Multiresolution Reproducing Kernel Particle Methods in Acoustics

In the analysis of complex phenomena of acoustic systems, the computational model-ing requires special attention for a realistic representation of the physics. As a powerful tool, the nite element method has been widely used in the study of complex systems. In order to capture the important physical phenomena, p-nite elements and/or hp-nite elements are employed. The reproducing kernel particle methods (RKPM) are emerging as an eeective alternative due to the absence of a mesh, and the ability to analyze a speciic frequency range. In this study, a wavelet particle method based on the multiresolution analysis encountered in signal processing has been developed. The interpolation functions consist of spline functions with a built-in window which permits translation as well as dilation. A variation in the size of the window implies a geometrical reenement, and allows the ltering of the desired frequency range. An adaptivity similar to hp-nite element method is obtained through the choice of an optimal dilation parameter. The analysis of the wave equation shows the eeectiveness of this approach. The frequency/wave number relationship of the continuum case can be closely simulated by using the reproducing kernel particle methods. A similar methodology is also developed for the Timoshenko beam.