Vibration and Acoustics Research Journal (VARJ)

Research Article

Vibration of Cantilevered Rectangular Plates with Circular Ends- A Study in Mode Shapes

C.Y. Wang

Departments of Mathematics and Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA.

Submitted: April 16, 2020; Accepted: December 11, 2020

Abstract

The vibrations of rectangular plates with circular ends, including the completely free stadium- shaped plate, the long cantilever plate and the wide cantilever plate are studied for the first time. Accurate archival frequencies and mode shapes are obtained by the Ritz method. In comparison to rectangular plates with the same area, the rounded rectangular plate has less boundary length and structurally stronger, while the frequencies change little. The vibration shapes show distinct flapping modes and twisting modes.

Keywords

Plate; Vibration; Free; Cantilever; Frequency; Mode .

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