Ehsan M. Miandoab - School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran
Hossein N. Pishkenari - Center of Excellence in Design, Robotics and Automation (CEDRA), Mechanical Engineering Department, Sharif University of Technology,Tehran, P.O. Box ۱۱۳۶۵-۹۴۶۵, Iran
Aghil Yousefi-Koma - School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran
Farid Tajaddodianfar - Mechanical Engineering Department, College of Engineering, University of Texas at Dallas, Texas ۷۵۰۸۰-۳۰۲۱, USA

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

NEMS, Nano-resonator, Strain gradient elasticity theory, Size effect