Surface Effects On The Dynamic Properties Of Micro And Nanomechanical Resonators

MEMS/NEMS are frontiers of interdisciplinary researches including mechanics,microelectronics,chemistry,which have many important applications in Mechatronics,Telematics,Aerospace,biomedicine,energy,the environment and so on.The rapid developments of micro and nanotechnology bring numerous unprecedented great challenges as well as new opportunities for the discipline of mechanical dynamics and vibration.As one of the key functional devices,high performance micro-and nanomechanical resonators also come up with many challenges for the dynamic theory and analysis method,such as the inherent surface characteristics of mechanical structures,adsorption-induced surface effect,surface stress,complex working environment including gas and liquid media.In this paper,we focus the topic on the model characterization of the mechanism of surface effects in micro-and nanomechanical resonators,surface effects on the dynamics of the devices,mechanism and method of experimental detection under surface adsorption.The main work is as follows:First,the modified continuous dynamical model and semi-continuous model are proposed to characterize the inherent surface effect of micro-and nanomechanical resonators due to the asymmetric atomic coordination number of the surface atoms.Considering the surface layer thickness,a modified core-shell model is developed to depict the scale-dependent Young's modulus of nanostructures,and the influence of surface layer thickness on the dynamical properties of devices has been revealed.Compare with the results of surface effects without considering the surface layer thickness,it is demonstrated that the surface layer thickness should be considered when the diameter of nanowires is smaller than 100 nm.Based on the above modified core-shell model,the semi-continuous and atomic model of surface effect under the surface relaxation and reconstruction has been developed,and the constitutive relation of the model satisfies the surface balance condition.The mechanical model of surface relaxation and reconstruction is established by the molecular statics method and energy method,and the relationship between the parameters(surface elasticity,surface density and surface residual stress)of the continuous model and the parameters(surface relaxation and reconstruction)of the atomic lattice model is derived to obtain the constitutive relation of semi-continuous model.Comparison of the results of the presented model with the reported experimental data validates the model.The results show the surface elasticity and density charge with the surface layer thickness exponentially.Surface elasticity and density mainly depends on the surface relaxation,surface residual stress depends on the surface reconstruction.In addition,the surface effect on the free vibrational frequencies of double-clamped nanobeams is further discussed.The work can be useful for the mechanism of the surface effect in the micro-and nanomechanical resonators.Second,based on the above model of surface effect,the influence of the inherent surface effect of nanostructures on the dynamical performance of the micro-and nanomechanical resonators.The theoretical model of the mode coupling in the nanomechanical resonators is developed based nonlocal elasticity theory.The scale effect on the strength of tension-induced intermodal coupling and the tuning effect of mode coupling on the pull-in instability and resonance frequency of the double-clamped beam resonators are analyzed.The results indicate that the coupling strength between the first in-plane mode and out-of-plane modes becomes stronger when the scale reduces,and the physical causes is that the introduction of the scale effect make energy transfer between different mechanical modes more easily.Moreover,surface effect on the crack propagation property of nanomechanical resonators and the dynamical behavior of the devices have been investigated,the inherent relationship between the surface effect and mixed mode crack propagation has been revealed,and the surface effect on the dynamical properties of cracked nanobeam is analyzed.The slant surface crack effect is proposed to demonstrate the intrinsic relation between the surface effect and the mixed mode surface crack propagation.The analytical expression of the stress intensity factor and the corresponding flexibility coefficient of I-mode and II-mode surface crack are derived by incorporating the surface residual stress into the crack tip stress field and a modified continue dynamical model of cracked nanobeams.The results indicated that the fracture toughness of mixed mode crack can be charged by the surface residual stress,and the flexibility coefficient symmetrically distributes with surface residual stress,which can postpone or accelerate the crack propagation.Therefore,it is significant that considering the intrinsic relation of surface energy and mixed crack propagation for the stress distribution of crack tip and the dynamical behaviors of resonators.Third,the paper has also presented the investigation of detection principle and experimental testing of the resonant sensors for adsorption-induce surface effects.A novel slowly varying parameter dynamical model of micromechanical sensors is proposed based on the modified Langmuir kinetic model,and the adsorption-induced surface effect on the nonlinear varying parameter vibration behavior of micromechanical resonant sensors is revealed.The mechanism and delay characteristics of in-situ real-time detection has been investigated.The relation between surface coverage rate and the analyte concentration is obtained by incorporating the slowly varying characteristics of the analyte concentration to modify the Langmuir kinetic model.Moreover,based on the modified Langmuir kinetic model,the slowly varying parameter dynamical model of the micromechanical resonant sensors under the coupled effect of surface adsorption and the inherent surface effect of nanostructures is developed by Hamilton principle.The mechanism of adsorption-induced surface effect and adsorption-induced frequency shift of the sensors are revealed.Furthermore,the nonlinear pull-in dynamical behavior of suspended multilayer graphene sensors under molecular adsorption is investigated.The electromechanical coupling model for suspended multilayer graphene sensors has been developed by inducing the built-in strain and two-sided fringing field effect.The results of built-in strains and pull-in voltage can well agree with the reported experimental data,and the tuning method of the pull-in voltages of the multilayer graphene sensors are discussed.The fracture failure and pull-in instability of the sensors are compared to derive the critical axial pre-stress of zigzag-oriented and armchair-oriented sensors.The results show that the pull-in voltages of sensors increase with temperatures due to the negative thermal expansion coefficient of graphene.Furthermore,the adsorption kinetic properties of gas molecules on the graphene surface have been studied experimentally,the adsorption times constant of different gas on the graphene surface have been tested,which validates the rationality of the adsorption nonlinear stiffness model.