Novel results in vibration analysis of nonlinear laminated composite beams (LCBs)

IF 2.2 3区工程技术 Q2 MECHANICS

Archive of Applied Mechanics Pub Date : 2024-07-22 DOI:10.1007/s00419-024-02650-1

M. Bayat, Mas. Bayat, L. Cveticanin

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Abstract

This study investigates vibrations of the laminated composite beam (LCB) subjected to axial load and settled on Winkler–Pasternak elastic foundation. The beam model is of Euler–Bernoulli type with cubic order nonlinear elastic load. Two different boundary conditions are considered: (i) Simply Supported (S–S) and (ii) Clamped–Clamped (C–C) ones. Mathematical model of the asymmetric LCB is a partial differential equation. Applying Galerkin procedure, the model is converted into a strong nonlinear ordinary equation. In the paper, the new analytical method, dubbed as the Max–Min Approach (MMA), is adopted to provide more accurate nonlinear analysis of beams. The analytical solution is inferred to investigate the effects of axial force and essential elasticity parameters of foundation on the nonlinear response of the beams. Analytical results are compared with numerical solutions and show good agreement. In addition, the results are compared with previously published ones. It is concluded that MMA used in LCB gives more accurate results than the previously used analytic methods and is practical applicable. The method can be easily extended to high nonlinear vibration problems in LCB under different boundary conditions.

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非线性层状复合梁（LCB）振动分析的新成果

本研究探讨了承受轴向载荷并安放在温克勒-帕斯捷尔纳克弹性地基上的层状复合梁（LCB）的振动。梁模型为欧拉-伯努利类型，具有立方阶非线性弹性载荷。考虑了两种不同的边界条件：(i) 简单支撑 (S-S) 和 (ii) 夹紧-夹紧 (C-C)。非对称 LCB 的数学模型是一个偏微分方程。应用 Galerkin 程序，该模型被转换为强非线性普通方程。本文采用新的分析方法，即 Max-Min 方法 (MMA)，对梁进行更精确的非线性分析。通过推导分析解，研究了轴向力和地基基本弹性参数对梁非线性响应的影响。分析结果与数值解进行了比较，结果显示两者吻合良好。此外，还将结果与之前公布的结果进行了比较。结论是，LCB 中使用的 MMA 比以前使用的分析方法得出的结果更准确，而且实用。该方法可以很容易地扩展到 LCB 中不同边界条件下的高非线性振动问题。

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

Archive of Applied Mechanics 物理-力学

CiteScore

4.40

自引率

10.70%

发文量

234

审稿时长

4-8 weeks

期刊介绍： Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.