Calculation of sound fields in small enclosures using a meshless model

The details are provided for the derivation and implementation of a meshless model based on the Element-free Galerkin Method for calculating sound fields. The model is applicable to three-dimensional small enclosures with arbitrary shape. In the model, the system equation for calculating the sound pressure of nodes is derived using the Galerkin weighted residual method. The shape functions are constructed using the moving least squares method, and the methods for calculating the integrals are described in detail. The frequency response function of a rectangular enclosure and a cylindrical enclosure are calculated using the model, and the results are compared with the results obtained using a theoretical method, Boundary Element Method (BEM), and with experimental results, respectively. Next, the factors that influence the performance of the method, which include the distribution and number of nodes, the number of integration points, the types of basis, and the weight functions, are discussed. The suitable support domain radius for the calculation of sound fields in small enclosures is also obtained through use of numerical experiments. Finally, the meshless model with suitable parameters is used to calculate the sound field of an airplane cabin. Comparison of the calculated sound pressure levels with the measured results has validated the model's accuracy and applicability to enclosures with complicated structures.