非规则封闭空间声场建模的Chebyshev-变分法及其固有声学特性分析

针对非规则封闭空间声场建模问题,提出了一种基于Chebyshev-变分原理的声场建模方法。该方法首先选取包络非规则声场的矩形空间并将此矩形空间内的声压函数展开成三重Chebyshev级数形式,然后通过坐标变换得到定义域空间中的声场势能和声场动能,最后按照里茨方法对声场的拉格朗日泛函进行求解,得到声场的特征方程并求得声场固有频率和模态。通过与曲面声场的数值结果对比,验证了本建模方法的正确性和有效性。在此基础上研究具有不同倾角的梯形声场固有特性,分析内部凹槽深度对"凹"型声场频率和模态的影响。结果表明,梯形声场模态会随着倾角增大而逐步演变;"凹"型声场低阶频率随凹槽深度的增加而逐渐减小,但第一阶频率却呈现先减小后增大的特点。 

Modeling and acoustic analysis of irregular sound enclosure by using Chebyshev-variational method

A modeling method for irregular sound enclosure is proposed based on the Chebyshev-variational theory. A rectangular space is firstly assumed to bound the irregular sound space and the sound pressure in the rectangular space is expressed as triple-Chebyshev series. Next, the coordinate transformation is performed and the Lagrangian functional of the irregular sound space is obtained. At last, the Lagrangian functional is solved under the frame work of Ritz method.The acoustic characteristic equation of the enclosure is deduced and the eigenpairs are obtained. The accuracy of the present method is validated according to the agreement between the present results and the finite element results for an enclosure with curved surface. Furthermore, the acoustic characteristics of trapezoidal enclosure and enclosure with inner groove are investigated. The results show that the mode shapes of trapezoidal sound space will change with the increase of inclination angle and the natural frequencies(except the first order) of sound space with rectangular inner groove will decrease with the increase of groove depth.