Nonlinear Resonant Responses, Mode Interactions, and Multitime Periodic and Chaotic Oscillations of a Cantilevered Pipe Conveying Pulsating Fluid under External Harmonic Force

Abstract

The nonlinear resonant responses, mode interactions, and multitime periodic and chaotic oscillations of the cantilevered pipe conveying pulsating fluid are studied under the harmonic external force in this research. According to the nonlinear dynamic model of the cantilevered beam derived using Hamilton’s principle under the uniformly distributed external harmonic excitation, we combine Galerkin technique and the method of multiple scales together to obtain the average equation of the cantilevered pipe conveying pulsating fluid under 1 : 3 internal resonance and principal parametric resonance. Based on the average equation in the polar form, several amplitude-frequency response curves are obtained corresponding to the certain parameters. It is found that there exist the hardening-spring type behaviors and jumping phenomena in the cantilevered pipe conveying pulsating fluid. The nonlinear oscillations of the cantilevered pipe conveying pulsating fluid can be excited more easily with the increase of the flow velocity, external excitation, and coupling degree of two order modes. Numerical simulations are performed to study the chaos of the cantilevered pipe conveying pulsating fluid with the external harmonic excitation. The simulation results exhibit the existence of the period, multiperiod, and chaotic responses with the variations of the fluid velocity or excitation. It is found that, in the cantilevered pipe conveying pulsating fluid, there are the multitime nonlinear vibrations around the left-mode and the right-mode positions, respectively. We also observe that there exist alternately the periodic and chaotic vibrations of the cantilevered pipe conveying pulsating fluid in the certain range.

Active Kriging-Based Adaptive Importance Sampling for Reliability and燬ensitivity Analyses of Stator Blade Regulator

“…To assess the effect of x i on the failure probability in its entire distribution ranges, a global sensitivity index is established [74,75] as (17) where P f | x i indicates the conditional failure probability, which can be rewritten as the condition expectation of the indicator function…”

“…Engineering practice shows that the HCF failure occurred in multiple rocker arms has become the main failure mode and seriously affects the structural reliability of stator blade regulator [2][3][4][5][6][7][8][9]. Moreover, on account of the multiple uncertainties of material variabilities, load variations and model randomness [10][11][12][13][14][15][16][17], large random behaviors physically emerge in these HCF lives [18][19][20][21][22][23][24][25]. Therefore, it is required to develop reasonable probabilistic analysis methods to address these multiple uncertainties, quantify the stochastic behaviors, and ensure the structural reliability of stator blade regulator.…”

Resonance response of fluid-conveying pipe with asymmetric elastic supports coupled to lever-type nonlinear energy sink

“…Meanwhile, various computation approaches and techniques have been developed and used to obtain geometrically exact governing equations [21][22][23] , to investigate the nonlinear dynamics and stability of the system [24][25][26][27][28] , and to calculate the resonance response [29] . Other researchers explore the material effects on resonance attenuation [30][31] , especially soft materials [32] .…”

Nonlinear Vibration Analysis for Stiffened Cylindrical Shells Subjected to Electromagnetic Environment

“…Under the coupling effects of various complex excitations, the nonlinear vibrations and bifurcation phenomenon of stiffened cylindrical shells would be incurred and may lead to significant noises and resonance issues [36][37][38]. At present, there are more and more researches focusing on the frequency, chaotic motions, and instability for circular cylindrical shells under complex multiple excitations, and fruitful results have been achieved.…”