Abstract
The problem of free harmonic vibrations of an elastic isotropic strip loaded in tension (compression) by uniformly distributed forces of assigned intensity over its transversal cross-section is studied. The deformations of the strip are assumed to be in-plane. In the absence of axial forces, the problem in question coincides with the classical problem of free vibrations of an elastic strip investigated by Rayleigh and Lamb, and for the zero frequency in the case of compression it coincides with the problem of stability of a strip considered by Ishlinsky. A relation between the frequencies of free vibrations and the loading and geometrical parameters is obtained in analytical form. The obtained solution of the problem for a strip is shown to be, at the same time, the exact solution of the same problem for rectangular plates of finite dimensions for boundary conditions generated by the invariability relative to displacements. The results of the asymptotic analysis of the solution of the problem are presented. Key words: free vibrations, stability, prestressed state.
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