The stability and local bifurcation of the lateral parameter-excited resonance of pipes induced by the pulsating fluid velocity and thermal load are studied. A mathematical model for a simply supported pipe is develop...The stability and local bifurcation of the lateral parameter-excited resonance of pipes induced by the pulsating fluid velocity and thermal load are studied. A mathematical model for a simply supported pipe is developed according to Hamilton principle. The Galerkin method is adopted to discretize the partial differential equations to the ordinary differential equations. The method of multiple scales and the singularity theory are utilized to analyze the stability and bifurcation of the trivial and non-trivial solutions. The transition sets and bifurcation diagrams are obtained both in the unfolding parameter space and physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe. The numerical results demonstrate the accuracy of the single-mode expansion of the solution and verify the stability and local bifurcation analyses. The critical thermal rates are obtained both by the numerical simulation and the local bifurcation analysis. The natural frequency of lateral vibration decreases as the mean fluid velocity or the thermal rate increases according to the numerical results. The present work can provide valuable information for the design of the pipeline and controllers to prevent structural instability.展开更多
The basic concepts, normal forms and universal unfoldings of Zn-equivariant singularity are investigated in the present paper. As an example, the normal forms and universal unfoldings of Zi-singularity are formulated....The basic concepts, normal forms and universal unfoldings of Zn-equivariant singularity are investigated in the present paper. As an example, the normal forms and universal unfoldings of Zi-singularity are formulated. As a matter of fact, the theory provides a useful tool to study the subharmonic resonance bifurcation of the periodic parameter-excited system.展开更多
基金Supported by the Natural Science Foundation of Shandong Province of China(No.ZR2013AL017)the Fundamental Research Funds for the Central Universities of China(No.11CX04049A,No.12CX04071A)
文摘The stability and local bifurcation of the lateral parameter-excited resonance of pipes induced by the pulsating fluid velocity and thermal load are studied. A mathematical model for a simply supported pipe is developed according to Hamilton principle. The Galerkin method is adopted to discretize the partial differential equations to the ordinary differential equations. The method of multiple scales and the singularity theory are utilized to analyze the stability and bifurcation of the trivial and non-trivial solutions. The transition sets and bifurcation diagrams are obtained both in the unfolding parameter space and physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe. The numerical results demonstrate the accuracy of the single-mode expansion of the solution and verify the stability and local bifurcation analyses. The critical thermal rates are obtained both by the numerical simulation and the local bifurcation analysis. The natural frequency of lateral vibration decreases as the mean fluid velocity or the thermal rate increases according to the numerical results. The present work can provide valuable information for the design of the pipeline and controllers to prevent structural instability.
文摘The basic concepts, normal forms and universal unfoldings of Zn-equivariant singularity are investigated in the present paper. As an example, the normal forms and universal unfoldings of Zi-singularity are formulated. As a matter of fact, the theory provides a useful tool to study the subharmonic resonance bifurcation of the periodic parameter-excited system.
