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Research Articles

Surface Stress Effect on the Vibrational Response of Circular Nanoplates With Various Edge Supports

[+] Author and Article Information
S. Sahmani

Department of Mechanical Engineering,
University of Guilan,
P.O. Box 3756,
Rasht, Iran

1Corresponding author: r_ansari@guilan.ac.ir

Manuscript received April 5, 2012; final manuscript received July 23, 2012; accepted manuscript posted July 27, 2012; published online January 25, 2013. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 80(2), 021021 (Jan 25, 2013) (7 pages) Paper No: JAM-12-1138; doi: 10.1115/1.4007255 History: Received April 05, 2012; Revised July 23, 2012; Accepted July 27, 2012

The classical continuum theory cannot be directly used to describe the behavior of nanostructures because of their size-dependent attribute. Surface stress effect is one of the most important size dependencies of structures at this submicron size, which is due to the high surface to volume ratio of nanoscale domain. In the present study, the nonclassical governing differential equation together with corresponding boundary conditions are derived using Hamilton's principle, into which the surface energies are incorporated through the Gurtin-Murdoch elasticity theory. The model developed herein contains intrinsic length scales to take the size effect into account and is used to analyze the free vibration response of circular nanoplates including surface stress effect. The generalized differential quadrature (GDQ) method is employed to discretize the governing size-dependent differential equation along with simply supported and clamped boundary conditions. The classical and nonclassical frequencies of circular nanoplates with various edge supports and thicknesses are calculated and are compared to each other. It is found that the influence of surface stress can be different for various circumferential mode numbers, boundary conditions, plate thicknesses, and surface elastic constants.

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References

Figures

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Fig. 1

Schematic of a circular nanoplate with upper and lower thin skin layers carrying surface effects: Kinematic parameters, coordinate system, and geometry

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Fig. 2

Variation of frequency ratio with thickness of nanoplates corresponding to various values of radius to thickness ratio (m=0)

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Fig. 3

Variation of frequency ratio with thickness of nanoplates corresponding to various values of radius to thickness ratio (m=1)

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Fig. 4

Variation of frequency ratio with thickness of nanoplates corresponding to various values of radius to thickness ratio (m=2)

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Fig. 5

Variation of frequency ratio with thickness of nanoplates corresponding to various values of radius to thickness ratio (m=3)

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Fig. 6

Variation of frequency ratio with circumferential wave number of nanoplates corresponding to various values of radius to thickness ratio (h=2 nm)

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Fig. 7

Variation of frequency ratio with radius to thickness ratio of nanoplates corresponding to various circumferential wave numbers (h=1 nm)

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Fig. 8

Variation of frequency ratio with thickness of nanoplate corresponding to different values of 2μs+λs with the assumption of τs=ρs=0 and m=2

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Fig. 9

Variation of frequency ratio with thickness of nanoplate corresponding to different values of ρs with the assumption of 2μs+λs=τs=0 and m=2

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Fig. 10

Variation of frequency ratio with thickness of nanoplate corresponding to different values of τs with the assumption of 2μs+λs=ρs=0 and m=2

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