基于改进高斯展开法的ABH板弯曲振动特性分析

In view of non-uniform wavelength distribution and variable wave-number in acoustic black hole (ABH) plates, a semi-analytical model based on an improved Gaussian expansion method (IGEM) was proposed to analyze the flexural vibration of ABH plates. In the framework of the Rayleigh-Ritz method, Gaussian functions were used as basic functions to describe the displacement field around ABH plates. The scale factor of the Gaussian functions was adjusted according to the variable thickness of the plate. Meanwhile, the distribution of the Gaussian functions will be a function of the scale factor and the shape of the ABH plates. In this process, the scale factor is not a constant anymore as in the traditional Gaussian expansion method. Therefore, the displacement of the plates with different thicknesses can be described more accurately, and the separation of x direction and y direction in the integration process can be realized to improve the efficiency and accuracy in computation. The singularity of the mass and stiffness matrix can be avoided when the IGEM was applied to the ABH plates in this paper, a rectangular plate with ABH indentations, a circular plate with ABH indentations, and a perforated plate with ABH indentations were taken account as examples. The results were compared with the finite element method. Results show that the proposed method demonstrates more accurate and less computation cost than the conventional Gaussian expansion method. This implies a potential application to predict the response characteristics of structures with thickness variation rapidly as ABH plates.