Journal of Korean Association for Spatial Structures (한국공간구조학회논문집)
- Volume 4 Issue 4 Serial No. 14
- /
- Pages.99-111
- /
- 2004
- /
- 1598-4095(pISSN)
- /
- 2287-7401(eISSN)
Free Vibrations and Buckling of Rectangular Plates with Linearly Varying In-Plane Loading
- Published : 2004.12.15
Abstract
An exact solution procedure is formulated for the free vibration and buckling analysis of rectangular plates having two opposite edges simply supported when these edges are subjected to linearly varying normal stresses. The other two edges may be clamped, simply supported or free, or they may be elastically supported. The transverse displacement (w) is assumed as sinusoidal in the direction of loading (x), and a power series is assumed in the lateral (y) direction (i.e., the method of Frobenius). Applying the boundary conditions yields the eigenvalue problem of finding the roots of a fourth order characteristic determinant. Care must be exercised to obtain adequate convergence for accurate vibration frequencies and buckling loads, as is demonstrated by two convergence tables. Some interesting and useful results for vibration frequencies and buckling loads, and their mode shapes, are presented for a variety of edge conditions and in-plane loadings, especially pure in-plane moments.
Keywords
- Free Vibration;
- Buckling;
- Exact Solution;
- Rectangular Plates;
- Frobenius Method;
- Linearly Varying In-Plane Stress