Experimental and analytical study on the superharmonic resonance of size-dependent cantilever microbeams

Abstract

The superharmonic resonance (SR) of size-dependent cantilever microbeams is investigated experimentally and analytically. Nickel cantilever microbeams are employed with concentrated harmonic force on the tip. The SR of order two, three, four, five, and six are observed. The frequency–response curves (FRCs) near the SR frequencies as well as the time histories are obtained. The FRCs indicate that the superharmonic resonant frequencies are different from the classical situation. Furthermore, a nonlinear model within the framework of modified couple stress theory is derived to interpret the observations by aid of Hamilton's variation principle. The resulting partial differential equation of motion is discretized into a series of ordinary differential equations (ODEs) by a two-mode Galerkin scheme. The ODEs are then solved analytically with the multi-dimensional Lindstedt–Poincaré method. Analytical results are in good agreement with experimental results in SR of order three. The effects of different nonlinear terms, length scale parameter, and damping coefficients on the nonlinear system are then discussed.