Static And Dynamic Behaviors Of Functionally Graded Pipes Conveying Fluid

In this study,static and dynamic behaviors of fluid-conveying pipes that are made of functionally graded materials are studied.Heterogenous material properties of the pipe,such as Young’s modulus,mass density and Poisson ratio,are assumed to vary continuously and smoothly across the radius,with a modified power-law function to represent the porous functionally graded materials.Based on the Euler-Bernoulli beam theory,planar and nonplanar nonlinear models of fluid-conveying pipes are considered in present work.Then,the accuracy and versatility of the proposed models are compared with existing research models.Based on theoretical analysis and numerical simulation,detailed parametric studies for the static and dynamic behaviors of the pipe sysytem are carried out numerically,with the effects of gradient index,porosity volume fraction and fluid velocity being discussed.Some important nonlinear behaviors are obtained,which have not been examined and reported before.In contrast to the existing research results,the present work has the following features:1.The nonlinear free and forced vibrations of fluid-conveying functionally graded pipes,which rest on nonlinear elastic foundation,are investigated.For the free vibration problem,the variational iteration method is adopted to obtain the analytical solutions of the nonlinear frequency,critical fluid velocity and free response;as for the forced vibration,system characteristics for the non-resonance case and primary resonance cases of this system are proposed using the method of multiple scales.The numerical analysis indicates that the variations of nonlinear frequency and critical fluid velocity are sensitive to the gradient index,porosity volume fraction and porosity distribution type.Moreover,non-resonance response has an exponential decreasing trend with respect to time,and in primary resonance analysis,the frequency-and force-response curves present hardening nonlinearity.2.The analytical study about the buckling and post-buckling vibration of an initially imperfect pipe is given,mainly focusing on the imperfection sensitivy to the buckling form of the pipe.Analytical solutions for critical fluid velocity and nonlinear static response are obtained and a complex solution procedure is proposed to study the post-buckling vibration characteristics,such as natural frequency and mode shape.The result demonstrates that the initial imperfection causes asymmetrical response and even influences the post-buckling frequency and mode shape.Moreover,this response asymmetry is also influenced by gradient index,porosity volume fraction and length-to-radius ratio.3.The nonlinear local and global dynamics of the functionally graded pipe conveying pulsatile fluid are studies.The governing equations are given based on higher order geometric nonlinearity.And using Galerkin method and pseudo-arclength continuation method,we obtain the amplitu-frequency curve and global bifurcation diagram.In numerical analysis,the pre-buckling resonance response of the perfect system exhibit hardening nonlinearity and cyclicfold bifurcation of periodic oscillation are detected;however,the imperfect system could present hardening,softening or softening-hardening nonlinearities,depending on the fluid velocity;the resonance response of the buckled pipe only exhibit softening nonlinearity.Moreover,the softening and hardening nonlinearities are also influenced by functionally graded material parameters.Through the phase-plane plot,time history and power spectrum diagram,complex periodic,quasi-periodic and chao motions are observed.4.The three-dimensional nonlinear forced vibration of the functionally graded pipe is studied under multi-direction excitation.The reduced-dimension model is obtained by employing Galerkin method and is solved by using the pseudo-arclength continuation method.The primary resonance response is deeply studied with the effects of material parameters,fluid velocity and load direction taken into account.The numerical results depict that nonplanar system have pitchfork bifurcation and Neimark-Sacker bifurcation leading to nonplaner solution branches,compared with the planar system.With considering the multi-direction excitation,the load direction influences the structural symmetry,the asymmetrical evolution of the basin of attraction,and the type and number of bifurcations.Finally,some concluding remarks are summarized and some plans for future works are given.