Wave Propagation,Vibration And Stability Analyses Of Porous Nanostructures

In recent years,nanostructures have been widely used in mechanical,aerospace,and other fields.For example,nano-energy harvesters,nano-resonators,nano-generators and nano-actuators.Compared with macro-materials and structures,nanostructures have special size-dependent properties.It means that when the external dimension or volume of structures changes into nano-scale,the size effect,which can be neglected in macro size,become significant and should be considered in nano-or micro-scale structures.Since the classical continuum theory is unable to explain the new mechanical phenomena at nano scale appropriately due to the lack of size effect in constitutive equation,several nonclassical theories have been proposed,such as nonlocal elasticity theory,strain gradient theory,and nonlocal strain gradient theory.Since the non-local strain gradient theory can account for both stiffness softening effect and stiffness strengthening effect,and this theory has been verified by experiments,therefore,this theory has been widely applied in the analysis of vibration,buckling,bending,wave propagation and other fields of nanostructures.This thesis aims to do some exploratory researches in mechanics(vibration,buckling,bending)and acoustics(fluctuation)for porous nanotubes and nanobeams.By considering shear deformation,temperature field,pore changes,material changes and siz e effects,elastic foundations and boundary conditions,some mechanical behaviors of nanotubes and nanobeams are studied.In view of this,this paper can be divided into four parts:(1)Analysis of wave propagation in porous nanotubesThe wave propagation characteristics of porous nanotubes are studied,the governing equations are established by using the Hamiltonian variational principle and the non-local strain gradient theory.The exact expressions of longitudinal wave,shear wave and bending wave are obtained.The propagation characteristics of Timoshenko beam model and Eulerbernoulli beam model are studied in detail.This work is then extended to the case of the analysis of the wave propagation of doubled-layered porous nanotubes in Hygro-thermal environment.(2)Vibration analysis of porous nanotubesThe vibration characteristics of porous nanotubes are studied,the governing equation is established by using the Hamiltonian variational principle and the non-local strain gradient theory,and the Navier solution method is used to obtain the expression of the eigenvalue frequency.On this basis,we studied the nonlinear vibration of porous nanotubes based on the two-step perturbation method,and the effects of amplitude,shear deformation,temperature field,pore change,material change and size effect on linear vibration and nonlinear vibration are studied.(3)Thermal buckling and post-buckling analysis of porous nanotubesWe study the buckling and post-buckling problems of porous nanotubes,in the process of analysis,we consider shear effects,temperature effects,size effect,porosity effects,boundary conditions,materials variations and other factors.The governing equations are established based on the non-local theory and the Hamiltonian variational principle,and the asymptotic solution of the equation is obtained by using the two-step perturbation method.(4)Nonlinear bending analysis of porous nanotubes and nanobeamsThe nonlinear bending and snap-buckling of porous nanotubes are studied,the shear deformation effects,temperature effects,size effects,geometric dimensions,pore defects,boundary conditions,power law index and other effects are considered.The governing equations are established by using Hamiltonian variational principle and non-local strain gradient theory,and the asymptotic solution of the equation is solved by the two-step perturbation method.This work is then extended to the case of the nonlinear bending characteristics of porous curved nanobeams resting on nonlinear elastic foundations.The results show that the elastic foundation can improve the stability of the nanobeam.