Fabrication and vibration analysis of micro-cross beams

In this investigation, the micro-cross beam is fabricated by the method of silicon bulk micromachining. The first torsion natural frequency included a torsion factor and the second bending natural frequency can be derived by using the characteristic of the first two decoupled vibration modes of the micro-cross beam. The Poisson´s ratio included a torsion factor and a frequency ratio can be defined in a simple form by setting the ratio of the length-width of long beams and short beams is designed to be equal. The frequency ratio can be obtained by using the measurement and simulation. In the measurement, a micro Laser Doppler Vibrometer with 20 MHz bandwidth and 0.1 nm resolution is used by using the resonant method. Effects of input voltages on the vibration at the tip point of long beams are also discussed. Measured dimensions of the fabricated microcross beam can be used as the information of input to simulate frequency ratio of the beam. The first torsion and the second bending modes can be constructed and the Poisson´s ratio can be obtained from the simulation results. A good agreement between the theoretical outcomes and experimental results is found.