Investigation of the effects of air on the dynamic behavior of a small cantilever beam

There has been a growing interest these past years in microsystems and understanding the mechanical properties essential for their design. In this context, an experimental technique is proposed to characterize a small dimensional structure surrounded by various air pressure levels. Dynamic tests were performed on three different cantilever beams (silicon single-crystal, quartz and lithium niobate) used in the realization of an energy converter. The beam is mounted on a support and excited by a shaker. The dynamic responses recorded by a laser vibrometer allow the corresponding modal parameters to be identified as a function of the air pressure inside the vacuum chamber. A nonlinear modal identification is then performed. It is based on the logarithmic decrement method applied in the time–frequency domain using a wavelet transform of the time responses. The evolution of the equivalent modal frequency and the equivalent modal damping of the beam versus time and vibration amplitude are identified for several pressure values ranging from a primary vacuum to atmospheric pressure. Finally, an analytical simulation with the Hosaka theoretical model is presented. Comparing this theoretical model with experimental results, a good agreement was obtained for silicon structure.