Effects Of Fluid Damping And Pre-stress On The Characteristics Of Micro And Nano Circular Diaphragm-based Resonators

Micromachined diaphragm-based resonators,as important structure and function applications,have been widely used in various fields such as biology,chemistry and medicine.These sensors vibrate at their excited resonance frequencies and detect the added mass by the changes in natural frequencies.This detection mechanism highly depends on the quality factor(Q-factor)of the sensors used.During the fabrication of the micro-diaphragms,prestress will be produced inevitably,and can significantly affect the Q-factor of resonators.It has been concluded that the increase of pre-stress can evaluate the Q-factor of resonators operating in vacuum significantly.However,numerous applications require these devices to operate in fluid environment.Due to the fluid interaction dependent damping,the applications of these devices have been heavily limited by low Q-factor in fluid environment.Therefore,it is of great importance to study the effects of fluid damping and pre-stress on the characteristics of circular diaphragm-based resonators.This paper proposed a Rayleigh-Ritz method to study the effects of fluid damping and pre-stress on the free vibrations of diaphragm-based resonators.Instead of the Bessel function used in the traditional method,a series of polynomial functions are used to construct the mode shape of the diaphragm.The natural frequencies,the nondimensional added virtual mass incremental factors and the quality factors can be easily obtained.The numerical results are validated by comparisons with published theoretical results.A fluid-structure coupling model is constructed by the finite element simulation software,and the results of simulation and theory show a good agreement.In addition,the results derived from the approximate mode shape and exact mode shape are compared.The results show that the effects of fluid damping and pre-stress on the performance of resonators are mainly caused by the change in mode shape.For lower mode,the dynamic characteristics of a diaphragm,including mode shapes,frequencies and quality factors,can be obtained by the approximate or exact mode shape.However,for higher modes,the error caused by the approximate mode shape is non-ignorable.Therefore,it is necessary to derive the dynamic response of a diaphragm by the exact mode shape.When operating in a fluid environment,the frequencies and the nondimensional added virtual mass incremental factors increase with the increase in pre-stress,while the vibration amplitudes and the quality factors show an opposite trend.When the pre-stress increases,the variations of the quality with respect to the mode number are different.For a plate,the quality factor decrease with the increase in mode number;for a membrane,the quality factor increase with in increase in mode number;and the change of quality factor with mode number is not monotonous for a diaphragm.