This paper investigates the internal energy transfer and modal interactions in the dynamical behavior of slightly curved microplates. Employing the third-order shear deformation theory, the microplate model is developed taking into account geometric nonlinearities as well as the modified couple stress theory; the initial curvature is modeled by an initial imperfection in the out-of-plane direction. The in-plane displacements and inertia are retained, and the coupled out-of-plane, rotational, and in-plane motion characteristics are analyzed. Specifically, continuous models are developed for kinetic and potential energies as well as damping and external works; these are balanced and reduced via Lagrange's equations along with an assumed-mode technique. The reduced-order model is then solved numerically by means of a continuation technique; stability analysis is performed by means of the Floquet theory. The possibility of the occurrence of modal interactions and internal energy transfers is verified via a linear analysis on different natural frequencies of the system. The nonlinear resonant response of the system is obtained for the cases with internal energy transfer, and energy transfer mechanisms are analyzed; as we shall see, the presence of an initial curvature affects the system dynamics substantially. The importance of taking into account small-size effects is also shown by discovering this fact that both the linear and nonlinear internal energy transfer mechanisms are shifted substantially if this effect is ignored.
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July 2016
Research-Article
Internal Energy Transfer in Dynamical Behavior of Slightly Curved Shear Deformable Microplates
Mergen H. Ghayesh,
Mergen H. Ghayesh
School of Mechanical, Materials, and
Mechatronic Engineering,
University of Wollongong,
Wollongong, NSW 2522, Australia
e-mail: mergen@uow.edu.au
Mechatronic Engineering,
University of Wollongong,
Wollongong, NSW 2522, Australia
e-mail: mergen@uow.edu.au
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Hamed Farokhi,
Hamed Farokhi
Department of Mechanical Engineering,
McGill University,
Montreal, QC H3A 0C3, Canada
e-mail: hamed.farokhi@mail.mcgill.ca
McGill University,
Montreal, QC H3A 0C3, Canada
e-mail: hamed.farokhi@mail.mcgill.ca
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Gursel Alici
Gursel Alici
School of Mechanical, Materials,
and Mechatronic Engineering,
University of Wollongong,
Wollongong, NSW 2522, Australia
e-mail: gursel@uow.edu.au
and Mechatronic Engineering,
University of Wollongong,
Wollongong, NSW 2522, Australia
e-mail: gursel@uow.edu.au
Search for other works by this author on:
Mergen H. Ghayesh
School of Mechanical, Materials, and
Mechatronic Engineering,
University of Wollongong,
Wollongong, NSW 2522, Australia
e-mail: mergen@uow.edu.au
Mechatronic Engineering,
University of Wollongong,
Wollongong, NSW 2522, Australia
e-mail: mergen@uow.edu.au
Hamed Farokhi
Department of Mechanical Engineering,
McGill University,
Montreal, QC H3A 0C3, Canada
e-mail: hamed.farokhi@mail.mcgill.ca
McGill University,
Montreal, QC H3A 0C3, Canada
e-mail: hamed.farokhi@mail.mcgill.ca
Gursel Alici
School of Mechanical, Materials,
and Mechatronic Engineering,
University of Wollongong,
Wollongong, NSW 2522, Australia
e-mail: gursel@uow.edu.au
and Mechatronic Engineering,
University of Wollongong,
Wollongong, NSW 2522, Australia
e-mail: gursel@uow.edu.au
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 25, 2015; final manuscript received August 5, 2015; published online November 13, 2015. Assoc. Editor: Ahmet S. Yigit.
J. Comput. Nonlinear Dynam. Jul 2016, 11(4): 041002 (11 pages)
Published Online: November 13, 2015
Article history
Received:
February 25, 2015
Revised:
August 5, 2015
Citation
Ghayesh, M. H., Farokhi, H., and Alici, G. (November 13, 2015). "Internal Energy Transfer in Dynamical Behavior of Slightly Curved Shear Deformable Microplates." ASME. J. Comput. Nonlinear Dynam. July 2016; 11(4): 041002. https://doi.org/10.1115/1.4031290
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