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Research Papers

Nonlinear Dynamics of Multilayered Microplates

[+] Author and Article Information
Mergen H. Ghayesh

School of Mechanical Engineering,
University of Adelaide,
South Australia 5005, Australia
e-mail: mergen.ghayesh@adelaide.edu.au

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 20, 2017; final manuscript received August 7, 2017; published online November 1, 2017. Assoc. Editor: Mohammad Younis.

J. Comput. Nonlinear Dynam 13(2), 021006 (Nov 01, 2017) (12 pages) Paper No: CND-17-1227; doi: 10.1115/1.4037596 History: Received May 20, 2017; Revised August 07, 2017

This paper, for the first time, investigates the nonlinear forced dynamics of a three-layered microplate taking into account all the in-plane and out-of-plane motions. The Kirchhoff's plate theory, along with von Kármán nonlinear strains, is employed to derive the nonlinear size-dependent transverse and in-plane equations of motion in the modified couple stress theory (MCST) framework, based on Hamilton's energy principle. A nonconservative damping force of viscous type as well as an external excitation load consisting of a harmonic term is considered in the model. All the transverse and in-plane displacements and inertia are accounted for in both the theoretical modeling and numerical simulations; this leads to further complexities in the nonlinear model and simulations. These complexities arising in the theoretical model are overcome through the use of a well-optimized numerical scheme. The effects of different layer arrangements and different layer material percentages on the force–amplitude and frequency–amplitude curves of the microsystem are investigated. The results of this study shed light in the nonlinear resonant behavior of multilayered microplates and could be helpful in design and analysis of multilayered microplates in microelectromechanical systems (MEMS) applications.

