Nonlinear Vibration Of Carbon Nanotubes Resonator Under Parametric Excitation

Carbon nanotube resonator system,as the main component of carbon nanotubesensors, attracts a lot of scholars and scientists to study. Relatively compared totraditional sensors, carbon nanotube sensor has further broaden the application fieldsof sensors by which includes excellent properties such as size miniaturization, lightquality, high precision, high sensitivity, high stability and operating convenience.Those sensors are widely used in fileds which are biochemistry, medicine, machinery,defense and aerospace etc. These sensors, based on carbon nanotube resonator system,have gas sensor, moisture sensor, pressure sensor, optical fiber nano fluorescencebiosensor, the light sensor, cell biosensor, nano stress sensors, nano probe and qualitysensors. According to the current research data, the research of carbon nanotuberesonator system is mainly concentrated in the various performance tests of theexperiment, such as the sensor validation, expansion and development, but its in termsof theory research is few, much less exploring the nonlinear dynamic response in thevarious parameters under the external excitation load and especially the nonlinearvibration has a great influence on the response of structure. Therefore, exploring thenonlinear dynamic response and effects under parametric excitation effect has thedeeper cognition and understanding for carbon nanotube resonator, and has importanttheoretical and practical significance for perfecting and making new functions tocarbon nanometer sensor.In this paper, the nonlinear vibration response of doubly-clamped carbonnanotube resonator under DC and AC harmonic excitation was investigated. Based onEuler Bernoulli beam theory, the nonlinear governing equations was derived by theHamilton’s principle where the nonlinear electrostatic force was disregarded and theprimary resonance of this system occurred when the excitation frequency wasapproaching to the natural frequency of the clamped-clamped carbon nanotube. In thiscase, the reduced-order equations were scattered by Galerkin method and the analysissolution of vibration response was obtained by perturbation method. Finally, itsamplitude frequency characteristic curve, bifurcation diagram and phase track diagramthat were obtained by the numerical software were carried on the thorough analysis.Then, the influence of the nonlinear dynamic response of the system was discussedunder some parametric excitation which includes damping, length, diameter, DC load, AC harmonic load and geometric cubic nonlinear terms or not without the initial axialforce condition, the initial axial force, the initial configuration and Van Der Waalsforce.