Dynamic Response of an Elastic Plate Containing Periodic Masses
NAVAL UNDERSEA WARFARE CENTER DIV NEWPORT RI
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This report develops an analytical model that incorporates an infinite number of periodically spaced discrete masses into the equations of elasticity of a two-dimensional solid. 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 transformed into stress field expressions with the appropriate boundary conditions in the wave number-frequency domain. These equations are indexed using an integer shift property to obtain expressions of the higher-order dynamics of the system. 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. The model results are compared to previously available low frequency 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 these results are discussed.
- Numerical Mathematics