Nonlinear Vibrations of Beams, Strings, Plates, and Membranes Without Initial Tension

[+] Author and Article Information
Zhongping Bao, Subrata Mukherjee

Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853

Max Roman, Nadine Aubry

Department of Mechanical Engineering, New Jersey Institute of Technology, Newark, NJ 07102

J. Appl. Mech 71(4), 551-559 (Sep 07, 2004) (9 pages) doi:10.1115/1.1767167 History: Received August 12, 2003; Revised January 21, 2004; Online September 07, 2004
Copyright © 2004 by ASME
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Grahic Jump Location
A suspended nanotube between two electrical contacts. (a) Schematic (b) SEM image.
Grahic Jump Location
Vibration of a clamped-clamped beam—fundamental mode. (a) Master curve—FEM 50 elements; xx Eq. (5) with α=0.04406; (b) SWNT: Eq. (5) with α=0.04406,E=705 GPa,ρ=1330 Kg/m3,L=600 nm,do=2 nm,h=0.335 nm.
Grahic Jump Location
Vibration of a square plate clamped on all sides—fundamental mode. (a) Master curve—FEM 8×8 elements, ν=0.22; xx Eq. (44) with α0=0.3670; (b) MEMS plate: Eq. (44) with α0=0.3670,E=169 GPa,ν=0.22,ρ=2300 Kg/m3,L=3 mm,h=2 μm.



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