Study On The Dynamic Characteristics Of Circular Micro-Diaphragms In Resonant Micro-biochemical Sensor

The resonant micro-biochemical sensor is one important form of micro-biochemical sensor.The performances of resonant micro-biochemical sensors depend mainly on the dynamic characteristics of micro-components.As a main structure form of resonant micro-components,micro-diaphragms have high quality factor both in gaseous and in liquids environments.Consequently,the study of micro-biochemical sensors based on micro-diaphragms gain much attention.In micro and nano scale,the dynamic characteristics of micro-diaphragms are influenced by surface effects,residual stresses,coupling effects of liquids and adsorption effects.Therefore,the combination of surface effects,coupling effects and adsoption effects is important to design the resonant micro-biochemical sensors.In this paper,taking the circular micro-diaphragm as the research object,the dynamic characteristics of circular micro-diaphragms with surface effects,mass loading of adsorbates,influence of liquids and residual stresses are analyzed.The main research aontents are shown as follows:Surface mechanical properties effects on two sides are considered to be different as one side of the diaphragm contacts with biochemical media.An analytical model is developed based on the thin plate theory and surface elasticity theory for the micro-diaphragm with different surface effects.The Galerkin procedure is used to solve the governing equation.The size-dependence of the natural frequency and mass sensitivity of the micro-diaphragm with different surface mechanical properties effects is discussed.Results show that the influences of different surface mechanical properties effects on the natural frequency and mass sensitivity are more significant for thinner micro-diaphragms.The influences depend on the differences in the surface mechanical properties of the two surfaces.If ?E0>0,the natural frequency and mass sensitivity increase with the decrease of thickness;If ?E0<0,the natural frequency and mass sensitivity decrease with the decrease of thickness.For both ?E0>0 and ?E0<0,the mass sensitivity increases as the non-dimensional distributed radius decreases.Ignoring the influence of adsorbates,the above model is reduced to a new model.The new model is used to analyze the influence of residual stresses on the vibration of a circular sensor diaphragm with surface effects.Analytical solutions are obtained by using the separate variable method.The results of the present model are compared with the model based on modified laminated plate theory.It is found that the influence of residual stresses on effective flexural rigidity can be ignored if the normalized tension parameter k is small;with the increase of k,the influence cannot be ignored,the results based on the present model are more accurate than the modified laminated plate theory.The influences of residual stresses on the vibration modes and natural frequency of the diaphragm are discussed.Results show that the transition range of vibration modes can be enlarged by the stiffened surface and be shortened by the softened surface.Considering the influences of liquids on the dynamic characteristics of a circular micro-diaphragm,the new model is used to discribe the vibration of micro-diaphragm attached a uniformly distributed mass.Assuming the liquid in infinite domain is incompressible and inviscid,the vibration of liquid is all caused by the vibration of micro-diaphragm,the movement of liquid can be described by the velocity potential.The approximate solution is obtained by introduceing the Hankel transformation and inverse transformation and using the Rayleigh-Ritz energy method.Then,the energy emission caused by acoustic radiation and the quality factor are obtained by far field method and Rayleigh surface integration.The influences of liquids on the natural frequency of the micro-diaphragm with surface effects were discussed.It is found that the natural frequency and quality factor of the micro-diaphragm in liquids have obvious size dependence.The stiffened surface decreases the quality factor while the softened surface increases the quality factor in liquids.If the thickness is less than 1×10-8,the natural frequency in liquids is only a small percentage of that in gas.The influence of liquids reduces with the increase of thickness.Moreover,the natural frequncy decreases with the increase of the liquid density.The circular micro-diaphragm can be simplified as a bilayered circular diaphragm based on the structure of the transducer.The governing equation of the bilayered circular plate including a piezoelectric layer is developed based on the Kirchhoff plate theory.Considering the energy emission caused by acoustic radiation and the effect of hysteresis characteristics of piezoelectric materials on the quality factor,the model of quality factor is developed.The results of the new model for a radius range of 300?m<a<700?m are between 66.3 and 86.7.Compared with the existing results and experiment,it is found that the results of new model are more consistent with the experimental values.Considering the surface effects in bilayered structures,the governing equation of a bilayered circular plate including surface effects is developed based on the Kirchhoff plate theory and continuum surface elasticity theory.The influence of the surface effects on the natural frequency of the bilayered circular micro-diaphragm is compared with that of the single layer circular micro-diaphragm.The results show that the natural frequency based on the single layer circular micro-diaphragm model will be small or large than the actual results;while it can be a very good prediction of the natural frequency by the present model.