Simulation and synthesis of elastic wave absorbers at the boundary of a rigid body: Incidence of longitudinal waves

Abstract

Results of a computer simulation of an impedance absorber for longitudinal plane elastic waves incident on a free boundary of a rigid body are presented. The absorbing elements are mechanical resonators (of the elasticity-mass type) with two degrees of freedom and, hence, with two resonance frequencies, which correspond to the normal and tangential oscillations of the resonator. Formulas for calculating the absorber efficiency as a function of frequency and angle of incidence of longitudinal waves are derived with allowance for the absorption of both longitudinal and shear waves at their reflection from the absorbing surface. These formulas are used to solve the problem of synthesizing optimal absorbers that are characterized by the maximal average value of the absorption coefficient in preset ranges of frequency and angle of incidence. The possibility of increasing this average value by increasing the loss coefficient of the resonators or by using two types of resonators with different resonance frequencies is studied. The results of the calculations are presented in graphic form.