Abstract

This paper contains a discussion of the velocities of propagation of long flexural and extensional waves in a plate or bar in the transition region between the states of generalized plane stress and plane strain; i.e., for arbitrary width-thickness ratios (h/a) of rectangular sections. The investigations are carried out mathematically on the basis of approximate equations of motion. It is found that, for flexural waves, as h/a increases from zero, the velocity remains close to that for generalized plane stress until quite large values of h/a are reached, after which the velocity rises asymptotically toward that for plane strain. For extensional waves the velocity is slightly smaller than that for generalized plane stress for all h/a > 0.

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