Dynamic response analysis of plates including acoustic black hole with discrete nonlinear supports at its corners

This paper presents a numerical analysis of the vibration damping effects of an acoustic black hole on a rectangular plate supported by four three-directional nonlinear springs at its four corners, with particular attention to how the nonlinear corner supports affect the acoustic black hole–related damping performance. Here, we adopt an acoustic black hole with a two-dimensional crater-like profile, and a viscoelastic damping material is layered in the crater region. To investigate the effects of the spring constant on the damping effects of the acoustic black hole using the finite element method with the modal strain-energy method, modal loss factors, resonant frequencies, and eigenmodes were obtained under small-amplitude conditions. Subsequently, linear eigenmodes were introduced as normal coordinates, and the discretized equations including the restoring force of the nonlinear springs were transformed into nonlinear ordinary differential equations for efficient nonlinear dynamic analysis. Half-triangular wave pulses were applied to these transformed equations to obtain the impact responses. The acoustic black hole reduces nonlinear impact responses. The linear and third-order nonlinear spring stiffnesses also affect higher harmonics, fractional components, modal coupling, and peak clustering. This suggests that discrete nonlinear corner supports affect the vibration mitigation performance of acoustic black hole plates.