Modal Energy Division in Semi-Infinite Plates

Abstract

The stress and displacements within a semi-infinite elastic plate resulting from a time-varying (sinusoidal) edge loading are determined in terms of the modes of the infinite plate. A uniform normal stress with zero shear stress was supplied at the edge. The coefficients in the expansion are determined by a method given previously [J. Acoust. Soc. Am. 41, 346–353 (1967)]. Frequencies up to the frequency where five propagating modes are present are considered and the fraction of the supplied energy going into each of the modes determined. In the frequency range considered, the dominant mode changes from the first to the second and then to the third. A method for predicting the dominant mode requiring only a knowledge of the real roots of the Rayleigh-Lamb equation is suggested.