Dynamic response of an elastic plate containing periodic masses

This paper develops an analytical model that incorporates an infinite number of periodically spaced discrete masses into the equations of elasticity of a two-dimensional solid that is excited by a harmonic force in both time and space. Two specific problems are addressed. The first is that of a plate with the masses on the bottom edge, and the second is that of a plate with the masses embedded in the medium. The equations of elasticity are written as stress field expressions with the appropriate boundary conditions in the spatial-frequency domain. An infinite number of indexed equations are generated using an orthogonalization procedure. Once this is accomplished, all the indexed equations of the system are written together in a single matrix equation. The problem is then solved using a truncated set of terms and the displacement fields are transferred into the wavenumber–frequency domain for analysis. These results are compared to previously available low frequency model results for solutions involving the flexural wave in the plate. A numerical example is then solved at high frequency that includes higher-order wave motion, and this example is discussed.