多边形板高频振动的能量虚源法研究

Research on energy image source method for high frequency vibration of polygonal plate

本研究的目的是将室内声学中的虚源法引入高频横向点激励作用下多边形板的能量辐射传递模型中,以预测结构弯曲振动的能量响应,其核心是如何构建多边形板的虚源云场。在多边形板的能量辐射传递模型框架中,以实源的镜像虚源替代结构的边界,以此来表示边界处能量的连续反射。基于直接场的能量密度和功率流强度核函数,结构内部任意一点的能量可由实源产生的能量和无限多的镜像源产生的能量叠加得到。对直角三角形板和方形板求解,获得了它们的能量密度与功率流强度分布特征。数值算例结果与能量辐射传递法以及解析解对比,验证了模型的准确性。最后讨论了阻尼、频率和虚源的阶数对计算结果收敛性的影响。

The purpose of this study is to introduce the image source method in room acoustics into the radiative energy transfer model of a polygonal plate under high frequency transverse point excitation to predict its energy response of structural bending vibrations.The key treatment is how to construct the image source cloud field of the polygonal plate.In the framework of the radiative energy transfer model for the polygonal plate,the mirror image of the real source is used to replace the boundary of the structure so as to represent the continuous reflection of energy at the boundary.Based on the energy density and power flow intensity kernel functions of the direct field,the energy at any point inside the structure can be obtained by superposition of the energy generated by the real source and the energy generated by an infinite number of image sources.By solving the right triangular plate and rectangular plate,we can obtain their distribution characteristics of energy density and power flow intensity.Numerical results are compared with those solved by the radiative energy transfer method and the analytical solutions to verify the accuracy of the proposed model.Finally,the effects of damping,frequency and order of image sources on the convergence of the computation results are discussed.