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Technical Brief

Design Aspects of Nonlinear Vibration Analysis of Rectangular Orthotropic Membranes

[+] Author and Article Information
Robert Wetherhold

Professor
Department of Mechanical and Aerospace Engineering,
University at Buffalo, SUNY,
Buffalo, NY 14260-4400
e-mail: mecrcw@buffalo.edu

Punit S. Padliya

Department of Mechanical and Aerospace Engineering,
University at Buffalo, SUNY,
Buffalo, NY 14260-4400

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 28, 2013; final manuscript received January 31, 2014; published online April 15, 2014. Assoc. Editor: Philip Bayly.

J. Vib. Acoust 136(3), 034506 (Apr 15, 2014) (4 pages) Paper No: VIB-13-1031; doi: 10.1115/1.4027148 History: Received January 28, 2013; Revised January 31, 2014

The natural frequencies of a specially orthotropic rectangular membrane are examined with respect to its design parameters. A method is presented for inferring the initial tensions from measured vibration frequencies and the sensitivity of the tensions with respect to imprecision in the measured frequencies is demonstrated. A sensitivity analysis is used to define the key design parameters, where relatively small changes in those parameters lead to large changes in the natural frequency. This analysis is useful in two senses: It permits the design to be rapidly changed in an efficient manner, and it indicates the physical parameters that must be closely controlled in order to achieve the desired frequency. The results of the theoretical analysis were compared with a finite element simulation using Abaqus for validation. The comparison showed that results were in close agreement up to an initial displacement magnitude-to-membrane thickness ratio (T0/h) value of about 25 for the given values of design parameters. This shows the limit of applicability of the analytical solution since the finite element (FE) simulation is fully updated at each time step with precision not available from the analytical solution.

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Figures

Grahic Jump Location
Fig. 1

The effect of magnitude of the initial displacement T0 on the natural frequency of a rectangular membrane

Grahic Jump Location
Fig. 2

Displacement of the membrane center point, plotted versus time, in response to an initial displacement field consisting of the (1,1) mode with amplitudes T0/h = 1, 25, and 50

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