由弹性圆板封闭的容器中理想液体的均匀旋转的小振荡

IF 0.7 Q4 MECHANICS
H. Essaouini, B. El, P. Capodanno
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引用次数: 0

摘要

摘要Kopachevskii和Krein在完全刚性容器[3]的情况下,研究了均匀旋转容器中理想液体的小振荡问题。我们在这里提出,通过考虑由弹性圆板封闭的容器的情况下,这个模型的推广。在这种情况下,导出了系统的线性化运动方程。利用泛函分析得到耦合系统在平衡位置附近的小振幅振动的变分方程,并在合适的Hilbert空间中给出了两个操作方程。我们证明了系统的谱是实数的,由一个可计数的特征值集合和一个填充区间的基本连续谱组成。最后利用半群理论证明了关联进化问题解的存在唯一性定理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Small oscillations of an ideal liquid contained in a vessel closed by an elastic circular plate, in uniform rotation
Abstract. The problem of the small oscillations of an ideal liquid contained in a vessel in uniform rotation has been studied by Kopachevskii and Krein in the case of an entirely rigid vessel [3]. We propose here, a generalization of this model by considering the case of a vessel closed by an elastic circular plate. In this context, the linearized equations of motion of the system plateliquid are derived. Functional analysis is used to obtain a variational equation of the small amplitude vibrations of the coupled system around its equilibrium position, and then two operatorial equations in a suitable Hilbert space are presented and analyzed. We show that the spectrum of the system is real and consists of a countable set of eigenvalues and an essential continuous spectrum filling an interval. Finally the existence and uniqueness theorem for the solution of the associated evolution problem is proved by means the semigroups theory.
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
4
审稿时长
32 weeks
期刊介绍: Theoretical and Applied Mechanics (TAM) invites submission of original scholarly work in all fields of theoretical and applied mechanics. TAM features selected high quality research articles that represent the broad spectrum of interest in mechanics.
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