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References

Rembe, C. , and Muller, R. S. , 2002, “ Measurement System for Full Three-Dimensional Motion Characterization of MEMS,” J. Microelectromech. Syst., 11(5), pp. 479–488. [CrossRef]
LaRose, R. P. , III, and Murphy, K. D. , 2010, “ Impact Dynamics of MEMS Switches,” Nonlinear Dyn., 60(3), pp. 327–339. [CrossRef]
Caruntu, D. I. , Martinez, I. , and Knecht, M. W. , 2013, “ Reduced Order Model Analysis of Frequency Response of Alternating Current Near Half Natural Frequency Electrostatically Actuated MEMS Cantilevers,” ASME J. Comput. Nonlinear Dyn., 8(3), p. 031011.
Ghayesh, M. H. , and Farokhi, H. , 2016, “ Coupled Nonlinear Dynamics of Geometrically Imperfect Shear Deformable Extensible Microbeams,” ASME J. Comput. Nonlinear Dyn., 11(4), p. 041001. [CrossRef]
Belardinelli, P. , Lenci, S. , and Brocchini, M. , 2014, “ Modeling and Analysis of an Electrically Actuated Microbeam Based on Nonclassical Beam Theory,” ASME J. Comput. Nonlinear Dyn., 9(3), p. 031016. [CrossRef]
Madinei, H. , Rezazadeh, G. , and Azizi, S. , 2015, “ Stability and Bifurcation Analysis of an Asymmetrically Electrostatically Actuated Microbeam,” ASME J. Comput. Nonlinear Dyn., 10(2), p. 021002. [CrossRef]
Ruzziconi, L. , Younis, M. I. , and Lenci, S. , 2013, “ An Efficient Reduced-Order Model to Investigate the Behavior of an Imperfect Microbeam Under Axial Load and Electric Excitation,” ASME J. Comput. Nonlinear Dyn., 8(1), p. 011014.
Awrejcewicz, J. , Krysko, A. V. , Pavlov, S. P. , Zhigalov, M. V. , and Krysko, V. A. , 2017, “ Chaotic Dynamics of Size Dependent Timoshenko Beams With Functionally Graded Properties Along Their Thickness,” Mech. Syst. Signal Process., 93, pp. 415–430. [CrossRef]
Dick, A. J. , Balachandran, B. , and Mote, C. D., Jr. , 2010, “ Localization in Microresonator Arrays: Influence of Natural Frequency Tuning,” ASME J. Comput. Nonlinear Dyn., 5(1), p. 011002.
Li, A. , Zhou, S. , Zhou, S. , and Wang, B. , 2014, “ Size-Dependent Analysis of a Three-Layer Microbeam Including Electromechanical Coupling,” Compos. Struct., 116, pp. 120–127. [CrossRef]
Banerjee, J. , Cheung, C. , Morishima, R. , Perera, M. , and Njuguna, J. , 2007, “ Free Vibration of a Three-Layered Sandwich Beam Using the Dynamic Stiffness Method and Experiment,” Int. J. Solids Struct., 44(22), pp. 7543–7563. [CrossRef]
Rezazadeh, G. , Keyvani, A. , and Jafarmadar, S. , 2012, “ On a MEMS Based Dynamic Remote Temperature Sensor Using Transverse Vibration of a Bi-Layer Micro-Cantilever,” Measurement, 45(3), pp. 580–589. [CrossRef]
Saghir, S. , Ilyas, S. , Jaber, N. , and Younis, M. I. , 2017, “ An Experimental and Theoretical Investigation of the Mechanical Behavior of Multilayer Initially Curved Microplates Under Electrostatic Actuation,” ASME J. Vib. Acoust., 139(4), p. 040901. [CrossRef]
Ilyas, S. , Arevalo, A. , Bayes, E. , Foulds, I. G. , and Younis, M. I. , 2015, “ Torsion Based Universal MEMS Logic Device,” Sens. Actuators A, 236, pp. 150–158. [CrossRef]
Krysko, A. V. , Awrejcewicz, J. , Saltykova, O. A. , Zhigalov, M. V. , and Krysko, V. A. , 2014, “ Investigations of Chaotic Dynamics of Multi-Layer Beams Taking Into Account Rotational Inertial Effects,” Commun. Nonlinear Sci. Numer. Simul., 19(8), pp. 2568–2589. [CrossRef]
Awrejcewicz, J. , Krysko, V. A., Jr. , Yakovleva, T. V. , and Krysko, V. A. , 2016, “ Noisy Contact Interactions of Multi-Layer Mechanical Structures Coupled by Boundary Conditions,” J. Sound Vib., 369, pp. 77–86. [CrossRef]
Krysko, A. V. , Awrejcewicz, J. , Saltykova, O. A. , Vetsel, S. S. , and Krysko, V. A. , 2016, “ Nonlinear Dynamics and Contact Interactions of the Structures Composed of Beam-Beam and Beam-Closed Cylindrical Shell Members,” Chaos, Solitons Fractals, 91, pp. 622–638. [CrossRef]
Krysko, A. V. , Awrejcewicz, J. , Kutepov, I. E. , and Krysko, V. A. , 2015, “ On a Contact Problem of Two-Layer Beams Coupled by Boundary Conditions in a Temperature Field,” J. Therm. Stresses, 38(5), pp. 468–484. [CrossRef]
Krysko, A. V. , Awrejcewicz, J. , Zhigalov, M. V. , and Krysko, V. A. , 2016, “ On the Contact Interaction Between Two Rectangular Plates,” Nonlinear Dyn., 85(4), pp. 2729–2748. [CrossRef]
