【摘要】 随着噪声控制标准的不断提升和装配式建筑的快速发展，提升平板结构的隔声性能并改进其测量技术有着重要意义。基于谱几何法(Spectral Geometry Method,SGM)建立一种可用于虚拟声学测试的隔声测量室动力学模型，分别通过二维和三维傅里叶级数法得到板表面的位移和腔内声场，可确保声压与振速在任意位置的连续性。将声源腔和接收腔分别设置为混响室和消声室，并通过在拉格朗日方程中添加阻抗能量项实现任意阻抗边界。然后基于哈密顿原理充分考虑两声腔与板之间的耦合关系，得到系统的振动方程。通过与有限元模型的对比，验证了该方法的正确性、良好的数值稳定性与极高的计算效率。最后，分析弹性安装条件、接收腔厚度对于腔内声能及构件振动的影响，结果表明两者均可使板结构受到的声压激励产生变化，从而对结构的声传递产生影响。更多还原

【Abstract】 With the promotion of noise control standards and the rapid development of prefabricated buildings, it is meaningful to improve the sound insulation performance of plate structures and their measurement technology. The structural sound insulation measurement model for virtual acoustic tests is established based on the spectral geometry method. The displacement of the plate and the sound field in the cavities are expressed as two-dimensional and threedimensional Fourier series respectively, so the continuity of sound pressure and vibration velocity at any position is ensured.The sound source chamber and receiving chamber are set as a reverberation chamber and a silencing chamber respectively,and the impedance boundary is realized by adding the energy terms of impedance into the Lagrange equation. Then, the coupling relationship between the cavities and the plate is fully considered based on the Hamilton principle, and the vibration equation of the system is obtained. By comparing the result with that of the finite element model, the correctness of this method is verified, and meanwhile it has good numerical stability and high computational efficiency. Finally, the effects of elastic installation conditions and the thickness of the receiving cavity on the sound energy inside the rooms are analyzed.The results show that both of them can change the sound pressure excitation of the plate structure and affect the sound transmission of the structure.更多还原