Nonlinear motion characteristics of microarches under axial loads based on modified couple stress theory

• Autorzy: Farokhi H. , Ghayesh M. H.

Identyfikatory

DOI

10.1016/j.acme.2014.12.012

• Języki publikacji: EN

Abstrakty

EN

The aim of the present study is to investigate the geometrically nonlinear size-dependent bending as well as resonant behaviour over the bent state of a microarch under an axial load. In particular, an axial load is applied on the system causing the initial curvature to increase by giving rise to a new bent configuration. A distributed harmonic transverse force is then exerted on the microarch and the nonlinear resonant response of the system over the new deflected configuration is investigated. The nonlinear partial differential equation of motion is obtained via Hamilton's principle based on the modified couple stress theory. The equation is discretized into a set of nonlinear ordinary differential equations through use of the Galerkin scheme. The pseudo-arclength continuation technique is then applied to the resultant set of ordinary differential equations. First, for the unforced system in the transverse direction, the axial load is increased and the new deflected configuration of the system is plotted versus the axial compression load; the nonlinear resonant response over the deflected configuration is then investigated through constructing frequency–response and force–response curves.

Słowa kluczowe

EN

modified couple stress theory; microarch; resonant response; axial force

PL

siła osiowa; dynamika; plastyczność gradientowa

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2015
• Tom: Vol. 15, no. 2
• Strony: 401--411
• Opis fizyczny: Bibliogr. 38 poz., wykr.

Twórcy

autor

Farokhi H.

• Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada H3A 0C3

autor

Ghayesh M. H.

• School of Mechanical, Materials and Mechatronic Engineering, University of Wollongong, NSW 2522, Australia