Kirichenko, V. F. , Awrejcewicz, J. , Kirichenko, A. V. , Krysko, A. V. , and Krysko, V. A. , 2015, “ On the Non-Classical Mathematical Models of Coupled Problems of Thermo-Elasticity for Multi-Layer Shallow Shells With Initial Imperfections,” Int. J. Non-Linear Mech., 74, pp. 51–72. [CrossRef]
Awrejcewicz, J. , Krysko, A. , Soldatov, V. , and Krysko, V. , 2012, “ Analysis of the Nonlinear Dynamics of the Timoshenko Flexible Beams Using Wavelets,” ASME J. Comput. Nonlinear Dyn., 7(1), p. 011005. [CrossRef]
Krysko, A. V. , Awrejcewicz, J. , Pavlov, S. P. , Zhigalov, M. V. , and Krysko, V. A. , 2017, “ Chaotic Dynamics of the Size-Dependent Non-Linear Micro-Beam Model,” Commun. Nonlinear Sci. Numer. Simul., 50, pp. 16–28. [CrossRef]
Krysko, A. V. , Awrejcewicz, J. , Zhigalov, M. V. , Pavlov, S. P. , and Krysko, V. A. , 2017, “ Nonlinear Behaviour of Different Flexible Size-Dependent Beams Models Based on the Modified Couple Stress Theory—Part 1: Governing Equations and Static Analysis of Flexible Beams,” Int. J. Non-Linear Mech., 93, pp. 96–105. [CrossRef]
Krysko, A. V. , Awrejcewicz, J. , Zhigalov, M. V. , Pavlov, S. P. , and Krysko, V. A. , 2017, “ Nonlinear Behaviour of Different Flexible Size-Dependent Beams Models Based on the Modified Couple Stress Theory—Part 2: Chaotic Dynamics of Flexible Beams,” Int. J. Non-Linear Mech., 93, pp. 106–121. [CrossRef]
Awrejcewicz, J. , Krysko, V. A. , Pavlov, S. P. , and Zhigalov, M. V. , 2017, “ Nonlinear Dynamics Size-Dependent Geometrically Nonlinear Tymoshenko Beams Based on a Modified Moment Theory,” Appl. Math. Sci., 11(5), pp. 237–247.
Awrejcewicz, J. , Krysko, A. V. , Pavlov, S. P. , Zhigalov, M. V. , and Krysko, V. A. , 2017, “ Stability of the Size-Dependent and Functionally Graded Curvilinear Timoshenko Beams,” ASME J. Comput. Nonlinear Dyn., 12(4), p. 041018. [CrossRef]
Shenas, A. G. , and Malekzadeh, P. , 2016, “ Free Vibration of Functionally Graded Quadrilateral Microplates in Thermal Environment,” Thin-Walled Struct., 106, pp. 294–315. [CrossRef]
Farahmand, H. , Ahmadi, A. R. , and Arabnejad, S. , 2011, “ Thermal Buckling Analysis of Rectangular Microplates Using Higher Continuity p-Version Finite Element Method,” Thin-Walled Struct., 49(12), pp. 1584–1591. [CrossRef]
Shenas, A. G. , Malekzadeh, P. , and Mohebpour, S. , 2016, “ Vibrational Behavior of Variable Section Functionally Graded Microbeams Carrying Microparticles in Thermal Environment,” Thin-Walled Struct., 108, pp. 122–137. [CrossRef]
Ma, H. M. , Gao, X. L. , and Reddy, J. N. , 2008, “ A Microstructure-Dependent Timoshenko Beam Model Based on a Modified Couple Stress Theory,” J. Mech. Phys. Solids, 56(12), pp. 3379–3391. [CrossRef]
Wang, L. , Xu, Y. Y. , and Ni, Q. , 2013, “ Size-Dependent Vibration Analysis of Three-Dimensional Cylindrical Microbeams Based on Modified Couple Stress Theory: A Unified Treatment,” Int. J. Eng. Sci., 68, pp. 1–10. [CrossRef]
Li, A. , Zhou, S. , Zhou, S. , and Wang, B. , 2014, “ A Size-Dependent Model for bi-Layered Kirchhoff Micro-Plate Based on Strain Gradient Elasticity Theory,” Compos. Struct., 113, pp. 272–280. [CrossRef]
Kamali, M. , Shodja, H. , and Forouzan, B. , 2015, “ Three-Dimensional Free Vibration of Arbitrarily Shaped Laminated Micro-Plates With Sliding Interfaces Within Couple Stress Theory,” J. Sound Vib., 339, pp. 176–195. [CrossRef]
Arani, A. G. , Arani, H. K. , and Maraghi, Z. K. , 2016, “ Vibration Analysis of Sandwich Composite Micro-Plate Under Electro-Magneto-Mechanical Loadings,” Appl. Math. Modell., 40(23), pp. 10596–10615. [CrossRef]
Zand, M. M. , and Ahmadian, M. , 2007, “ Characterization of Coupled-Domain Multi-Layer Microplates in Pull-in Phenomenon, Vibrations and Dynamics,” Int. J. Mech. Sci., 49(11), pp. 1226–1237. [CrossRef]
Yang, F. , Chong, A. C. M. , Lam, D. C. C. , and Tong, P. , 2002, “ Couple Stress Based Strain Gradient Theory for Elasticity,” Int. J. Solids Struct, 39(10), pp. 2731–2743. [CrossRef]
Reddy, J. N. , and Kim, J. , 2012, “ A Nonlinear Modified Couple Stress-Based Third-Order Theory of Functionally Graded Plates,” Compos. Struct., 94(3), pp. 1128–1143. [CrossRef]
Ghayesh, M. H. , and Farokhi, H. , 2015, “ Nonlinear Dynamics of Microplates,” Int. J. Eng. Sci., 86, pp. 60–73. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic representation of a three-layered rectangular microplate

