Wavelet based damage identification and dynamic pull-in instability analysis of electrostatically actuated coupled domain microsystems using generalized differential quadrature method

摘要

In this study, the effects of edged-crack on dynamic pull-in instability of fixed-fixed microbeams under suddenly applied electrostatic excitations and nonlinear squeeze film damping are investigated. The deformable electrode is modeled based on size dependent Euler-bernoulli beam formulations with modified couple stress theory. Also fluid interaction with electrode is modeled by nonlinear Reynolds equation. The model accounts for the von Karman nonlinear strains and edge crack in the domain. The edged crack is modeled as a massless torsional spring and is incorporated in the continuity equations of micro-beam formulations. Employing the Hamilton's principle, the governing nonlinear equations are attained and are then discretized by generalized differential quadrature method. This approach is combined with Newmark time integration and direct iteration method and is employed to investigate dynamic pull-in instability of the microsystem. The stability analysis of the cracked microbeam is also implemented by evaluating the largest Lyapunov exponent, the sign of which describes the character of the time dependent response. Wavelet transform based on Gabor function is applied for identifying the damage in microstructure. The location of damage is determined from the sudden peaks in the spatial variation of the transformed response of damped microbeam by this algorithm. Finally, a comprehensive study is carried out to examine the influence of the crack depth and crack position on pull-in instability characteristics of microbeams. Also, the efficiency of proposed wavelet analysis for damage detection in microstructures is assessed.