Nir Dick

A large array of elastically coupled micro cantilevers of variable length is studied experimentally and numerically. Full-scale finite element (FE) modal analysis is implemented to determine the spectral behavior of the array and to extract a global coupling matrix. A compact reduced-order (RO) model is used for numerical investigation of the array's dynamic response. Our model results show that at a given excitation frequency within a propagation band, only a finite number of beams respond. Spectral characteristics of individual cantilevers, inertially excited by an external piezoelectric actuator, were measured in vacuum using laser interferometry. The theoretical and experimental results collectively show that the resonant peaks corresponding to individual beams are clearly separated when operating in vacuum at the third harmonic. Distinct resonant peak separation, coupled with the spatially confined modal response, make higher harmonic operation of tailored, variable-length cantilever arrays well suited for a variety of resonant-based sensing applications.

Results of theoretical investigation of the transient dynamics of an initially curved electrostatically actuated clamped-clamped micro beam are presented. A reduced order model of the shallow Euler-Bernoulli arch developed using the Galerkin procedure with eigenmodes of a straight beam as a basis accounts for the distributed electrostatic and inertial loading, fringing electric fields and nonlinear squeeze film damping. Due to the unique combination of mechanical and electrostatic nonlinearities which is intrinsic in micro devices but is not encountered naturally in large-scale structures, the voltage-deflection characteristic of the sufficiently curved beam may have two maxima implying the existence of sequential mechanical (snap-through) and electrostatic (pull-in) instabilities. Phase plane analysis performed for the case of a suddenly applied electrostatic loading along with the simulation results show that critical voltages corresponding to the dynamic snap-through and pull-in instabilities are lower than their static counterparts while the minimal curvature required for the appearance of the dynamic snap-through is higher than in the static case. Clear functional advantages of this kind of structures, namely extended stable deflections and ability to tune the device frequencies in a very large range may result in improved performance of switches, inertial sensors and micromechanical non-volatile memory devices.