Flexural Vibrations of Rectangular and Other Polygonal Plates

by Yau-Kai Cheung, Prof. of Civ. Engrg.; Univ. of Calgary, Calgary, Alberta, Canada,
M. S. Cheung, Grad. Student; Dept. of Civ. Engrg., Univ. of Calgary, Calgary, Alberta, Canada,

Serial Information: Journal of the Engineering Mechanics Division, 1971, Vol. 97, Issue 2, Pg. 391-411

Document Type: Journal Paper


The finite strip method is used for the flexural vibration analysis of elastic plates. The plates can be isotropic or orthotropic in property, of constant or variable thickness, and with distributed or concentrated masses. It can have any combination of free, simply-supported and clamped boundary conditions and can also be continuous in one direction. The stiffness matrix of a strip with two opposite ends simply-supported, free or clamped is formed by assuming suitable basic function series in the longitudinal direction which satisfies the end conditions and a simple cubic polynomial in the transverse direction. A consistent mass matrix can also be formed for each strip. The stiffness and mass matrices of all the strips making up a plate are then assembled to form an eigenvalue matrix in the same way as for a beam problem. The method is simple but versatile, and all the natural frequencies and corresponding modal shapes can be obtained rapidly from an intermediate or even small size electronic digital computer.

Subject Headings: Matrix (mathematics) | Flexural strength | Vibration | Plates | Finite strip method | Elastic analysis | Stiffening | Isotropy

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