Nonlinear vibration of an electrostatically actuated micro-beam made of anelastic material considering compressible fluid media

摘要

Similar to elasticity and viscoelasticity, anelasticity is one of the rheological models of materials. Like the viscoelastic materials, anelastic deformation is time dependent, while unlike viscoelasticity, it is full recoverable. Anelastic behavior is very sensitive to microstructure and is significant when things become small. In this paper, the nonlinear vibrations of an electrostatically actuated micro-beam made of anelastic material are studied based on the modified couple stress theory and considering compressible fluid media. The constitutive equation of micro-beams has been developed regarding the stress-strain behavior of classic anelastic materials. Considering the dependency of the effective viscosity on variable gap distance, an analytical model of an electrostatically actuated anelastic micro-beam has been developed through the variable Knudsen number. Then, multiple scales method has been applied to obtain an approximate analytical solution for nonlinear resonant curves. Additionally, the effects of different mechanical behaviors of materials including elasticity, viscoelasticity and anelasticity on the nonlinear dynamic response have been studied. Furthermore, influences of some effective parameters such as length scale, anelastic relaxation time, relaxation intensity, mid-plane stretching force, residual axial force, air-gap pressure and compressible fluid media on the nonlinear vibration analysis have been investigated and discussed in detail. The results demonstrate that resonance curves are strongly dependent on the mechanical behavior of materials. It is found that the relaxation intensity, relaxation time and air-gap pressure change the resonant amplitude significantly. Moreover, the results reveal that considering compressible fluid media, both the frequency response and the softening behavior of the system decrease.