Scholarlink

<p>This paper proposes a discrete physical model (DPM) for the transverse free vibrations of non-uniform bi-directional functionally graded (2D-FGM) beams. The material properties vary in both the axial and thickness directions according to exponential laws, and the beam rest on a spatially variable elastic foundation and satisfy general support conditions. In the proposed formulation, the continuous beam is replaced by a multi-degree-of-freedom chain of lumped masses connected by bars and linear rotational and vertical springs. An adaptive discretization strategy is employed to construct consistent mass, stiffness, and foundation matrices. By applying Hamilton’s principle, the governing equations are reduced to an algebraic eigenvalue problem, from which nondimensional natural frequencies and associated mode shapes are obtained. Comparison with published results confirms the accuracy and reliability of the DPM. Owing to its simplicity and low computational cost, the model is well suited for extensive parametric studies and design-oriented analyses, including frequency tuning through geometric parameters, the material gradation exponents <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((n_x, n_y)\)</EquationSource> </InlineEquation>, the taper ratio <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\gamma\)</EquationSource> </InlineEquation>, and foundation characteristics (position <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\chi\)</EquationSource> </InlineEquation>, intensity <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\eta\)</EquationSource> </InlineEquation>) under various boundary conditions. The proposed approach provides a practical and efficient tool for analyzing and optimizing complex FGM beam structures.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A discrete model for analyzing the free vibrations of a non-uniform 2D-FGM beam under elastic foundations and different support conditions

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年12月23日

查看全文
  • Anass Moukhliss,
  • Abdellatif Rahmouni,
  • Rhali Benamar

摘要

This paper proposes a discrete physical model (DPM) for the transverse free vibrations of non-uniform bi-directional functionally graded (2D-FGM) beams. The material properties vary in both the axial and thickness directions according to exponential laws, and the beam rest on a spatially variable elastic foundation and satisfy general support conditions. In the proposed formulation, the continuous beam is replaced by a multi-degree-of-freedom chain of lumped masses connected by bars and linear rotational and vertical springs. An adaptive discretization strategy is employed to construct consistent mass, stiffness, and foundation matrices. By applying Hamilton’s principle, the governing equations are reduced to an algebraic eigenvalue problem, from which nondimensional natural frequencies and associated mode shapes are obtained. Comparison with published results confirms the accuracy and reliability of the DPM. Owing to its simplicity and low computational cost, the model is well suited for extensive parametric studies and design-oriented analyses, including frequency tuning through geometric parameters, the material gradation exponents \((n_x, n_y)\) , the taper ratio \(\gamma\) , and foundation characteristics (position \(\chi\) , intensity \(\eta\) ) under various boundary conditions. The proposed approach provides a practical and efficient tool for analyzing and optimizing complex FGM beam structures.