用Galerkin方法研究Winkler-Pasternak环境下复合材料网格结构的固有频率

IF 1.5 4区工程技术 Q2 MATHEMATICS, APPLIED Advances in Applied Mathematics and Mechanics Pub Date : 2023-09-01 DOI:10.4208/aamm.oa-2021-0148

Ehsaneh Mohammadpour Hamedani and Amir H. Hashemian

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引用次数: 0

摘要

本文给出了夹边Winkler–Pasternak弹性地基包围的复合材料格构圆柱壳自由振动问题的解析表达式和求解方法。使用大量具有可变刚度的线性、均匀剪切和径向弹簧对基础进行模拟。根据Winkler–Pasternak项在傅立叶分解和Galerkin方法的基础上实现的壳体运动方程，导出了计算网格结构及其基础固有频率的积分公式。考虑基础单元和格构参数的基频公式是早期设计阶段估计频率的有效手段，也是在设计分析和数值求解中评估弹性基础包围的复合材料格构圆柱壳振动分析的工具。使用有限元分析对结果进行了验证和确认，结果非常一致。

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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Natural Frequencies of Composite Lattice Structure Surrounded by Winkler--Pasternak Ambient using Galerkin Method

. The present work contains an analytical expression and solution for free vibration problem of a composite lattice cylindrical shell surrounded by Winkler– Pasternak elastic foundation with clamped edges. The foundation is simulated using a large number of linear, homogenous shear and radial springs with variable stiffness. An integrated formula for calculation of the natural frequency of lattice structure and its foundation is derived from the equations of motion of the shell implemented by Winkler–Pasternak terms based on Fourier decomposition and Galerkin method. The fundamental frequency formula concerning the foundation elements and lattice parameters is an effective means of estimation frequency in earlier design phase and also a tool to assess the vibration analysis of composite lattice cylindrical shell surrounded by an elastic foundation in design analysis and numerical solutions. The results are veriﬁed and conﬁrmed using ﬁnite element analysis which show a very good agreement.

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来源期刊

Advances in Applied Mathematics and Mechanics MATHEMATICS, APPLIED-MECHANICS

CiteScore

2.60

自引率

7.10%

发文量

审稿时长

6 months

期刊介绍： Advances in Applied Mathematics and Mechanics (AAMM) provides a fast communication platform among researchers using mathematics as a tool for solving problems in mechanics and engineering, with particular emphasis in the integration of theory and applications. To cover as wide audiences as possible, abstract or axiomatic mathematics is not encouraged. Innovative numerical analysis, numerical methods, and interdisciplinary applications are particularly welcome.