Technical Brief

Vibrations of Completely Free Rounded Rectangular Plates

[+] Author and Article Information
C. Y. Wang

Departments of Mathematics and
Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: cywang@mth.msu.edu

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 12, 2013; final manuscript received November 13, 2014; published online January 20, 2015. Assoc. Editor: Olivier A. Bauchau.

J. Vib. Acoust 137(2), 024502 (Apr 01, 2015) (5 pages) Paper No: VIB-13-1049; doi: 10.1115/1.4029159 History: Received February 12, 2013; Revised November 13, 2014; Online January 20, 2015

The natural vibration of rectangular plates with rounded corners is studied by using a family of homotopy shapes and an efficient Ritz method.

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Grahic Jump Location
Fig. 1

The rounded rectangular plate. The width is 2L and the height is 2bL. From outside: α = 0, 0.01, 0.05, 0.15, 0.3, 0.6, and 1.

Grahic Jump Location
Fig. 2

First five mode shapes for b = 0.7. Lowest (fundamental) modes are on top. From left: ellipse (α = 1), rounded rectangle (α = 0.15), and rectangle (α = 0). Note the switching of modes.



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