This study examines the nonlinear behaviors of a clamped-clamped porous pipe made of a functionally graded material(FGM)that conveys fluids and is equipped with a retaining clip,focusing on primary resonance and subcr...This study examines the nonlinear behaviors of a clamped-clamped porous pipe made of a functionally graded material(FGM)that conveys fluids and is equipped with a retaining clip,focusing on primary resonance and subcritical dynamics.The nonlinear governing equations for the FGM pipe are derived by the extended Hamilton's principle,and subsequently discretized through the application of the Galerkin method.The direct method of multi-scales is then used to solve the derived equations.A thorough analysis of various parameters,including the clip stiffness,the power-law index,the porosity,and the clip location,is conducted to gain a comprehensive understanding of the system's nonlinear dynamics.Through the analysis of the first natural frequency,the study highlights the influence of the flow velocity and the clip stiffness,while the comparisons with metallic pipes emphasize the role of FGM composition.The examination of the forced response curves reveals saddle-node bifurcations and their dependence on parameters such as the detuning parameter and the power-law index,offering valuable insights into the system's nonlinear resonant behavior.Furthermore,the frequency-response curves illustrate the hardening nonlinearities influenced by factors such as the porosity and the clip stiffness,revealing nuanced effects on the system response and resonance characteristics.This comprehensive analysis enhances the understanding of nonlinear behaviors in FGM porous pipes with a retaining clip,providing key insights for practical engineering applications in system design and optimization.展开更多
Although most pipes are restrained by retaining clips in aircraft,the influence of the clip parameters on the vibration of the fluid-conveying pipe has not been revealed.By considering the clip width,a new dynamic mod...Although most pipes are restrained by retaining clips in aircraft,the influence of the clip parameters on the vibration of the fluid-conveying pipe has not been revealed.By considering the clip width,a new dynamic model of a fluid-conveying pipe restrained by an intermediate clip is established in this paper.To demonstrate the necessity of the proposed model,a half pipe model is established by modeling the clip as one end.By comparing the two models,it is found that the half pipe model overestimates the critical velocity and may estimate the dynamical behavior of the pipe incorrectly.In addition,with the increase in the clip stiffness,the conversion processes of the first two modes of the pipe are shown.Furthermore,by ignoring the width of the clip,the effect of the flow velocity on the accuracy of a concentrated restraint clip model is presented.When the flow velocity is close to the critical velocity,the accuracy of the concentrated restraint clip model significantly reduces,especially when the width of the clip is large.In general,the contribution of this paper is to establish a dynamic model of the fluid-conveying pipe which can describe the influence of the clip parameters,and to demonstrate the necessity of this model.展开更多
文摘This study examines the nonlinear behaviors of a clamped-clamped porous pipe made of a functionally graded material(FGM)that conveys fluids and is equipped with a retaining clip,focusing on primary resonance and subcritical dynamics.The nonlinear governing equations for the FGM pipe are derived by the extended Hamilton's principle,and subsequently discretized through the application of the Galerkin method.The direct method of multi-scales is then used to solve the derived equations.A thorough analysis of various parameters,including the clip stiffness,the power-law index,the porosity,and the clip location,is conducted to gain a comprehensive understanding of the system's nonlinear dynamics.Through the analysis of the first natural frequency,the study highlights the influence of the flow velocity and the clip stiffness,while the comparisons with metallic pipes emphasize the role of FGM composition.The examination of the forced response curves reveals saddle-node bifurcations and their dependence on parameters such as the detuning parameter and the power-law index,offering valuable insights into the system's nonlinear resonant behavior.Furthermore,the frequency-response curves illustrate the hardening nonlinearities influenced by factors such as the porosity and the clip stiffness,revealing nuanced effects on the system response and resonance characteristics.This comprehensive analysis enhances the understanding of nonlinear behaviors in FGM porous pipes with a retaining clip,providing key insights for practical engineering applications in system design and optimization.
基金supported by the National Science Funds for Distinguished Young Scholars of China(No.12025204)the Shanghai Municipal Education Commission of China(No.2019-01-07-00-09-E00018)。
文摘Although most pipes are restrained by retaining clips in aircraft,the influence of the clip parameters on the vibration of the fluid-conveying pipe has not been revealed.By considering the clip width,a new dynamic model of a fluid-conveying pipe restrained by an intermediate clip is established in this paper.To demonstrate the necessity of the proposed model,a half pipe model is established by modeling the clip as one end.By comparing the two models,it is found that the half pipe model overestimates the critical velocity and may estimate the dynamical behavior of the pipe incorrectly.In addition,with the increase in the clip stiffness,the conversion processes of the first two modes of the pipe are shown.Furthermore,by ignoring the width of the clip,the effect of the flow velocity on the accuracy of a concentrated restraint clip model is presented.When the flow velocity is close to the critical velocity,the accuracy of the concentrated restraint clip model significantly reduces,especially when the width of the clip is large.In general,the contribution of this paper is to establish a dynamic model of the fluid-conveying pipe which can describe the influence of the clip parameters,and to demonstrate the necessity of this model.
基金supported by the National Science Funds for Distinguished Young Scholars (Grant No.12025204)the Shanghai Municipal Education Commission (Grant No.2019-01-07-00-09-E00018).
