Elastic wave propagation energy dissipation characteristics analysis on the viscoelastic damping material structures embedded with acoustic black hole based on semi-analytical homogeneous asymptotic method

Abstract Elastic wave energy dissipation and absorption properties of viscoelastic damping material (VDM) composite plates embedded with acoustic black hole (ABH) are analyzed in this paper. Considering the periodic distribution of the ABH-embedded VDM structure in the composite plate, semi-analytical homogeneous asymptotic theory is applied, which transforms the macroscopic to a microscopic problem. In-plane variables of the composite structure are defined and generated by the third-order shear deformation theory of Reddy, and the equilibrium equations are derived by extended Hamilton's principle and the internal balance is consequently determined by representative volume element theory. Determining the constitutive equations of the composite laminate structure allow the equivalent shear and strain equilibrium equations to be achieved. Subsequently, the complex equivalent stiffness is defined according to the general Hooke's law, and the dimensionless equivalent loss tangent tan δ of the composite sandwich plate is finally evaluated from the equivalent loss and storage modulus. The ABH and VDM layer factors which affect tan δ are thoroughly analyzed and discussed. The investigation can supply a new efficient method to dissipate and absorb propagation wave energy with a wide bandwidth at low frequency. Additionally, the analysis is validated by numerical simulation and Galerkin methods.