Exact Solutions of the Thin Beam with Degrading Hysteresis Behavior

In the article, a fourth-order partial differential equation for vibration of a homogeneous thin cantilever beam is considered as an oscillating system with deteriorating hysteresis behavior. Exact solutions of this equation are obtained in the form of a hypergeometric function, which describe the rigidity of the material and the first natural frequency. Some properties of the generalized hypergeometric function are proved and, in particular cases, the exact solutions of this equation in terms of generalized hypergeometric functions are determined. The asymptotic behavior of some exact solutions are studied.

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