考虑任意阻抗壁面条件管腔结构声场特性分析

针对任意阻抗壁面条件一维管腔声学系统建模,对系统动力学特性进行预报。为了满足阻抗边界条件对声压一阶导数连续性要求,管腔声压函数通过在标准傅里叶级数端点位置引入边界光滑辅助多项式进行构建。结合壁面阻抗声学边界和管腔声学Helmholtz控制微分方程得到强形式标准特征值问题,获得相应的声学模态信息。在数值仿真中,通过算例给出各种边界条件下管腔声学模态频率、声压振型、声压和质点振速频率响应曲线,与现有文献中相关结果进行对比,充分验证了本文求解方法的正确性和有效性,证明该方法可对任意阻抗壁面条件管腔系统声学特性进行准确预报。 

Acoustic characteristics analysis of slender cavity system with arbitrary impedance end conditions

A modeling method for the dynamic characteristics analysis of slender acoustical cavity with impedance end conditions is established. In order to satisfy the continuity requirement at impedance ends for the first order differential of sound pressure, filed function is constructed as the standard Fourier series supplemented by boundary smoothed auxiliary polynomials. System characteristic equation is derived by solving governing differential equation and impedance acoustic boundary of slender acoustical cavity system simultaneously, relevant acoustical modal information is obtained via the state space solution procedure. In the numerical simulation, various acoustic variables, such as acoustical modal frequency, sound pressure modal shape, sound pressure frequency response and the particle velocity,are presented for the slender acoustical cavity system with different boundary conditions and compared with those results in the existing literature. The correctness and effectiveness of the proposed method are then fully validated.