Bibliografia

• [1] Q. Li, S. Fan, Z. Tang, W. Xing, Non-linear dynamics of an electrothermally excited resonant pressure sensor, Sensors and Actuators A: Physical 188 (2012) 19–28.
• [2] M. Ghayesh, H. Farokhi, M. Amabili, Coupled nonlinear size-dependent behaviour of microbeams, Applied Physics A 112 (2013) 329–338.
• [3] H. Farokhi, M.H. Ghayesh, M. Amabili, Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory, International Journal of Engineering Science 68 (2013) 11–23.
• [4] M.H. Ghayesh, M. Amabili, H. Farokhi, Three-dimensional nonlinear size-dependent behaviour of Timoshenko microbeams, International Journal of Engineering Science 71 (2013) 1–14.
• [5] M.I. Younis, A.H. Nayfeh, A study of the nonlinear response of a resonant microbeam to an electric actuation, Nonlinear Dynamics 31 (2003) 91–117.
• [6] M.H. Ghayesh, H. Farokhi, M. Amabili, Nonlinear behaviour of electrically actuated MEMS resonators, International Journal of Engineering Science 71 (2013) 137–155.
• [7] M.H. Ghayesh, H. Farokhi, M. Amabili, In-plane and out-of- plane motion characteristics of microbeams with modal interactions, Composites Part B: Engineering 60 (2014) 423–439.
• [8] W.J. Poole, M.F. Ashby, N.A. Fleck, Micro-hardness of annealed and work-hardened copper polycrystals, Journal Name: Scripta Materialia 34 (4) (1996) 559–564, Other Information: PBD: 15 Feb 1996; Medium: X; Size.
• [9] D.C.C. Lam, A.C.M. Chong, Indentation model and strain gradient plasticity law for glassy polymers, Journal of Materials Research 14 (1999) 3784–3788.
• [10] I. Chasiotis, W.G. Knauss, The mechanical strength of polysilicon films: Part 2. Size effects associated withelliptical and circular perforations, Journal of the Mechanics and Physics of Solids 51 (2003) 1551–1572.
• [11] A.W. McFarland, J.S. Colton, Role of material microstructure in plate stiffness with relevance to microcantilever sensors, Journal of Micromechanics and Microengineering 15 (2005) 1060.
• [12] N.A. Fleck, G.M. Muller, M.F. Ashby, J.W. Hutchinson, Strain gradient plasticity: theory and experiment, Acta Metallurgica et Materialia 42 (1994) 475–487.
• [13] D. Liu, Y. He, X. Tang, H. Ding, P. Hu, P. Cao, Size effects in the torsion of microscale copper wires: experiment and analysis, Scripta Materialia 66 (2012) 406–409.
• [14] M. Asghari, M.T. Ahmadian, M.H. Kahrobaiyan, M. Rahaeifard, On the size-dependent behavior of functionally graded micro-beams, Materials & Design 31 (2010) 2324–2329.
• [15] S. Ramezani, A micro scale geometrically non-linear Timoshenko beam model based on strain gradient elasticity theory, International Journal of Non-Linear Mechanics 47 (2012) 863–873.
• [16] M. Salamat-talab, F. Shahabi, A. Assadi, Size dependent analysis of functionally graded microbeams using strain gradient elasticity incorporated with surface energy, Applied Mathematical Modelling (2012).
• [17] B. Wang, J. Zhao, S. Zhou, A micro scale Timoshenko beam model based on strain gradient elasticity theory, European Journal of Mechanics - A/Solids 29 (2010) 591–599.
• [18] A. Nateghi, M. Salamat-talab, J. Rezapour, B. Daneshian, Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory, Applied Mathematical Modelling 36 (2012) 4971–4987.
• [19] H.M. Ma, X.L. Gao, J.N. Reddy, A microstructure-dependent Timoshenko beam model based on a modified couple stress theory, Journal of the Mechanics and Physics of Solids 56 (2008) 3379–3391.
• [20] M. Asghari, M. Kahrobaiyan, M. Rahaeifard, M. Ahmadian, Investigation of the size effects in Timoshenko beams based on the couple stress theory, Archive of Applied Mechanics 81 (2011) 863–874.
• [21] C.M.C. Roque, D.S. Fidalgo, A.J.M. Ferreira, J.N. Reddy, A study of a microstructure-dependent composite laminated Timoshenko beam using a modified couple stress theory and a meshless method, Composite Structures 96 (2013) 532–537.
• [22] D.S. Ross, A. Cabal, D. Trauernicht, J. Lebens, Temperature- dependent vibrations of bilayer microbeams, Sensors and Actuators A: Physical 119 (2005) 537–543.
• [23] L.-L. Ke, Y.-S. Wang, Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory, Composite Structures 93 (2011) 342–350.
• [24] L. Wang, Y.Y. Xu, Q. Ni, Size-dependent vibration analysis of three-dimensional cylindrical microbeams based on modified couple stress theory: a unified treatment, International Journal of Engineering Science 68 (2013) 1–10.
• [25] M. Asghari, M.H. Kahrobaiyan, M.T. Ahmadian, A nonlinear Timoshenko beam formulation based on the modified couple stress theory, International Journal of Engineering Science 48 (2010) 1749–1761.
• [26] R. Ansari, R. Gholami, M. Faghih Shojaei, V. Mohammadi, S. Sahmani, Size-dependent bending, buckling and free vibration of functionally graded Timoshenko microbeams based on the most general strain gradient theory, Composite Structures 100 (2013) 385–397.
• [27] M. Şimşek, J.N. Reddy, A unified higher order beam theory for buckling of a functionally graded microbeam embedded in elastic medium using modified couple stress theory,, Composite Structures 101 (2013) 47–58.
• [28] L.-L. Ke, Y.-S. Wang, Z.-D. Wang, Thermal effect on free vibration and buckling of size-dependent microbeams, Physica E: Low-dimensional Systems and Nanostructures 43 (2011) 1387–1393.
• [29] B. Akgöz, Ö. Civalek, Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams, International Journal of Engineering Science 49 (2011) 1268–1280.
• [30] W. Xia, L. Wang, L. Yin, Nonlinear non-classical microscale beams: static bending, postbuckling and free vibration, International Journal of Engineering Science 48 (2010) 2044– 2053.
• [31] H. Mohammadi, M. Mahzoon, Thermal effects on postbuckling of nonlinear microbeams based on the modified strain gradient theory, Composite Structures 106 (2013) 764–776.
• [32] M.H. Ghayesh, S. Kazemirad, M. Amabili, Coupled longitudinal-transverse dynamics of an axially moving beam with an internal resonance, Mechanism and Machine Theory 52 (2012) 18–34.
• [33] M.H. Ghayesh, Coupled longitudinal–transverse dynamics of an axially accelerating beam, Journal of Sound and Vibration 331 (2012) 5107–5124.
• [34] M.H. Ghayesh, Subharmonic dynamics of an axially accelerating beam, Archive of Applied Mechanics 82 (2012) 1169–1181.
• [35] M.H. Ghayesh, S. Kazemirad, M.A. Darabi, A general solution procedure for vibrations of systems with cubic nonlinearities and nonlinear/time-dependent internal boundary conditions, Journal of Sound and Vibration 330 (2011) 5382–5400.
• [36] F. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures 39 (2002) 2731–2743.
• [37] E. Doedel, R. Paffenroth, A. Champneys, T. Fairgrieve, Y.A. Kuznetsov, B. Oldeman, B. Sandstede, X. Wang, AUTO-07P. Continuation and bifurcation software for ordinary differential equations (2007), 2007.
• [38] M.H. Ghayesh, H. Farokhi, M. Amabili, Nonlinear dynamics of a microscale beam based on the modified couple stresstheory, Composites Part B: Engineering 50 (2013) 318–324.