A Study on the Nonlinear Vibrations of Electrostatically Actuated Micro Beams with Anelastic Stress-Strain Behavior

In this paper the nonlinear dynamic of an electrostatically actuated microbeam with viscoelastic-anelastic behavior considering size effect is studied. The micro-beam is deflected using a bias DC voltage and then driven to vibrate around its deflected position by a harmonic AC load. Regarding the stress-strain behavior of anelastic materials, the constitutive equation of microbeams is derived based on the modified couple stress theory (MCST). Assuming electrostatic and mid-plane stretching forces as the main sources of the nonlinearity and taking advantage of the Galerkin projection method, the partial differential equation is transformed to a set of nonlinear ordinary differential equation (ODE). Multiple scales method is used to obtain an approximate analytical solution for nonlinear resonant curves. The effect of different mechanical behaviors of materials including elasticity, viscoelasticity and anelasticity, length scale parameter, anelastic relaxation time and relaxation intensity on the nonlinear vibration analysis are studied. The results demonstrate that there is very large dependence of resonance curves on the different mechanical behavior of materials. It is seen that there are special conditions which the elastic and anelastic models predict similar results while the predicted results from anelastic and viscoelastic models are different from each other. It is found that the relaxation intensity and anelastic relxation time can change the resonant curves significantly.