Research On The Free Vibration Characteristics Of Nano-cylindrical Shells Based On Non-local Theory

Because cylindrical shell structural materials have good properties in thermal,electrical,magnetic and mechanical aspects that other materials do not have,this makes it widely used in mechanical,chemical,biomedical,aviation,and shipbuilding and other important industrial fields.The application of composite materials is becoming more and more extensive,and composite nano-cylindrical shell structural materials are one of the typical forms of composite materials.But when the size of the material is reduced to nanometers,the classical theory of continuity can no longer represent the scale effect.Based on the non-local theory,this thesis systematically studies the vibration characteristics of different nano-thin-walled cylindrical shells by using specific methods.The main contents are as follows:According to the Rayleigh-Ritz method,non-local theory and Schmidt orthogonalization method,the linear free vibration problem of single-layer nanocystical shells was studied.Using the set of orthogonal polynomials as the allowable function,the equations of motion of thin-walled cylindrical shells were derived using the Rayleigh-Ritz method.On this basis,non-local theory is introduced to obtain the differential equation of linear motion of a non-local monolayer nanocylindrical shell.The numerical solution of the nano-cylindrical shell under different boundary conditions was solved by differential product method.The numerical results show that with the continuous increase of non-local parameters,the frequency of nano-thin-walled cylindrical shells gradually decreases,and the magnitude of the reduction gradually increases.The geometric parameters and the number of ring waves have an important influence on the frequency of non-local monolayer nanoclindrical shells.According to non-local theory,Rayleigh-Ritz method and Lagrange equation,the linear free vibration problem of composite multilayer nanoclinical cylindrical shells was studied.On the basis of the linear free vibration of a single-layer nano-cylindrical shell,a non-local theory is introduced,a non-local composite multilayer nanocylindrical shell is derived from the linear motion differential equation,and the numerical solution of the multilayer nano-cylindrical shell is obtained by DQ method.The numerical results show that as the number of annular waves gradually increases,the frequency of nano-multilayer cylindrical shells gradually increases.With the continuous increase of non-local parameters,the frequency of composite multilayer nanoclinical shells gradually decreases.Geometric parameters have an important influence on the frequency of non-local multilayer nanocylindrical shells.According to Donnell’s nonlinear flat shell theory,non-local theory,Rayleigh-Ritz method and Lagrange equation,the nonlinear free vibration problem of composite multilayer nanocysterical cylindrical shells is studied.The frequency and corresponding modality of the non-local multilayer nanocylindrical shell were obtained by linear analysis,and the nonlinear motion differential equation of the non-local multilayer nanocylindrical shell was established by using the Lagrange equation.The Rayleigh-Ritz method was used to obtain the linear and nonlinear analytical solutions of multilayer nanocosks.It is found that non-local parameters have an important influence on the nonlinear free vibration of multilayer nanocylindrical shells.