Grahic Jump Location
Fig. 2

Frequency–amplitude curves of the three-layered microplate: (a) maximum of w1,1; (b) maximum of w3,1; (c) minimum of u2,1; (d) minimum of v1,2; ls = 0.35, ζ = 0.015, and f1 = 32.0. Solid: stable; dashed: unstable.

Grahic Jump Location
Fig. 3

Force–amplitude curves of the three-layered microplate: (a) maximum of w1,1; (b) maximum of w3,1; (c) minimum of u2,1; (d) minimum of v1,2; ls = 0.35, ζ = 0.015, and Ω/ω1,1 = 1.13. Solid: stable; dashed: unstable.

Grahic Jump Location
Fig. 4

Frequency–amplitude curves of the three-layered microplate for different layers: (a) maximum of w1,1; (b) maximum of w3,1; (c) minimum of u2,1; (d) minimum of v1,2; ls = 0.35, ζ = 0.015, and f1 = 32.0

Grahic Jump Location
Fig. 5

Frequency–amplitude curves of the three-layered microplate for different layer-percentage: (a) maximum of w1,1; (b) maximum of w3,1; (c) minimum of u2,1; (d) minimum of v1,2; ls = 0.35, ζ = 0.015, and f1 = 32.0

Grahic Jump Location
Fig. 6

Force–amplitude curves of the three-layered microplate for different layer-percentage: (a) maximum of w1,1; (b) maximum of w3,1; (c) minimum of u2,1; (d) minimum of v1,2; ls = 0.35, ζ = 0.015, and Ω/ω1,1 = 1.13

Grahic Jump Location
Fig. 7

Frequency–amplitude curves of the three-layered microplate for different values of ls: (a) maximum of w1,1; (b) maximum of w3,1; (c) minimum of u2,1; (d) minimum of v1,2; ζ = 0.015 and f1 = 32.0

Grahic Jump Location
Fig. 8

Force–amplitude curves of the three-layered microplate for different values of ls: (a) maximum of w1,1; (b) maximum of w3,1; (c) minimum of u2,1; (d) minimum of v1,2; ζ = 0.015; and Ω/ω1,1 = 1.13

Grahic Jump Location
Fig. 9

Comparison of the frequency–amplitude of a microplate obtained by Ref. [38] (symbols) and the model developed in the present study (solid line)

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