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Research Papers

Buckling and Vibration of Circular Auxetic Plates

[+] Author and Article Information
Teik-Cheng Lim

School of Science and Technology,
SIM University,
461 Clementi Road,
S599491, Singapore
e-mail: alan_tc_lim@yahoo.com

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received December 18, 2013; final manuscript received January 27, 2014; published online February 19, 2014. Assoc. Editor: Irene Beyerlein.

J. Eng. Mater. Technol 136(2), 021007 (Feb 19, 2014) (6 pages) Paper No: MATS-13-1235; doi: 10.1115/1.4026617 History: Received December 18, 2013; Revised January 27, 2014

This paper evaluates the elastic stability and vibration characteristics of circular plates made from auxetic materials. By solving the general solutions for buckling and vibration of circular plates under various boundary conditions, the critical buckling load factors and fundamental frequencies of circular plates, within the scope of the first axisymmetric modes, were obtained for the entire range of Poisson's ratio for isotropic solids, i.e., from −1 to 0.5. Results for elastic stability reveal that as the Poisson's ratio of the plate becomes more negative, the critical bucking load gradually reduces. In the case of vibration, the decrease in Poisson's ratio not only decreases the fundamental frequency, but the decrease becomes very rapid as the Poisson's ratio approaches its lower limit. For both buckling and vibration, the plate's Poisson's ratio has no effect if the edge is fully clamped. The results obtained herein suggest that auxetic materials can be employed for attaining static and dynamic properties which are not common in plates made from conventional materials. Based on the exact results, empirical models were generated for design purposes so that both the critical buckling load factors and the frequency parameters can be conveniently obtained without calculating the Bessel functions.

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Figures

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Fig. 1

Schematics for buckling of a circular plate: (a) top and side views and (b) boundary conditions

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Fig. 2

A family of critical buckling load factor plotted against the Poisson's ratio of circular plates for various rotational restraints

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Fig. 3

Critical buckling load factor versus Poisson's ratio of circular plates for various rotational restraints: exact solution (circles) and empirical model (curves)

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Fig. 4

Plots of λ2 versus Poisson's ratio of circular plates for clamped edge (C), free edge (F), and SS edge

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Fig. 5

Comparison between exact (circles) and empirical (curves) results of λ2 versus Poisson's ratio of simply supported and free circular plates

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