A 2D daubechies wavelet model on the vibration of rectangular plates containing strip indentations with a parabolic thickness profile

Abstract

This paper presents a 2-D semi-analytical model for the vibration analyses of a plate with a power-law-profiled thickness variation, referred to as an Acoustic Black Hole (ABH) plate. The proposed model, along with the associated wavelet-based solution procedure, is intended to overcome major technical difficulties which are specific to ABH structures: the non-uniform wavelength distribution and ABH-induced wave compressions at the high frequency range in a realistic structure of finite size. Under the general Rayleigh-Ritz framework, Daubechies wavelet (DW) scaling functions are chosen as the admissible functions to decompose the transverse displacement of the plate with ABH indentations featuring a thickness variation along one direction of the panel. Modal and forced vibration analyses are carried out with results compared with those obtained by the FEM. It is shown that the model allows an accurate prediction of various vibration parameters and a realistic description of the typical ABH phenomena. Meanwhile, the use of Daubechies wavelet functions allows enhancing the effectiveness of the Rayleigh-Ritz method to reach the high frequency range, where systematic Acoustic Black Hole (ABH) effects are expected. Numerical analyses also reveal the potential of using strip ABH indentations in a plate to achieve a light-weight design with appealing vibration reduction properties. Analyses on the ABH-induced damping enhancement demonstrate the dominant effect of the local structural modes within indented area, which exhibit lower-order deformations (containing typically half and one wave along the direction in which the thickness is tailored).