Simultaneous planar free and forced vibrations analysis of an electrostatically actuated beam oscillator

Abstract

Abstract Electrostatically driven beam oscillators have many applications in MEMS and NEMS devices. The objective of this investigation is to systematically study the hardening–softening nature of primary resonance curves of a doubly clamped cylindrical beam oscillator which represents a silicon nanowire. The investigation has been carried out by simultaneously studying both planar free and forced vibration responses using Galerkin based reduced order modelling technique. The free and forced vibration responses have been first investigated numerically, and it has been demonstrated that amplitude–frequency curves of free vibration can serve as a backbone for resonance curves of forced vibration. We have also observed that hardening, softening, or mixed softening–hardening nature of resonance or backbone curves is dependent on the magnitude of electrostatic actuation. Further, the free vibration responses have also been investigated using harmonic balance method to gain analytical insights into the effects of DC voltage on the nature of backbone curves. The obtained expression of amplitude–frequency curve using harmonic balance method is generic in nature and can be used to compute amplitude–frequency curves of oscillators having nonlinearity in the form of power series.