Size Effect Impact on the Mechanical Behavior of an Electrically Actuated Polysilicon Nanobeam based NEMS Resonator

Document Type : Research Paper

Authors

1 School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran

2 Center of Excellence in Design, Robotics and Automation (CEDRA), Mechanical Engineering Department, Sharif University of Technology, Tehran, Iran

3 Mechanical Engineering Department, College of Engineering, University of Texas at Dallas, Texas 75080-3021, USA

4 Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals 31261, Dhahran, Kingdom of Saudi Arabia

Abstract

In this paper, the dynamic response of resonating nano-beams is investigated using a strain gradient elasticity theory. A nonlinear model is obtained based on the Galerkin decomposition method to find the dynamic response of the investigated beam around its statically deflected position. The mid-plane stretching, axial residual stress and nonlinear interaction due to the electrostatic force on the deflected beam are included in the proposed nonlinear beam model. Comparing the beam natural frequency using strain gradient theory with experimental data shows an excellent agreement among both approaches. The normalized natural frequency is shown to be increasing nonlinearly with the decrease of the applied DC voltage as well as beam thickness. The results also reveal that increasing the tension axial stress increases the natural frequency; however its influence decreases when decreasing the beam thickness. To investigate the effect of AC actuation voltage on the beam resonant frequency, a Lindstedt-Poincare based perturbation method is utilized and validated by comparison with experimental data. The results show that increasing the AC actuation voltage makes the beam stiffer by increasing its resonant frequency.

Keywords

Main Subjects

1.             Braghin, F., et al., Nonlinear dynamics of vibrating MEMS. Sensors and Actuators A: Physical, 2007. 134(1): p. 98-108.
2.             Mestrom, R., et al., Modelling the dynamics of a MEMS resonator: Simulations and experiments. Sensors and Actuators A: Physical, 2008. 142(1): p. 306-315.
3.             Fu, Y., J. Zhang, and L. Wan, Application of the energy balance method to a nonlinear oscillator arising in the microelectromechanical system (MEMS). Current Applied Physics, 2011. 11(3): p. 482-485.
4.             Chaterjee, S. and G. Pohit, Dynamics of nonlinearly damped microcantilevers under electrostatic excitation. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2013. 227(3): p. 630-646.
5.             Abbas, I.A., Exact Solution of Thermoelastic Damping and Frequency Shifts in a Nano-Beam Resonator. International Journal of Structural Stability and Dynamics, 2014: p. 1450082.
6.             Abdel-Rahman, E.M., M.I. Younis, and A.H. Nayfeh, Characterization of the mechanical behavior of an electrically actuated microbeam. Journal of Micromechanics and Microengineering, 2002. 12(6): p. 759.
7.             Kuang, J.-H. and C.-J. Chen, Dynamic characteristics of shaped micro-actuators solved using the differential quadrature method. Journal of Micromechanics and Microengineering, 2004. 14(4): p. 647.
8.             Moghimi Zand, M. and M. Ahmadian, Characterization of coupled-domain multi-layer microplates in pull-in phenomenon, vibrations and dynamics. International Journal of Mechanical Sciences, 2007. 49(11): p. 1226-1237.
9.             Moghimi Zand, M. and M. Ahmadian, Vibrational analysis of electrostatically actuated microstructures considering nonlinear effects. Communications in Nonlinear Science and Numerical Simulations, 2009. 14: p. 1664-1678.
10.          Younis, M. and A. Nayfeh, A study of the nonlinear response of a resonant microbeam to an electric actuation. Nonlinear Dynamics, 2003. 31(1): p. 91-117.
11.           Moghimi Zand, M. and M.T. Ahmadian, Application of homotopy analysis method in studying dynamic pull-in instability of microsystems. Mechanics Research Communications, 2009. 36(7): p. 851-858.
12.          Namazu, T., Y. Isono, and T. Tanaka, Evaluation of size effect on mechanical properties of single crystal silicon by nanoscale bending test using AFM. Microelectromechanical Systems, Journal of, 2000. 9(4): p. 450-459.
13.          Stölken, J. and A. Evans, A microbend test method for measuring the plasticity length scale. Acta Materialia, 1998. 46(14): p. 5109-5115.
14.         Fu, Y., J. Zhang, and Y. Jiang, Influences of the surface energies on the nonlinear static and dynamic behaviors of nanobeams. Physica E: Low-dimensional Systems and Nanostructures, 2010. 42(9): p. 2268-2273.
15.          Kong, S., et al., The size-dependent natural frequency of Bernoulli–Euler micro-beams. International Journal of Engineering Science, 2008. 46(5): p. 427-437.
16.          Kong, S., et al., Static and dynamic analysis of micro beams based on strain gradient elasticity theory. International Journal of Engineering Science, 2009. 47(4): p. 487-498.
17.          Lim, C., Is a nanorod (or nanotube) with a lower Young’s modulus stiffer? Is not Young’s modulus a stiffness indicator? SCIENCE CHINA Physics, Mechanics & Astronomy, 2010. 53(4): p. 712-724.
18.          Reddy, J., Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates. International Journal of Engineering Science, 2010. 48(11): p. 1507-1518.
19.          Akgöz, B. and Ö. Civalek, Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams. International Journal of Engineering Science, 2011. 49(11): p. 1268-1280.
20.          Abbasi, M. and A.K. Mohammadi, Study of the sensitivity and resonant frequency of the flexural modes of an atomic force microscopy microcantilever modeled by strain gradient elasticity theory. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2013: p. 0954406213507918.
21.          Rahaeifard, M., M.T. Ahmadian, and K. Firoozbakhsh, Size-dependent dynamic behavior of microcantilevers under suddenly applied DC voltage. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2013: p. 0954406213490376.
22.          Gheshlaghi, B. and S.M. Hasheminejad, Vibration analysis of piezoelectric nanowires with surface and small scale effects. Current Applied Physics, 2012. 12(4): p. 1096-1099.
23.          Gholami, R., et al., Axial buckling and dynamic stability of functionally graded microshells based on the modified couple stress theory. International Journal of Structural Stability and Dynamics, 2015. 15(04): p. 1450070.
24.          Akgöz, B. and Ö. Civalek, Comment on “Static and dynamic analysis of micro beams based on strain gradient elasticity theory” by S. Kong, S. Zhou, Z. Nie, and K. Wang,(International Journal of Engineering Science, 47, 487–498, 2009). International Journal of Engineering Science, 2012. 50(1): p. 279-281.
25.          Miandoab, E.M., H.N. Pishkenari, and A. Yousefi-Koma, Dynamic analysis of electrostatically actuated nanobeam based on strain gradient theory. International Journal of Structural Stability and Dynamics, 2015. 15(04): p. 1450059.
26.          Miandoab, E.M., A. Yousefi-Koma, and H.N. Pishkenari, Poly silicon nanobeam model based on strain gradient theory. Mechanics Research Communications, 2014. 62: p. 83-88.
27.          Tilmans, H.A. and R. Legtenberg, Electrostatically driven vacuum-encapsulated polysilicon resonators: Part II. Theory and performance. Sensors and Actuators A: Physical, 1994. 45(1): p. 67-84.
28.          Nayfeh, A.H., Introduction to perturbation techniques2011: Wiley-VCH.
29.          Nayfeh, A.H. and D.T. Mook, Nonlinear oscillations2008: Wiley-VCH.