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

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-15 DOI:10.1134/s0001434624050158

I. A. Rudakov

引用次数: 0

Abstract

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.

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带弹性固定端梁的欧拉-伯努利准线性振动方程的周期解

摘要我们考虑了沿水平轴受拉梁的准线性欧拉-伯努利振动方程的时间周期解问题。边界条件分别对应于弹性固定端、夹紧端和铰链端。非线性项在无穷远处满足非共振条件。利用 Schauder 原理，我们证明了周期解的存在性和唯一性定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.