FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD

• Published in: Applied mathematics and mechanics Vol. 27; no. 4; pp. 461 - 467
• Main Author: 黄炎 雷勇军 申慧君
• Format: Journal Article
• Language: English
• Published: College of Aerospace and Material Engineering, National University of Defense Technology,Changsha 410073, P. R. China 01-04-2006
• Subjects: Algebra; Anisotropy; Boundary conditions; Corners; Free vibration; Mathematical analysis; Rectangular plates; Vibration mode; 一般分析方法; 各向异性板; 自由振动; mode shape; anisotropic plate; free vibration; general analytical method; frequency
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-006-0405-y

According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed.