Stability and Bifurcation Analysis of a Pipe Conveying Pulsating Fluid with Combination Parametric and Internal Resonances

[摘要] The stability and bifurcations of a hinged-hinged pipe conveying pulsating fluid with combination parametric and internal resonances are studied with both analytical and numerical methods. The system has geometric cubic nonlinearity. Three types of critical points for the bifurcation response equations are considered. These points are characterized by a double zero and two negative eigenvalues, double zero and a pair of purely imaginary eigenvalues, and two pairs of purely imaginary eigenvalues, respectively. With the aid of normal form theory, the expressions for the critical bifurcation lines leading to incipient and secondary bifurcations are obtained. Possible bifurcations leading to 2-D tori are also investigated. Numerical simulations confirm the analytical results.

[学科分类] 计算数学

[关键词] pipe with pulsating fluid;nonlinear vibration;perturbation methods;parametric resonances;stability;bifurcation