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.
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July 1995
Research Papers
Accurate Vibration Analysis of Simply Supported Rhombic Plates by Considering Stress Singularities
C. S. Huang,
C. S. Huang
National Center of Research in Earthquake Engineering (NCREE), Taipei, Taiwan ROC
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O. G. McGee,
O. G. McGee
School of Civil Engineering, Georgia Institute of Technology, Atlanta, GA
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A. W. Leissa,
A. W. Leissa
Department of Engineering Mechanics, The Ohio State University, Columbus, Ohio
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J. W. Kim
J. W. Kim
School of Civil Engineering, Georgia Institute of Technology, Atlanta, GA
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C. S. Huang
National Center of Research in Earthquake Engineering (NCREE), Taipei, Taiwan ROC
O. G. McGee
School of Civil Engineering, Georgia Institute of Technology, Atlanta, GA
A. W. Leissa
Department of Engineering Mechanics, The Ohio State University, Columbus, Ohio
J. W. Kim
School of Civil Engineering, Georgia Institute of Technology, Atlanta, GA
J. Vib. Acoust. Jul 1995, 117(3A): 245-251 (7 pages)
Published Online: July 1, 1995
Article history
Received:
September 1, 1992
Revised:
September 1, 1993
Online:
February 26, 2008
Connected Content
A companion article has been published:
Experimental Study on Seismic Responses of Piping Systems With
Friction—Part 2: Simplified Analysis Method on the Effect of
Friction
Citation
Huang, C. S., McGee, O. G., Leissa, A. W., and Kim, J. W. (July 1, 1995). "Accurate Vibration Analysis of Simply Supported Rhombic Plates by Considering Stress Singularities." ASME. J. Vib. Acoust. July 1995; 117(3A): 245–251. https://doi.org/10.1115/1.2874440
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