Analytical solution for forced vibration response of rectangular thin plates attached by straight and curved acoustic black hole beams based on symplectic and impedance method

Abstract

In recent years, due to the excellent vibration reduction performance of the acoustic black hole (ABH), its application in engineering has become increasingly widespread. This paper proposes an analytical method which combines the symplectic method with the impedance method, for solving the forced response of the rectangular thin plates attached by the straight and curved ABH beams. The ABH beams and plate are connected by a short bar. Firstly, the impedance method is used to obtain the dynamic stiffness of the coupling end of the ABH beam. Secondly, the symplectic method is used to obtain analytical waves of the plates. By utilizing the relationship between force and displacement at plate-beam junction, the dynamic stiffness of the plate at the coupling point can be obtained. Finally, based on wave propagation analysis, the forced vibration response of the hybrid system are obtained. The numerical examples compared the calculation results of this method with the finite element method. The results show that the proposed method can effectively predict the forced response of the hybrid system considered in this paper. Then, the influence of the relative position between the coupling point and the excitation point on the vibration reduction effect was analyzed. This method is analytical, with accurate results and high computational efficiency.