The dynamics of a doubly clamped microbeam near the primary resonance: Experimental and analytical investigation

We present experimental and analytical investigation of the dynamics of a doubly clamped microbeam near its primary resonance. The microbeam is excited electrostatically by an electrode on the first half of the beam. These microbeams are fabricated using polyimide as structural layer coated with nickel from top and chromium and gold layers from bottom. A noise signal is applied to experimentally detect the natural frequencies. Then, frequency sweep tests are generated for various values of DC bias revealing hardening, transition, and softening behavior of the microbeam. We report for the first time the transition from lower stable state, to unstable state, and then to large stable state experimentally. A multi-mode Galerkin method is used to develop a reduced order model (ROM) of the beam. Shooting method is used to find the periodic motion and is utilized to generate frequency response curves. The curves show good agreement with the experimental results with hardening behavior at lower DC voltage then softening at higher voltage loads and dynamic pull-in.