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Shafiee, Ali A.,Daneshmand, Farhang,Askari, Ehsan,Mahzoon, Mojtaba Techno-Press 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.50 No.1
A semi-analytical method is developed to consider free vibrations of a functionally graded elastic plate resting on Winkler elastic foundation and in contact with a quiescent fluid. Material properties are assumed to be graded distribution along the thickness direction according to a power-law in terms of the volume fractions of the constituents. The fluid is considered to be incompressible and inviscid. In the analysis, the effect of an in-plane force in the plate due to the weight of the fluid is taken into account. By satisfying the compatibility conditions along the interface of fluid and plate, the fluid-structure interaction is taken into account and natural frequencies and mode shapes of the coupled system are acquired by employing energy methods. The results obtained from the present approach are verified by those from a finite element analysis. Besides, the effects of volume fractions of functionally graded materials, Winkler foundation stiffness and in-plane forces on the dynamic of plate are elucidated.
Hamid M. Sedighi,Farhang Daneshmand 대한기계학회 2014 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.28 No.9
A continuum model is utilized to extract the nonlinear governing equation for Carbon nanotube (CNT) probes near graphite sheets. The van der Waals (vdW) intermolecular force and electrostatic actuation are included in the equation of motion. Static and dynamicpull-in behavior of the system is investigated in this paper. To this end, a new asymptotic procedure is presented to predict the pull-ininstability of electrically actuated CNTs by employing an analytic approach namely He's iteration perturbation method (IPM). The effectsof basic non-dimensional parameters such as initial amplitude, intermolecular force, geometrical parameter and actuation voltage on thepull-in instability as well as the fundamental frequency are studied. The obtained results from numerical simulations by employing threemode assumptions verify the strength of the analytical procedure. The qualitative analysis of the system dynamics shows that the equilibriumpoints of the autonomous system include stable center points and unstable saddle nodes. The phase portraits of the carbon nanotubeactuator exhibit periodic and homoclinic orbits.
Ali A. Shafiee,Farhang Daneshmand,Ehsan Askari,Mojtaba Mahzoon 국제구조공학회 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.50 No.1
A semi-analytical method is developed to consider free vibrations of a functionally graded elastic plate resting on Winkler elastic foundation and in contact with a quiescent fluid. Material properties are assumed to be graded distribution along the thickness direction according to a power-law in terms of the volume fractions of the constituents. The fluid is considered to be incompressible and inviscid. In the analysis, the effect of an in-plane force in the plate due to the weight of the fluid is taken into account. By satisfying the compatibility conditions along the interface of fluid and plate, the fluid-structure interaction is taken into account and natural frequencies and mode shapes of the coupled system are acquired by employing energy methods. The results obtained from the present approach are verified by those from a finite element analysis. Besides, the effects of volume fractions of functionally graded materials, Winkler foundation stiffness and in-plane forces on the dynamic of plate are elucidated.