Abstract
A suitably chosen deflection function is used to analyze the free vibration of rotationally restrained infinite periodic beams on transversely rigid supports by the wave approach. The assumed complex modes of wave motion which satisfy the wave boundary conditions are used in a Galerkin type of analysis to predict the vibration frequencies in any desired pair of adjacent propagation bands for a wide range of rotational constraint parameter. Since the function satisfies the geometric and force boundary conditions of the beam, it yields better results than those that can be obtained by using functions satisfying only the geometric boundary conditions. The function can be used to formulate deflection functions for plates for analyzing two-dimensional wave propagation in periodic plates, rotationally restrained at the transversely rigid supports.
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