Numerical Study on the Free Vibration Behaviors of Functionally Graded CNT-Reinforced Composite Beams and Shells

Author:Fan Jian Yu

Supervisor:huang jin


Degree Year:2019





Carbon nanotubes(CNTs)are new advanced materials with high strength,high stiffness,low density and high aspect ratio,which have been considered as a promising reinforcement of polymer composites.Functionally graded materials(FGMs)are a new breed of composite materials with properties that spatially according to a certain non-uniform distribuution of the reinforcement phase.In order to maximize the enhancement of CNTs in the matrix material and further improve the mechanical properties of structures,the functionally graded distribution pattem of reinforcement has been successfully applied for CNT-reinforced composites.In actual applications,functionally graded CNT-reinforced composites(FG-CNTRCs)may be incorporated in the form of beams,plates,or shells as structural components.Exploring the mechanical behaviors of FG-CNTRC beams,plates and shells in complex environment is of great significance for their design and application.In the present study,the free vibration behaviors of FG-CNTRC beams and shells in the given environment are investigated by means of the combination of theoretical derivation and numerical calculation,and the convergence and accuracy of the proposed numerical methods are evaluated.Furthermore,the influences of the material properties,loading conditions and geometric parameters on the vibration characteristics of structures are revealed.The main contents and achievements of this dissertation are as follows:1.The nonlinear free vibration analysis of FG-CNTRC beams resting on a nonlinear elastic foundation in a thermal environment is presented by means of the Haar wavelet discretization method(HWDM).Based on Hamilton principle,the nonlinear governing equations of CNTRC beams resting on nonlinear elastic foundations in thermal environment are derived,which not only introduces the influence of nonlinear elastic foundation but also considers the effects of the temperature-dependent material properties and the initial thermal stress.The obtained nonlinear governing equations are solved by means of the HWDM in conjunction with a direct iteration technique,which produced the linear and nonlinear natural frequencies of the beam.The convergence and comparison studies are carried out,and the results indicate that the proposed method has stable convergence and good accuracy.The effects of CNT volume fraction,distribution type of CNTs,foundation stiffness coefficients,boundary condition,temperature rise,and initial thermal stress on the linear frequencies and the nonlinear frequency ratios are also reported.The numerical results indicate that the beams with FG-X distribution have higher natural frequencies than other types.Moreover,the nonlinear elastic foundation,the temperature rise and initial thermal stresses have significant effects on the nonlinear vibration behavior of CNTRC beams and cannot be neglected in design.The present method provides an effective way for the quantitative analysis of such nonlinear issues.2.The free vibration characteristics of FG-CNTRC open conical shells integrated with piezoelectric layers subjected to arbitrary elastically restrained boundary conditions are investigated.The boundary spring technique is used to implement elastically restrained boundary conditions.By means of the energy-oriented Rayleigh–Ritz method,the complete sets of electromechanically coupled governing equations are derived.Then the resulting governing equations are solved to obtain natural frequencies and mode shapes of the piezoelectric open conical shell.Parametric study is examined to reveal the influences of the boundary spring stiffnesses,electrical boundary condition,material properties,geometrical parameters,and temperatures on the vibration behaviors of the hybrid shell.The numerical results indicate that the hybrid shell with the open-circuit electrical boundary condition has a higher fundamental frequency than that with the closed-circuit one.The natural frequencies of the hybrid shell under arbitrary boundary conditions,including classical and elastic ones,can be obtained by setting the boundary springs’ stiffness to proper value.Moreover,the increase in the temperature results in the decrease in the frequencies of the hybrid shell.3.The free vibration behaviors of FG-CNTRC conical-cylindrical combination shells(CCCSs)resting on elastic foundation are studies using the HWDM.The equations of motion for each individual shell segments on the elastic foundation are derived.Then the HWDM is respectively used to discretize the equations of motion for each individual segment,the displacement and force continuous conditions at the junction and the boundary conditions,which leads to a set of algebraic equations.The natural frequencies and modes of the CCCSs are achieved by solving the resulting algebraic equations.The convergence and accuracy of the proposed method are evaluated and the results demonstrate that the adopted HWDM has stable convergence,high efficiency and excellent accuracy.Furthermore,an exhaustive parametric study is conducted to reveal the effects of the foundation stiffness coefficients,boundary conditions,material properties and geometric parameters on the natural frequencies of the CCCS.The results show that the natural frequencies of the CCCSs are greatly influenced by the elastic foundation,which should not be ignored in application.4.A novel numerical method based on the Walsh series(WS)is proposed for free vibration analysis of functionally graded material(FGM)and FG-CNTRC cylindrical shells.The convergence and comparison studies demonstrate that the proposed method has the characteristics of simple implementation,stable convergence and good accuracy.In addition,a parametric study is carried out to examine the effects of several significant aspects including boundary conditions,material propeties,and geometric parameters on the natural frequencies of FGM and FG-CNTRC cylindrical shells.The WS method proposed in this study offers a new and effective approach for the mechanical analysis of composite plates and shells.This study provides theoretical support for the application of functionally graded CNT-reinforced composites in actual engineering.