Accurate Vibration Analysis of Simply Supported Rhombic Plates by Considering Stress Singularities

[+] Author and Article Information
C. S. Huang

National Center of Research in Earthquake Engineering (NCREE), Taipei, Taiwan ROC

O. G. McGee, J. W. Kim

School of Civil Engineering, Georgia Institute of Technology, Atlanta, GA

A. W. Leissa

Department of Engineering Mechanics, The Ohio State University, Columbus, Ohio

J. Vib. Acoust 117(3A), 245-251 (Jul 01, 1995) (7 pages) doi:10.1115/1.2874440 History: Received September 01, 1992; Revised September 01, 1993; Online February 26, 2008


This is the first known work which explicitly considers the bending stress singularities that occur in the two opposite, obtuse corner angles of simply supported rhombic plates undergoing free, transverse vibration. The importance of these singularities increases as the rhombic plate becomes highly skewed (i.e., the obtuse angles increase). The analysis is carried out by the Ritz method using a hybrid set consisting of two types of displacement functions, e.g., (1) algebraic polynomials and (2) corner functions accounting for the singularities in the obtuse corners. It is shown that the corner functions accelerate the convergence of solution, and that these functions are required if accurate solutions are to be obtained for highly skewed plates. Accurate nondimensional frequencies and normalized contours of the vibratory transverse displacement are presented for simply supported rhombic plates with skew angles ranging to 75 deg. (i.e., obtuse angles of 165 deg.). Frequency and mode shapes of isosceles and right triangular plates with all edges simply supported are also available from the data presented.

Copyright © 1995 by The American Society of Mechanical Engineers
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