Abstract
We consider self-excited vibrations of strongly nonlinear mechanical systems obeying the hereditary theory of viscoelasticity. using the Bubnov-Galerkin method, the problem is reduced to a system of ordinary nonlinear integrodifferential equations. The normal modes of vibration of nonlinear conservative elastic systems are chosen as the unperturbed solutions. Self-vibrating solutions are found by iteration to any degree of accuracy. The process converges for certain restrictions on the unperturbed functions and on the small parameter of the problem.
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