Nonlinear forced vibration of a curved micro beam with a surface-mounted light-driven actuator

Abstract

This study addresses the nonlinear forced vibration of a deep curved microbeam with a noncontact actuator. The photostrictive actuator is subjected to an ultraviolet-switching excitation and the governing equations are derived based on the couple stress theory (CST). The von Kármán geometric nonlinearity is utilized to obtain the fundamental equations of thin curved beams in a curvilinear coordinate system. According to the type of boundaries, inextensional condition is applied as a new strategy in such a structure to obtain solution analytically. By using the Galerkin method, the equation of motion is discretized and reduced to the ordinary differential equation. Nonlinear analysis is then carried out on the reduced-order equation by employing the multiple scales method. Based on the obtained results, for the first time, it is reported that qualitative and quantitative response of a deep curved beam is highly affected by the geometrical characteristics and the micro-interactions. It is found that considering the deepness term (1+z/R) in a curved beam makes nonlinear behavior more prominent, whereas ignoring this term could lead to erroneous dynamic predictions particularly when the beam thickness increases. Furthermore, the prominent role of the radius of curvature on the large-amplitude response of the system is investigated. It is shown that as the beam's curvature increases, namely when the beam becomes deeper or a straight beam tends to a curved one, contribution of the nonlinear behavior of the system increases.