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 r...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2021-12, Vol.42 (15), p.3637-3644
Main Authors: Hasanov, A., Djuraev, N.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Asymptotic properties
Cantilever beams
Exact solutions
Geometry
Hypergeometric functions
Hysteresis
Mathematical analysis
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Partial differential equations
Probability Theory and Stochastic Processes
Resonant frequencies
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Summary: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.
ISSN:1995-0802
1818-9962
DOI:10.1134/S199508022203009X