Symplectic space wave propagation method for forced vibration of acoustic black hole assemblies

Recently, acoustic black holes (ABHs) have been widely used for vibration and noise reduction. Compared with a single ABH, multiple ABHs embedded in a structure can achieve better vibration suppression. However, most of the current research focuses on embedding a single ABH. In this study, a symplectic space wave propagation method was proposed for the forced vibration of ABH assemblies. The governing differential equations based on the Euler-Bernoulli beam model of the ABH beam for vibration were first converted into Hamiltonian canonical equations. A symplectic eigenvalue problem was then formed, and the wave propagation parameters and wave shapes were obtained analytically. A Gaussian-discretization scheme was used to discretize the ABH beam, whereas the proposed method was used to evaluate the wave amplitude at each point. Second, a combination of the ABH beams of various forms was considered, in which the ABH beams are coupled directly or through a joint. A semi-analytical solution for the forced vibration of ABH assemblies was established by satisfying the dynamic coupling between the ABH beams and the joint. Because the proposed method utilizes symplectic analytical solutions of wave modes, its computational efficiency and precision are high.