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Purpose <p>Due to the diversity of the application in various fields such as aerospace and transportation engineering, functionally graded (FG) materials have attracted increasing research interest during the past few decades. As is well known, FG materials show several advantages in elevated temperature conditions, and mechanical properties in the thickness direction may vary continuously. Hence they can be used to improve structural vibration responses. Based on the classical plate theory and the improved Fourier series method, the free vibration characteristics of FG rectangular thin plates subjected to different boundary conditions are investigated in the present study.</p> Methods <p>Each boundary of the FG rectangular thin plate is assumed to be uniformly connected by transverse and rotational restraint springs, and the purpose of such an innovative model assumption is to efficiently simulate different boundary conditions by manually setting the spring stiffness. Accordingly, the free vibration is analyzed and solved by establishing an eigenvalue problem in combination with the minimum energy principle and the improved Fourier series method.</p> Results <p>The convergence of the proposed mathematical model and the accuracy of results are validated through some comparative examples. Parametric studies are also carried out and effects of different parameters on the vibration behavior of FG plates are analyzed and discussed in detail.</p>

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A Fast Solution Technique for the Free Vibration of FG Thin Plates with Spring Based Arbitrary Boundary Constraints

  • 期刊论文

  • 发表日期：

    2025年8月8日

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  • Siyuan Bao,
  • Junwei Li,
  • Hang Yin,
  • Feng Shen,
  • Cheng Li

摘要

Purpose

Due to the diversity of the application in various fields such as aerospace and transportation engineering, functionally graded (FG) materials have attracted increasing research interest during the past few decades. As is well known, FG materials show several advantages in elevated temperature conditions, and mechanical properties in the thickness direction may vary continuously. Hence they can be used to improve structural vibration responses. Based on the classical plate theory and the improved Fourier series method, the free vibration characteristics of FG rectangular thin plates subjected to different boundary conditions are investigated in the present study.

Methods

Each boundary of the FG rectangular thin plate is assumed to be uniformly connected by transverse and rotational restraint springs, and the purpose of such an innovative model assumption is to efficiently simulate different boundary conditions by manually setting the spring stiffness. Accordingly, the free vibration is analyzed and solved by establishing an eigenvalue problem in combination with the minimum energy principle and the improved Fourier series method.

Results

The convergence of the proposed mathematical model and the accuracy of results are validated through some comparative examples. Parametric studies are also carried out and effects of different parameters on the vibration behavior of FG plates are analyzed and discussed in detail.