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Research Papers

Internal Energy Transfer in Dynamical Behavior of Slightly Curved Shear Deformable Microplates

[+] Author and Article Information
Mergen H. Ghayesh

School of Mechanical, Materials, and
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

Gursel Alici

School of Mechanical, Materials,
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 11(4), 041002 (Nov 13, 2015) (11 pages) Paper No: CND-15-1051; doi: 10.1115/1.4031290 History: Received February 25, 2015; Revised August 05, 2015

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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Figures

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Fig. 1

Schematic representation of an initially slightly curved shear deformable microplate

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Fig. 2

Variations of the dimensionless natural frequencies of the out-of-plane motion of the microplate with the amplitude of the initial curvature

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Fig. 3

Frequency-response curves of the system for the generalized coordinates w1,1, w3,1, w3,3, and u2,1; f1 = 12.00, A0/h = 0.36, and ω1,1 = 24.8747

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Fig. 4

Frequency-response curves of the system for the generalized coordinates w1,1, w3,1, w3,3, and u2,1, obtained via modified couple stress and classical continuum theories; f1 = 12.00 and A0/h = 0.36

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Fig. 5

Force-response curves of the system for the generalized coordinates w1,1, w3,1, w3,3, and u2,1; Ω = 29.1033 and A0/h = 0.36

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Fig. 6

Frequency-response curves of the system for the generalized coordinates w1,1, w3,1, w3,3, and u2,1; f1 = 11.00, A0/h = 0.535, and ω1,1 = 28.0375

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Fig. 7

Frequency-response curves of the system for the generalized coordinates w1,1, w3,1, w3,3, and u2,1, obtained via modified couple stress and classical continuum theories; f1 = 11.00 and A0/h = 0.535

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Fig. 8

The effect of forcing amplitude on the frequency-response curves of the system for the generalized coordinates w1,1, w3,1, w3,3, and u2,1; A0/h = 0.535 and ω1,1 = 28.0375

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Fig. 9

Frequency-response curves of the system for the generalized coordinates w1,1, w3,1, w3,3, and u2,1; f1 = 14.50, A0/h = 1.00, and ω1,1 = 39.3379

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Fig. 10

Frequency–response of a macroplate for the w1,1 mode: solid line and symbols represent the results obtained by the numerical simulations employed in the present study and those given in Ref. [51], respectively

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