Analytical solutions for forced vibration and dispersion property of periodic multilayer elastically connected plate structures

An analytical approach is developed based on the wave propagation theory for the forced vibration and dispersion analysis of a system of periodic multilayer elastically connected plates. On the one hand, the proposed approach makes up for the traditional analytical methods that cannot consider the mass of the connection junction between two adjacent plates, on the other hand, it fills the gap in the analytical method for the vibration and dispersion analysis of periodic multilayer elastically connected plate structures. First, the coupled vibration equations of the multilayer plates considering the mass of the connection junction are established and decoupled; and a general vibration state is introduced and transferred into the dual system. Next, the general vibration state is described in terms of analytical waves. By considering the periodic condition and compatibility condition on the discontinuous boundaries of the unit cell, an eigenvalue equation for dispersion analysis is formed. Finally, by using the boundary conditions and wave scattering relationships, the forced responses of the periodic multilayer elastically connected plate system are analytically calculated. In the numerical examples, the forced vibration and dispersion properties of a double-plate system are investigated. The effectiveness of the proposed method is validated by comparing the present results with the finite element method (FEM) results. The accuracy of the FEM model is verified by experimental tests on a specimen prepared by additive manufacturing. The numerical results show that the mass of the connection junction cannot be ignored when performing the vibration analysis of a multilayer plate system. In addition, the periodic multilayer plate structure has rich dispersion characteristics and is a good candidate for band gap design.