Abstract
A one-dimensional approximate theory is derived that accounts for the first eight modes of propagation of extensional waves in uniform, isotropic, linear elastic bars of rectangular cross section. The theory provides an optimal quadratic approximation to the lateral spatial dependence of the three-dimensional bar response. Applicable to motions in bars of arbitrary rectangular section, it is possible to predict bar responses that are neither plane stress nor plane strain, but are transitional between the two. The relation of bar to plate theory is established, and an identification of bar and plate modes is proposed. Discussion of dispersion of harmonic waves is limited to bars of square section. Typical spectra are given, and their variation with Poisson's ratio is established.
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