عنوان مقاله [English]
In recent years, many experimental observations showed that by decreasing the micro- and nano-beams thicknesses size effect appears and classical continuum theory cannot be used for micro- and nano-beams modeling. To model the nano-beams with more accuracy, non-classical continuum theories should be utilized. In this paper, non-local elasticity theory is used to analyze the frequency response of a nano-resonator. To this aim, first of all, nonlinear partial differential equation of nano-resonator is developed based on non-local theory and converted to ordinary differential equation using Galerkin projection method. The multiple time scales method is used to find the nano-resonator frequency response and the results are compared with the numerical simulation results and effect the variation of actuation amplitude, damping ratio and axial force on frequency response are investigated. Reducing actuation amplitude, increasing damping ratio and axial tension force, will reduce amplitude of frequency response. Based on the classical and non-classical continuum theories, frequency responses for different nano-beam dimensions are plotted and compared with together. It is shown that by decreasing the nano-beam thickness, size effect appear which results in lower vibration amplitude in comparison with classical continuum theory.
 Younis, M. I. (2010). “Microsystems: Mems Linear and Nonlinear Statics and Dynamics”. vol. 20.
 Hajjam, A., Pourkamali, S. (2012). “Fabrication and characterization of MEMS-based resonant organic gas sensors”. Sensors Journal, IEEE, vol. 12, pp. 1958-1964.
 Sharma, M., Sarraf, E. H., Baskaran, R., Cretu, E. (2012). “Parametric resonance: Amplification and damping in MEMS gyroscopes”. Sensors and Actuators A: Physical, vol. 177, pp. 79-86.
 Timurdogan, E., Alaca, B. E., Kavakli, I. H., Urey, H. (2011). “MEMS biosensor for detection of Hepatitis A and C viruses in serum”. Biosensors and Bioelectronics, vol. 28, pp. 189-194.
 Tocchio, A., Caspani, A., Langfelder, G. (2012). “Mechanical and electronic amplitude-limiting techniques in a MEMS resonant accelerometer”. Sensors Journal, IEEE, vol. 12, pp. 1719-1725.
 Torrents, A., Azgin, K., Godfrey, S., Topalli, E., Akin, T., Valdevit, L. (2010). “MEMS resonant load cells for micro-mechanical test frames: feasibility study and optimal design”. Journal of Micromechanics and Microengineering, vol. 20, p. 125004.
 Braghin, F., Resta, F., Leo, E., Spinola, G. (2007). “Nonlinear dynamics of vibrating MEMS”. Sensors and Actuators A: Physical, vol. 134, pp. 98-108.
 Mestrom, R., Fey, R., Van Beek, J., Phan, K., Nijmeijer, H. (2008). “Modelling the dynamics of a MEMS resonator: Simulations and experiments”. Sensors and Actuators A: Physical, vol. 142, pp. 306-315.
 Younis, M., Nayfeh, A. (2003). “A study of the nonlinear response of a resonant microbeam to an electric actuation”. Nonlinear Dynamics, vol. 31, pp. 91-117.
 De, S. K., Aluru, N., (2006). “Complex nonlinear oscillations in electrostatically actuated microstructures”. Microelectromechanical Systems, Journal of, vol. 15, pp. 355-369.
 Luo, A. C., Wang, F. Y. (2002). “Chaotic motion in a micro-electro–mechanical system with non-linearity from capacitors”. Communications in Nonlinear Science and Numerical Simulation, vol. 7, pp. 31-49.
 Wang, Y. C., Adams, S. G., Thorp, J. S., MacDonald, N. C., Hartwell, P., Bertsch, F. (1998). “Chaos in MEMS, parameter estimation and its potential application”. Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, vol. 45, pp. 1013-1020.
 Haghighi, H. S., Markazi, A. H. (2010). “Chaos prediction and control in MEMS resonators”. Communications in Nonlinear Science and Numerical Simulation, vol. 15, pp. 3091-3099.
 Collard, D., Takeuchi, S., Fujita, H. (2008). “MEMS technology for nanobio research”. Drug discovery today, vol. 13, pp. 989-996.
 Fleck, N., Muller, G., Ashby, M., Hutchinson, J. (1994). “Strain gradient plasticity: theory and experiment”. Acta Metallurgica et Materialia, vol. 42, pp. 475-487.
 Namazu, T., Isono, Y., Tanaka, T. (2000). “Evaluation of size effect on mechanical properties of single crystal silicon by nanoscale bending test using AFM”. Microelectromechanical Systems, Journal of, vol. 9, pp. 450-459.
 Stölken, J., Evans, A. (1998). “A microbend test method for measuring the plasticity length scale” Acta Materialia, vol. 46, pp. 5109-5115.
 Tang, C., Alici,G. (2011). “Evaluation of length-scale effects for mechanical behaviour of micro-and nanocantilevers: I. Experimental determination of length-scale factors”. Journal of Physics D: Applied Physics, vol. 44, p. 335501.
 Eringen, A. C. (1972). “Linear theory of non-local elasticity and dispersion of plane waves”. International Journal of Engineering Science, vol. 10, pp. 425-435.
 Eringen, A. C. (2002). “Non-local continuum field theories”.
 Lim, C., Li, C., Yu, J. L. (2010). “Dynamic behavior of axially moving nanobeams based on non-local elasticity approach”. Acta Mechanica Sinica, vol. 26, pp. 755-765.