Steady-state responses and wave propagations in the periodic plate

Expressions that describe the steady-state behavior of a multi-span rib-stiffened rectangular plate and the flexural wave propagation are derived, and lateral disturbances are taken into account. The vibrational behavior of periodic plate systems can be expressed in terms of waves of both propagating and near-field types. A wave incident upon the line discontinuities gives rise to transmitted and reflected waves of both kinds whose amplitudes may be found from the reflection and transmission coefficients. Here, all of the transmitted and reflected waves of given flexural wave incident upon the periodic plate systems at some specified location are found and superposed, and the approach is extended to the case of incident near-field wave. A method is developed for numerical analysis of quasi-one-dimensional periodic flexural systems, and the relation between the wave-field of incident waves and the wave-field of resulting waves on any span can be expressed by use of it. As an example, the application of the results to the analysis of a multi-span rib-stiffened rectangular plate is then demonstrated. The steady-state responses from a given wave injected at a given span are determined.