For a nonlinear beam-mass system used to harvest vibratory energy, the two-mode approximation of the response is computed and compared to the single-mode approximation of the response. To this end, the discretized equations of generalized coordinates are developed and studied using a computational method. By obtaining phase-portraits and time-histories of the displacement and voltage, it is shown that the strong nonlinearity of the system affects the system dynamics considerably. By comparing the results of single- and two-mode approximations, it is shown that the number of mode shapes affects the dynamics of the response. Varying the tip-mass results in different structural configurations namely linear, pre-buckled nonlinear, and post-buckled nonlinear configurations. The nonlinear dynamics of the system response are investigated for vibrations about static equilibrium points arising from the buckling of the beam. Furthermore, it is demonstrated that the harvested power is affected by the system configuration.
A cantilever beam-rigid body microgyroscope under electrostatic force is introduced and analytically modeled. The linear dynamics of the microsystem are studied in detail and the main parameters of the sensor are investigated. The square beam carries an eccentric end rigid body affecting the dynamic and static characteristics of the sensor. A detailed sensitivity analysis is performed and the effects of the base rotation rate, the excitation frequency, and the damping ratio (quality factor) on the dynamics of the system are explored.