中文摘要：

基于小波的紧支性、正交性及Daubechies小波函数与其尺度函数的可微性，以Daubechies小波尺度函数作为Galerkin方法的基函数，研究求解任意复杂封闭空腔结构一声耦合场的方法。Galerkin法须要涉及Daubechies小波尺度函数的求导和积分，即所谓关联系数，而Daubechies小波不存在解析表达式且具有强烈振荡性，采用数值求导和积分存在很大误差。因此根据小波双尺度方程，给出求解结构—声耦合场中涉及的关联系数的精确计算格式。而后利用小波迦辽金法对一类似轿车车身的复杂封闭空腔，在20～250 Hz频段内进行结构—声耦合场预报，将计算值和试验测量值进行比较，证明该方法能够准确预报耦合场的固有频率和腔内声压分布情况。

英文摘要：

A method for solving vibro-acoustic coupling field in complex enclosures based on Daubechies wavelet scaling functions under Galerkin framework is developed considering the compactly supported orthogonal property of wavelets and differentiable natures of Daubechies wavelets and their scaling functions. Due to the derivatives and integrals of Daubechies wavelet being highly oscillatory, it is unstable to compute the connection coefficients by the numerical evaluation. Dedicated algorithms are devised for the exact evaluation of connection coefficients occurred in solving vibro-acoustic system based on the two-scale equation. Then an example of a car-like cavity is given and the wavelet-Galerkin method is applied to the cavity to get the distribution of the pressure in it at a frequency between 20 Hz and 250 Hz. An experiment is carried out to show the validity of the new method. The compared result demonstrates that the new method is efficient for predicting the natural frequencies and the pressure distribution of the coupling field.