Variational principles for a double Rayleigh beam system undergoing vibrations and connected by a nonlinear Winkler–Pasternak elastic layer

IF 2.4 Q2 ENGINEERING, MECHANICAL
S. Adali
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引用次数: 0

Abstract

Abstract Variational principles and variationally consistent boundary conditions are derived for a system of double Rayleigh beams undergoing vibrations and subject to axial loads. The elastic layer connecting the beams are modelled as a three-parameter nonlinear Winkler–Pasternak layer with the Winkler layer having linear and nonlinear components and Pasternak layer having only a linear component. Variational principles are derived for the forced and freely vibrating double beam system using a semi-inverse approach. Hamilton’s principle for the system is given and the Rayleigh quotients are derived for the vibration frequency of the freely vibrating system and for the buckling load. Natural and geometric variationally consistent boundary conditions are derived which leads to a set of coupled boundary conditions due to the presence of Pasternak layer connecting the beams.
非线性温克勒-帕斯捷尔纳克弹性层连接的振动双瑞利梁系统的变分原理
摘要推导了双瑞利梁受轴向载荷振动系统的变分原理和变分一致边界条件。将连接梁的弹性层建模为三参数非线性温克勒-帕斯捷尔纳克层,其中温克勒层具有线性和非线性分量,而帕斯捷尔纳克层仅具有线性分量。采用半逆方法推导了受迫和自由振动双梁系统的变分原理。给出了系统的Hamilton原理,推导了自由振动系统的振动频率和屈曲载荷的瑞利商。导出了自然变分一致和几何变分一致的边界条件,由于存在连接梁的帕斯捷尔纳克层而导致了一组耦合的边界条件。
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来源期刊
CiteScore
6.20
自引率
3.60%
发文量
49
审稿时长
44 weeks
期刊介绍: The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.
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