Nonlinear Size-Dependent Analysis of an Initially Curved Microbeam

Nonlinear behavior of an initially curved fully clamped microbeam is investigated in this paper. The microbeam is laminated between two thin piezoelectric layers along its length. Applying voltage to the piezoelectric layers induces a lengthwise force in the microbeam which, in turn, changes the initial rise and the bending stiffness of the microbeam. This feature is used to tune the frequency and the bistability band of the initially curved microbeam for the first time in this paper. The microbeam is electrostatically actuated as well. The governing equation of motion is obtained, using the Hamilton’s principle and the size effect is considered in the formulation of the problem utilizing the strain gradient theory. Static response of the system is obtained, using the Newton-Raphson numerical approach. The natural frequency of the system is obtained for various electrostatic voltages. The influence of piezoelectric actuation and size effect is studied on the static behavior and the frequency of the microbeam. Dynamic response of the microbeam in the vicinity of the primary resonance is obtained, using shooting technique and in some cases by the method of multiple scales. The effect of size and piezoelectric excitation on the primary resonance is investigated. The secondary resonance of the microbeam subjected to subharmonic resonance of order 1/2 and the influence of size on it is also studied.