Abstract
The Kane-Mindlin differential equations appropriate for the study of low and high frequency extensional vibrations in elastic plate strips are solved by means of perturbation techniques. These procedures permit the development of simple expressions that can be used for the rapid calculation of the natural frequencies of vibration as a function of material and geometric parameters. A regular perturbation expansion yields an approximate form of the frequency relationship that is useful in the high frequency range, whereas in the low frequency range a singular perturbation procedure is used since the expansion parameter appears in the coefficient of the highest order derivative in the fundamental differential equation. Approximate formulas and some numerical results are presented for three types of boundary conditions.
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