦合模型,验证分片传递函数法的有效性,并讨论了分片传递函数的算法原理和计算误差。

In the case of strong coupling,analyzing a complex system by finite element method costs so much due to the degrees of freedom.Although introducing modal superposition technique is able to reduce the sum of coupling system’s freedoms,it is still based on the assumption of neglecting the coupling influence between the high⁃order modes and low⁃order modes belonging to different subsystems.And it may result in non⁃convergence when uncoupling modes are used.Based on the undamped acoustic and vibration coupling equation,this paper presents a new coupling method called patch transfer function method(PTFM),by which the coupling face is tackled as a series of independent patches.The patch transfer functions of each patch are calculated by the average value of the nodal value,then the coupling system PTFs can be obtained by the continuity equation.It is faster to predict the coupling system response,as the inversion of coupling equation is substituted for the transfer function from source to receiver.At last,with the model of plate and air⁃cavity coupling system,this paper reveals the accuracy of PTFM by comparing the result of direct coupling method(DCM).And the theory and calculation error of the method are discussed.