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Technical Briefs

Fundamental Frequencies of Rounded Polygonal Membranes—A Class of Homotopy Shapes

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

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

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 4, 2011; final manuscript received April 2, 2012; published online February 4, 2013. Assoc. Editor: Massimo Ruzzene.

J. Vib. Acoust 135(1), 014501 (Feb 04, 2013) (4 pages) Paper No: VIB-11-1269; doi: 10.1115/1.4007259 History: Received November 04, 2011; Revised April 02, 2012

Rounding of sharp corners of a membrane (or waveguide) is unavoidable in practice. The natural vibration frequencies of polygonal membranes with rounded vertices are studied by introducing a new family of homotopy shapes and using an efficient improved Ritz method.

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Copyright © 2013 by ASME
Topics: Membranes , Shapes
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Figures

Grahic Jump Location
Fig. 1

(a) Rounded triangular membranes. From outside, α = 0, 0.01, 0.05, 0.2, 0.5, 1. (b) Rounded square membranes. From outside, α = 0, 0.01, 0.05, 0.15, 0.3, 0.6, 1. (c) Rounded pentagonal membranes. From outside, α = 0, 0.05, 0.2, 0.5, 1. (d) Rounded hexagonal membranes. From outside, α = 0, 0.05, 0.2, 1.

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