Periodic Solutions of the Euler–Bernoulli Quasilinear Vibration Equation for a Beam with an Elastically Fixed End

We consider the problem about time-periodic solutions of the quasilinear Euler–Bernoulli vibration equation for a beam subjected to tension along the horizontal axis. The boundary conditions correspond to the cases of elastically fixed, clamped, and hinged ends. The nonlinear term satisfies the nonr...

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Bibliographic Details
Published in:Mathematical Notes 2024-06, Vol.115 (5-6), p.800-808
Main Author: Rudakov, I. A.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Boundary conditions
Existence theorems
Mathematics
Mathematics and Statistics
Nonresonance
Uniqueness theorems
Vibration
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Summary:We consider the problem about time-periodic solutions of the quasilinear Euler–Bernoulli vibration equation for a beam subjected to tension along the horizontal axis. The boundary conditions correspond to the cases of elastically fixed, clamped, and hinged ends. The nonlinear term satisfies the nonresonance condition at infinity. Using the Schauder principle, we prove a theorem on the existence and uniqueness of a periodic solution.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434624050158