Vibration Characteristics Of Micro/Nano Mass Sensor Via Nonlocal Elasticity Theory

Materials and structures at nano scale such as carbon nanotubes and graphenesheets, have small scale, low weight, extremely high rigidity as well as high intensity,and are highly sensitive to their environment change. Therefore, they are very promisingcandidates as atomic-resolution mass sensors that are used to detect the micro-masssuch as bacteria, virus or molecule of some gas. The principle of mass detection usingthe nanosized mass sensor from a vibration analysis is in quantifying the change in itsresonant frequency due to added mass. Therefore, the study of the vibrationcharacteristic of carbon nanotubes/graphenes based mass sensor is significant both intheory and in practical application. The emphasis of this dissertation is to establishtheoretical models suiting for dynamic behaviors of micro/nano-mass sensor. Themodels are based on nonlocal elasticity theory, which captures scale-dependent elasticmodulus of carbon nanotubes/graphenes. The transfer function method(TFM) orGalerkin method is used to solve the governing equations. The main achievements aresummarized as follows:The nonlocal Euler beam model is established to analyze the vibrationcharacteristics of single-walled carbon nanotube(SWCNT) based mass sensor. ASWCNT mass sensor carrying an attached micro-mass is modeled as a nonlocal Eulerbeam with a concentrated mass. Taking into account the support conditions ofcantilevers and clamped-clamped beams, the governing equations are solved by TFM.Furthermore, the critical buckling stress and natural frequencies of the SWCNT basedsensors under initial axial stress are computed using TFM. The effects of nonlocalparameter, attached mass, support condition and axial stress on the natural frequenciesand frequency shifts are discussed. The obtained results show that the mass sensitivityof the carbon nanotube based mass sensor can reach at least10-21g.Nonlocal Euler beam model for vibration characteristic analysis of double-walledcarbon nanotube (DWCNT) based mass sensor is established. The DWCNT mass sensorcarrying a nanoparticle is modeled as two nonlocal Euler-Bernoulli beams, and theinteraction between two tubes is governed by van der Waals force. The nonlocal Eulerbeam theory and TFM are used to analyze the vibration characteristic of cantilever andclamped-clamped DWCNT with different inner and outer wall lengths. Moreover, theeffect of different initial axial stress in inner tubes and outer tubes on the naturalfrequencies and frequency shift of clamped DWCNT based sensor is discussed.A nonlocal Timoshenko beam model is established to analyze the dynamicbehavior of SWCNT based mass sensor. Taking into account the effects of sheardeformation and rotary inertia, the nonlocal Timoshenko beam model with aconcentrated mass is used to model a SWCNT sensor with an attached micro-mass. The natural frequencies are computed by the TFM. The difference of the vibrationcharacteristic of SWCNT according to the theories of Timoshenko beams and of Eulerbeams is analyzed. The results show that Timoshenko beam model is more adequatethan Euler beam model, especially for short beams or higher-order vibration modes.Nonlocal Timoshenko beam model for vibration characteristic of multiwall-walledcarbon nanotubes(MWCNT) based mass sensor is established. Based on the nonlocalTimoshenko beam model, TFM is used to obtain the natural frequencies of theclamped-free and clamped-clamped DWCNT with different inner and outer wall lengths.The natural frequencies of a MWCNT-based biosensor carrying a spherical nanoscalebio-object at the free end are calculated using the nonlocal Timoshenko beam theoryand TFM. The influence of the rotary inertia of the bio-object itself is considered. Thedifference between single-walled and double-walled Timoshenko model, as well as theTimoshenko and Euler beam theory in vibration of DWCNT based mass sensor isanalyzed. The results show that the rotary inertia decreases the fundamental frequenciesof MWCNT based biosensor.The nonlocal Kirchhoff plate model is established for vibration characteristic ofsingle-layered graphene sheet (SLGS) based mass sensor. Using the nonlocal Kirchhoffplate theory, the dynamic governing equations of the rectangle and circular SLGS withan attached micro-mass is derived under Cartesian coordinate system and cylindricalcoordinate system, respectively. The Galerkin method is used to obtain the naturalfrequencies. In the analysis, the clamped and simply supported support conditions areboth considered. The effect of nonlocal parameter, attached mass and the shape ofSLGS on the natural frequency are discussed.The elastic modulus of materials and structures at nano scale exhibits strongscale-dependent property, and this property cannot be interpreted by the classicalcontinuum mechanics approach. In the present dissertation, the nonlocal elasticitytheory is developed to study the vibration of CNT/grapheme based micro/nano-masssensor. Moreover, the classical TFM and Galerkin method are extended tomicro-/nano-mechanics. The obtained results provide a theoretical foundation and arehelpful to the design of CNT/SLGS based resonator as nanomechanical mass sensor.