Uncertainty Analysis Of Natural Vibration Characteristics Of Functionally Graded Carbon Nanotube Reinforced Composite Structures

Functionally Graded Carbon Nanotube Reinforced Composite Structures(FG-CNTRCs)have such excellent properties as high stiffness,high strength,good flexibility,which have been widely used in micro-electro-mechanical systems.The thesis focuses on the free vibration of functionally graded carbon nanotube-reinforced composite structures.Based on the classical beam and plate theory,the dimensionless control differential equation is derived.In order to carry out the uncertainty analysis of natural vibration characteristics of beam and plate structure,the uncertain physical properties of functionally graded carbon nanotube reinforced composite beams are characterized based on the K-L extended random field method.The main contents of this paper include:(1)Considering the common functional gradient distribution form of carbon nanotubes,the effective physical parameters of FG-CNTRCs are obtained by the extended rule of mixture.Based on the Karhunen-Loeve expansion method of random field discretization and characterization,the eigenvalues,analytical solutions of eigenfunctions and multidimensional random field discretization methods of three common correlation models are compared and analyzed.It also reveals the influence of truncation and correlation length on the discrete accuracy of random fields.(2)The uncertainty analysis method of inherent characteristics of functionally graded carbon nanotube reinforced composite beams based on Galerkin method is studied.According to the Timoshenko beam theory and the first-order shear deformation theory,as well as the Hamilton variational principle,the dimensionless motion control differential equation of the FG-CNTRCs beam is derived and established.The Galerkin method is used to discretize the motion partial differential equation and the solution is obtained.The natural frequency is compared with the results obtained by the Ritz method and the differential quadrature(DQ)method.Based on the two-dimensional random field developed by K-L method,the uncertainty analysis of the natural frequency of the FG-CNTRCs beam and the analysis of its probability and statistics characteristics are studied.The effects of CNT distributions,CNT volume fraction,slenderness ratio,boundary conditions on the stochastic property analysis are revealed.(3)The uncertainty analysis method of the inherent characteristics of the functionally graded carbon nanotube reinforced composite rectangular thin plates is studied.According to the classical plate theory,the first-order shear deformation theory and the Hamilton’s principle,the dimensionless motion differential equation is established.Galerkin method is used to discretize partial differential equations and the eigenvalues is solved.In the process of Ritz method,the orthogonal polynomial method is used to express the displacement function.And the maximum kinetic energy and maximum strain energy expressions of FG-CNTRCs plate are derived.By minimizing the Lagrangian energy function,the inherent characteristics are obtained.Three-dimensional random field based on K-L expansion was established to characterize the material properties of the FG-CNTRCs plate.Then stochastic natural frequency analysis is performed based on it.The volume rate random field was simulated 104 times to obtain the probability statistical distribution of the natural frequency.The effects of CNT distributions,width-to-thickness ratio,CNT volume fraction on the stochastic property analysis are also revealed.(4)The stability Analysis of functionally graded carbon nanotubes reinforced composites structures.Considering the FG-CNTRCs beam under axial pressure at one end,the governing equation of the buckling motion of the FG-CNTRCs beam is obtained according to the principle of minimum potential energy and variational principle.The maximum critical buckling load of the FG-CNTRCs beam is solved based on the differential quadrature method and the stability analysis is carried out.The probability distribution of dimensionless critical buckling load was obtained based on the K-L expansion random field of volume ratio and the differential quadrature method.The effects of CNT distributions,CNT volume fraction,slenderness ratio,boundary conditions on the stochastic random dimensionless critical buckling load are revealed.Considering the axial velocity of FG-CNTRCS plate,the critical instability velocity change with the axial movement speed is studied.And the influences of CNT volume fraction and width-to-thickness ratio on the critical instability velocity are discussed.