Vibration Characteristics Of Nanostructures Embedded In Viscoelastic Medium Via Nonlocal Theory

Vibration analysis of nanostructures has become a research hotspot in the field of nanomechanics in recent years.Taking carbon nanotubes(CNTs),piezoelectric nanobeams and nanoplates,flexoelectric nanobeams and nanoplates as the research object in this dissertation,the vibration characteristics of typical nanostructures embedded in viscoelastic medium are studied,the nonlocal model for vibration analysis of nanostructures is developed,the transfer function method(TFM)for vibration analysis is proposed,and the influences of various factors(such as nonlocal parameter,piezoelectric effect,flexoelectric effect,magnetic field and viscoelastic medium)on the vibration characteristics of nanostructures are investigated.The main work and achievements are summarized as follows:The nonlocal model is established for vibration analysis of single-walled carbon nanotubes(SWCNTs)embedded in viscoelastic medium.Based on the nonlocal Euler-Bernoulli beam model,the governing equations of motion are derived for the embedded SWCNT subjected to longitudinal magnetic field by introducing the general Maxwell model,Winkler viscoelastic foundation model and Lorentz magnetic forces.Then the TFM is utilized to obtain the natural frequencies in closed form for the SWCNT with arbitrary boundary conditions.The developed mechanics model and solving method are validated by comparing the obtained results with those available in the literature.On this basis,the effects of nonlocal parameter,boundary conditions,longitudinal magnetic field and surrounding viscoelastic medium are discussed in detail for vibration characteristics of SWCNTs.A nonlocal model is proposed for vibration analysis of double-walled carbon nanotubes(DWCNTs)embedded in viscoelastic medium.In doing this,the governing equations of embedded DWCNTs subjected to longitudinal magnetic field are established considering the surrounding viscoelastic medium,longitudinal magnetic field and intertube van der Waals forces simultaneously.The natural frequencies in closed form of DWCNTs with arbitrary boundary conditions are computed by using the TFM.Also,the influences of nonlocal parameter,boundary conditions,longitudinal magnetic field and surrounding viscoelastic medium on the vibration characteristics of DWCNTs are examined.The obtained results show that the strongest influence of longitudinal magnetic field on the natural frequencies can be achieved for the DWCNTs at a certain value of aspect ratio.The nonlocal model for vibration analysis of horn-shaped SWCNTs embedded in viscoelastic medium is proposed.The governing equations of embedded horn-shaped SWCNTs subjected to longitudinal magnetic field are first derived by considering the variable cross-section.Subsequently,the perturbation method(PM)and TFM are employed to compute the natural frequencies of horn-shaped SWCNTs with arbitrary boundary conditions.This is followed by a detailed parametric study of the effects of nonlocal parameter,longitudinal magnetic field and taper parameter on the vibration responses of the horn-shaped SWCNT.The results show that nonlocal effect on the natural frequencies decreases significantly with increasing both taper parameter and the strength of longitudinal magnetic field.The nonlocal model is established for thermo-electro-mechanical vibration analysis of piezoelectric nanobeams embedded in viscoelastic medium.The governing equations of embedded piezoelectric nanobeams are derived by considering nonlocal effect,piezoelectric effect and thermo-electro-mechanical loadings simultaneously.The natural frequencies in closed form for piezoelectric nanobeams with arbitrary boundary conditions are obtained by using the TFM.Moreover,the effects of nonlocal parameter,boundary conditions,external electric voltage,temperature change and initial biaxial force are carefully discussed.The results indicate that it is possible to find optimal aspect ratios of piezoelectric nanobeams for the most sensibility of natural frequencies to the external electric voltage,temperature change and initial biaxial force.The nonlocal model is proposed for vibration analysis of flexoelectric nanobeams embedded in viscoelastic medium.Taking nonlocal effect,piezoelectric effect,flexoelectric effect and viscoelasticity of surrounding medium into account,the governing equations of the system are established.The TFM is then utilized to solve the governing equations to obtain the natural frequencies in closed form for flexoelectric nanobeams with arbitrary boundary conditions.A detailed parametric study is also conducted,which shows that the rigidity of the nanobeam is enhanced by the flexoelectricity.In addition,the effect of flexoelectricity turns out to be less pronounced as nonlocal parameter and slenderness ratio increase or mode number and electric voltage decrease.The nonlocal model is developed for thermo-electro-mechanical vibration analysis of piezoelectric nanoplates resting on a viscoelastic foundation.Based on the nonlocal Kirchhoff plate model,the governing equations for piezoelectric nanoplates resting on a viscoelastic foundation are derived by considering nonlocal effect,piezoelectric effect,viscoelasticity of surrounding medium and thermo-electro-mechanical loadings simultaneously.A new numerical approach called the Galerkin strip distributed transfer function method(GSDTFM)is proposed to solve the mathematical problem which can not write out the explicit expression of the energy function in physics.The semi-analytical solutions of natural frequencies are also obtained for piezoelectric nanoplates with arbitrary boundary conditions.In addition,the influences of nonlocal parameter,boundary conditions,viscoelastic medium,external electric voltage,increment temperature and biaxial forces are examined for the vibration characteristics of piezoelectric nanoplates.The nonlocal model is established for vibration analysis of flexoelectric nanoplates resting on viscoelastic medium.By using Hamilton's principle,the governing equations of flexoelectric nanoplates resting on viscoelastic medium are derived.Moreover,the GSDTFM is applied to obtain the semi-analytical solutions of natural frequencies for flexoelectric nanoplates with arbitrary boundary conditions.The influences of nonlocal parameter,boundary conditions,flexoelectric coefficient,temperature change and viscoelastic medium on vibration characteristics are also investigated.In conclusion,the theoretical analytic model and transfer function method are developed based on the nonlocal theory for vibration analysis of typical nanostructures embedded in viscoelastic medium.The present work can provide a theoretical foundation for the applications of nanostructures in the fields of nanosensors,micro/nano-electromechanical systems and nanogenerators.