Exploring gradual material rigidity degradation effects on the nonlinear coupled axial-transversal nonlinear response of a capacitive micro-beam

Abstract

The accumulation of damage in materials due to crack propagation can lead them to unpredicted failures. This phenomenon is particularly relevant in materials science, engineering, and other fields where structures or components are subjected to repeated loading, cyclic stresses, or environmental factors. In this paper, the mechanical behavior of a microelectromechanical system subjected to cyclic loads has been modeled, when the stiffness of the material gradually is decreased. As a case study the dynamic response of a micro-beam to DC bias voltage as a static load and AC harmonic voltage as a cyclic load has been studied. The nonlinear coupled equations have been formed and converted to time-dependent ones using a spatial discretization method. Due to long-term integration over time, to achieve more accurate results besides direct 4th order Runge-Kutta integration method, a temporal decomposition method has been used to solve the coupled nonlinear ordinary differential equations. To realize this method, a temporal decomposed solution based on the physical nature of the problem is presented in the form of slow-growing terms and fast-altering harmonic terms with gradually-growing amplitudes. To find the coefficient of these terms a least square method has been utilized to minimize a cost function in a given dynamic time-interval, where the independency of the results to this interval has been assessed. Also, the nonlinear frequency behavior of the proposed model has been studied when the system has suffered various damages. Due to considering gradual rigidity degradation of the material interesting dynamic responses have been observed, that can help to expand the insight in the design of structures.