Vibration Analysis of a Plate Embedded or Attached with Acoustic Black Hole Using a Virtual Spring Energy Method

Acoustic black hole (ABH) with the power-law profile has the advantages of strong designability and vibration suppression. This study provides a novel virtual spring energy method (VEM) to solve the vibration characteristics of a plate embedded or attached with acoustic black hole. Firstly, the virtual springs in this study can deal with boundary conditions, continuity conditions, and periodic conditions. After solving the kinetic and potential energy of a plate cell embedded with acoustic black hole, the periodic structure’s kinetic and potential energy need not be calculated repeatedly. The method is verified by the finite element method. Secondly, to overcome the stiffness reduction owing to the varying thickness of ABH in the primary bearing structure, a composite ABH structure called “Plate–ABH” is proposed, in which a damping layer is designed with an ABH profile and attached to the primary plate structure. The two layers connect each other through the virtual springs. The vibration characteristics of the composite ABH plate are given by employing the VEM. The composite ABH structure shows strong damping ability and lighter weight compared with a plate attached with the uniform thickness damping layer. Plate–ABH can be effectively used in the engineering of vibration reduction.