WBEM-based analysis of band structures of solid-solid and fluid-fluid phononic crystals with frequency-independent fundamental solutions. (June 2023) - Wei, Qi; Xiang, Jiawei; Zhu, Weiping; Hu, Hongjiu
Highlights: Using frequency-independent fundamental solutions to establish integral equations. The nonlinear eigenvalue problem is avoided and the computing time is saved. Applying B-spline wavelet on the interval and wavelet coefficients to approximate physical fields. The system matrices are compressed by the given matrix compression technique. Both sweeping frequency and wave vector technique are given to determine the band structures. Abstract: A novel method is presented to determine the band structures of two-dimensional solid-solid and fluid-fluid phononic crystals (PCs) with square and triangular lattices using the wavelet-based boundary element method (WBEM). Both sweeping frequency technique and sweeping wave vector technique are used to determine the band structures of PCs. The fundamental solutions for integral equations established in primitive cell are independent of angular frequency, resulting in an avoidance of solving nonlinear eigenvalue problems and much reduction of computing time. The radial integration method and dual reciprocity method are respectively applied to handle the domain integral terms arising from the use of frequency-independent fundamental solutions, and to make the dimension reduction. The physical fields are approximated by B-spline wavelet on the interval and wavelet coefficients in wavelet space. It is proved that the wavelet coefficients still meet the relationship of their corresponding physical quantities, such as Bloch theorem. By means of the vanishing moment characteristic of wavelets, some small entries are produced in the system matrices which are further compressed into sparse ones, and the influence of sparse matrices on the results is discussed. Finally, the high computing speed and accuracy of the proposed method are shown in examples.