Investigation On The Dynamical Characteristic Of Two-Dimensional Acoustic Black Hole Plates

An acoustic black hole(ABH)plate is a structure that controls waves through a unique geometric design,with advantages such as simplicity and versatility.ABH plates have essential applications in industries such as transportation and construction.By studying the principles and characteristics of ABH,more efficient acoustic isolation,noise reduction,and piezoelectric energy harvesting devices can be designed.This article is based on Kirchhoff plate theory and mechanical analysis of twodimensional elastic bodies to obtain the equilibrium differential equation of the ABH plate vibration in two dimensions.A more suitable integral equation for research is obtained using the variational method,energy method,and Hamilton principle.The finite element method,Galerkin method,and finite difference method are used to comprehensively analyze the model and study the natural frequency and mode of the ABH plate.The solution formulas for each method are derived,which are also applicable to thin plates with varying heights.The characteristics and limitations of different techniques are analyzed.The study shows that most energy during vibration is concentrated in the ABH region,indicating good wave control performance.The active-passive piezoelectric networks(APPN)structure is a method that can be used for vibration system control.This article proposes an innovative combination structure of APPN and ABH and analyzes the vibration control effect of the new system.Firstly,the vibration modes of the ABH plate are obtained by the finite element method.Then,the dynamic model is derived using Hamilton’s principle and the Rayleigh-Ritz method.Next,the open-loop and closed-loop control characteristics are analyzed separately.The data show that the ABH plate with the active-passive piezoelectric network performs better than the plate with active vibration control.Finally,the parameters(resistance and inductance)in APPN are optimized to obtain the best vibration control performance.The research findings can provide the theoretical basis for the application of ABH in vibration control,noise reduction,and energy harvesting.