Abstract
An investigation into the dynamic behavior of a slightly curved resonant microbeam having nonideal boundary conditions is presented. The model accounts for midplane stretching, an applied axial load, and a small AC harmonic force. The ends of the curved microbeam are on immovable simple supports and the microbeam is resting on a nonlinear elastic foundation. The forced vibration response of curved microbeam due to the small AC load is obtained analytically by means of direct application of the method of multiple scales (a perturbation method). The effects of the nonlinear elastic foundation as well as the effect of curvature on the vibrations of the microbeam are examined. It is found that the effect of curvature is of softening type. For sufficiently high values of the coefficients, the elastic foundation and the axial load may suppress the softening behavior resulting in hardening behavior of the nonlinearity. The frequencies and mode shapes obtained are compared with the ideal boundary conditions case and the differences between them are contrasted on frequency-response curves. The frequency response and nonlinear frequency curves obtained may provide a reference for the choice of reasonable resonant conditions, design, and industrial applications of such systems. Results may be beneficial for future experimental and theoretical works on MEMS.
Highlights
Actuated microbeams are mostly used in microelectromechanical systems
A gradual small increase of frequencies is observed as the linear elastic coefficient increases
To describe the dynamic response of the microbeam, frequency-response curves are analyzed with respect to the effective physical parameters which are the linear and nonlinear elastic foundation coefficients, the voltage amplitudes, the axial forces, and the strength of the midplane stretching
Summary
Actuated microbeams are mostly used in microelectromechanical systems. They have superior features such as compact size, high resolution, high sensitivity, digital output, and low-power consumption. Presented a simplified model to study the resonant responses and nonlinear dynamics of idealized electrostatically actuated microcantilever-based devices in microelectromechanical systems (MEMS) They discussed the effects of different applied voltages, the cubic nonlinear spring, and the squeeze film damping on the nonlinear and chaotic behaviors of the system. Ekici and Boyaci [17] investigated the effect of nonideal boundary conditions on the vibrations of straight microbeams They showed that the nonideal boundary conditions could cause shifting of the frequencies or the frequency-response curves to the left or right side or no shifting, depending on the mode numbers, axial forces, deflections, and moments on the boundaries. The frequencies and mode shapes obtained are compared with the ideal boundary conditions case and the deviations from the ideal case are shown on the frequency-response curves This investigation provides an understanding of the nonlinear dynamic characteristics of slightly curved microbeams having nonideal boundary conditions
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