Semi-analytical solutions for the forced vibration of plate structures terminated by multiple acoustic black hole beams

Based on the symplectic and higher-order WKB theory, a semi-analytical method is developed for the forced vibration of a built-up system comprising rectangular thin plate terminated by multiple acoustic black hole beams. The analytical waves are used to describe the vibration of the plate and ABH beam components. The dynamic flexibility matrix and dynamic stiffness matrix are derived based on the analytical wave expressions for the plate and ABH beam component, respectively. By enforcing the displacement continuity and equilibrium of force at the connection interface, the dynamic coupling between the plate component and the ABH beam component is established. The proposed method can obtain the system balance equation by assembling the component matrix just like the traditional finite element method and has a much less degree of freedom. Numerical examples compare results from the proposed method with those from the finite element method. The comparison illustrates that the proposed method gives good predictions for the forced response of the built-up system considered here. The present approach is of high accuracy and can be used to provide benchmark solutions for other prediction methods.