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Research Papers

Propagation of In-Plane Shear Waves in Magnetically Affected Highly Conductive Nanofilms by Considering Both Surface and Nonlocality Effects

[+] Author and Article Information
Keivan Kiani

Department of Civil Engineering,
K. N. Toosi University of Technology,
Valiasr Avenue,
P.O. Box 15875-4416,
Tehran 19967-15433, Iran
e-mails: k_kiani@kntu.ac.ir;
keivankiani@yahoo.com

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 18, 2014; final manuscript received November 14, 2015; published online March 21, 2016. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 138(3), 031001 (Mar 21, 2016) (9 pages) Paper No: VIB-14-1397; doi: 10.1115/1.4032716 History: Received October 18, 2014; Revised November 14, 2015

To study the size and surface effects on characteristics of in-plane shear waves in magnetically affected nanofilms, a novel model is developed. Using nonlocal and surface continuum theories, the governing equations are established and appropriate boundary conditions are imposed at the bottom and top surfaces of the nanofilm. The dispersion relations associated with symmetric and asymmetric modes are obtained. The effects of the surface energy, small-scale parameter, nanofilm's thickness, and magnetic field strength on dispersion curves are addressed. The limitations of the classical theory of elasticity are discussed. The obtained results show that the phase velocity of the propagated in-plane shear waves magnifies by an increase of the thickness as well as magnetic field strength. However, the phase velocity commonly decreases as the effect of the surface energy or nonlocality increases. Such a fact is more obvious for higher modes of vibration. Generally, the cutoff frequency reaches a lower value as the nanofilm's thickness reduces or the small-scale parameter increases. Additionally, variation of the magnetic field strength has fairly no influence on the cutoff frequency.

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Figures

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Fig. 1

A highly conducting nanofilm in the presence of an in-plane magnetic field acted upon by in-plane shear waves

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Fig. 2

Plots of dispersion curves in a special case: (a) symmetric modes and (b) asymmetric modes ( Liu et al. [39] and (—) present study; H = 0 and e0a = 0)

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Fig. 3

Effect of the small-scale parameter on the dispersion curves: (a) symmetric modes and (b) asymmetric modes ( ) e0a = 0 nm, e0a = 1 nm, ( ) e0a = 1.5 nm, and (– – –) CCT; H¯=0.5 and h = 60 nm)

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Fig. 4

Effect of the magnetic field strength on the dispersion curves: (a) symmetric modes and (b) asymmetric modes ( ) NSCT and H¯=0.2, NSCT and H¯=0.4, NSCT and H¯=0.8, CCT and H¯=0.2, CCT and H¯=0.4, and CCT and H¯=0.8 ; h = 30 nm and e0a = 1 nm)

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Fig. 5

Effect of the nanofilm's thickness on the dispersion curves: (a) symmetric modes and (b) asymmetric modes ((– – –) CCT, h = 30 nm, h = 60 nm, and h = 90 nm; H¯=0.5 and e0a = 1 nm)

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