Abstract
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.
Highlights
The linear and nonlinear dynamics of pipes conveying fluid has been studied widely during the last decades
A lot of investigations based on linearized analytical models of these parametric instability problems for supported pipes were done by Chen [4], Padoussis and Issid[5], Padoussis and Sundararajan [6], Ginsberg [7] and Ariaratnam and Namachchivaya [8], Jayaraman and Tien [9]
In [10], Panda and Kar studied the nonlinear dynamics of a hingedhinged pipe conveying pulsating fluid subjected to combination and principle parametric resonance in the presence of internal resonance with the method of multiple scales and numerical methods
Summary
The linear and nonlinear dynamics of pipes conveying fluid has been studied widely during the last decades. A lot of investigations based on linearized analytical models of these parametric instability problems for supported pipes were done by Chen [4], Padoussis and Issid[5], Padoussis and Sundararajan [6], Ginsberg [7] and Ariaratnam and Namachchivaya [8], Jayaraman and Tien [9]. They studied the parametric and combination resonances and evaluated instability with numerical methods. The stability and bifurcations of a hinged-hinged pipe conveying pulsating fluid with combination parametric and internal resonances are studied both analytically and numerically. Numerical simulations are given, which verify the analytical results
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