Nonlinear analysis of coupled transversal-longitudinal vibration in electrostatically actuated nanoresonators

Abstract

Nanoresonators can be used in some engineering fields such as high quality factor filters for electronic signals and sensors. So, the main purpose of this paper is to analyze the nonlinear dynamic behavior of electrostatically actuated nanoresonators. In the framework of the Von Karman's theory and the Euler-Bernoulli beam model, the nonlinear governing equations of motion are developed using the Hamilton's principle. Also, the coupling of lateral and longitudinal vibrations is considered. The governing partial differential equations are discretized by means of the Galerkin’s method. The analytical and numerical solution are obtained using the multiple-scales method and Runge–Kutta method, respectively. The variation of natural frequencies and the response of the nanoresonator with the levels of the electrostatic load are investigated. The results show that the nonlinear frequency response curves are greatly affected by the gap distance and detuning frequency. A hardening behavior is observed in the nonlinear frequency responses of the nanoresonator. Also, through the comparison between the effect of gap distance and dc voltage, it is found that the natural frequencies of the nanoresonator are more sensitive to the variation of the dc voltage. So, this suggests a tunable resonator over a wide range of frequencies.

Keywords

• multiple scales method
• nanoresonators
• electrostatic actuation
• lateral&ndash
• longitudinal coupling