The parametric excited vibration of a pipe under thermal loading may occur because the fluid is often transported heatedly. The effects of thermal loading on the pipe stability and local bifurcations have rarely been ...The parametric excited vibration of a pipe under thermal loading may occur because the fluid is often transported heatedly. The effects of thermal loading on the pipe stability and local bifurcations have rarely been studied. The stability and the local bifurcations of the lateral parametric resonance of the pipe induced by the pulsating fluid velocity and the thermal loading are studied. A mathematical model for a simply supported pipe is developed according to the Hamilton principle. Two partial differential equations describing the lateral and longitudinal vibration are obtained. The singularity theory is utilized to anMyze the stability and the bifurcation of the system solutions. The transition sets and the bifurcation diagrams are obtained both in the unfolding parameter space and the physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe. The frequency response and the relationship between the critical thermal rate and the pulsating fluid velocity are obtained. The numerical results demonstrate the accuracy of the single-mode expansion of the solution and the stability and local bifurcation analyses. It also confirms the existence of the chaos. The presented work can provide valuable information for the design of the pipeline and the controllers to prevent the structural instability.展开更多
The high temperature gas occurs behind shock or near the wall surface of vehicle in the hypersonic flight. As the temperature exceeds 2 000 K, 4 000 K, respectively, O2 and N2 molecules are successively dissociated. B...The high temperature gas occurs behind shock or near the wall surface of vehicle in the hypersonic flight. As the temperature exceeds 2 000 K, 4 000 K, respectively, O2 and N2 molecules are successively dissociated. Because of variable components at dif- ferent temperatures and pressures, the dissociated air is no longer a perfect gas, In this paper, a new method is developed to calculate accurate thermal physical parameters with the dissociation degree providing the thermochemical equilibrium procedure. Based on the dissociation degree, it is concluded that few numbers of equations and the solutions are easily obtained. In addition, a set of formulas relating the parameter to the dissociation degree are set up four-species, O2 molecule The thermodynamic properties of dissociated air containing and N2 molecule, O atom and N atom, are studied with the new method, and the results are consistent with those with the traditional equilibrium constant method. It is shown that this method is reliable for solving thermal physical parameters easily and directly.展开更多
基金Project supported by the National Natural Science Foundation of Shandong Province(No.ZR2013AL017)the National Natural Science Foundation of China(No.11272357)the Fundamental Research Funds for the Central Universities of China(No.11CX04049A)
文摘The parametric excited vibration of a pipe under thermal loading may occur because the fluid is often transported heatedly. The effects of thermal loading on the pipe stability and local bifurcations have rarely been studied. The stability and the local bifurcations of the lateral parametric resonance of the pipe induced by the pulsating fluid velocity and the thermal loading are studied. A mathematical model for a simply supported pipe is developed according to the Hamilton principle. Two partial differential equations describing the lateral and longitudinal vibration are obtained. The singularity theory is utilized to anMyze the stability and the bifurcation of the system solutions. The transition sets and the bifurcation diagrams are obtained both in the unfolding parameter space and the physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe. The frequency response and the relationship between the critical thermal rate and the pulsating fluid velocity are obtained. The numerical results demonstrate the accuracy of the single-mode expansion of the solution and the stability and local bifurcation analyses. It also confirms the existence of the chaos. The presented work can provide valuable information for the design of the pipeline and the controllers to prevent the structural instability.
基金supported by the National Natural Science Foundation of China(Nos.11732011,11672205,and 11332007)the National Key Research and Development Program of China(No.2016YFA0401200)
文摘The high temperature gas occurs behind shock or near the wall surface of vehicle in the hypersonic flight. As the temperature exceeds 2 000 K, 4 000 K, respectively, O2 and N2 molecules are successively dissociated. Because of variable components at dif- ferent temperatures and pressures, the dissociated air is no longer a perfect gas, In this paper, a new method is developed to calculate accurate thermal physical parameters with the dissociation degree providing the thermochemical equilibrium procedure. Based on the dissociation degree, it is concluded that few numbers of equations and the solutions are easily obtained. In addition, a set of formulas relating the parameter to the dissociation degree are set up four-species, O2 molecule The thermodynamic properties of dissociated air containing and N2 molecule, O atom and N atom, are studied with the new method, and the results are consistent with those with the traditional equilibrium constant method. It is shown that this method is reliable for solving thermal physical parameters easily and directly.
