Colored noise characterized by correlated time dependence is frequently encountered in practical engineering applications. This study investigates the random responses, reliability, and first-passage time of a fluid-conveying pipe subjected to colored noise excitations. The governing equation of the fluid-conveying pipe system excited by colored noise is derived based on the Hamilton principle. Subsequently, the probability density function (PDF) of the steady-state responses for the fluid-conveying pipe is calculated through the modified stochastic average method. The effectiveness of the analysis results is verified through the Monte Carlo method. Additionally, PDFs of reliability and first-passage time are obtained by solving the backward Kolmogorov equation using the finite difference approach. The influences of fluid speed, noise intensity as well as filter factor on the dynamic behavior of the system are discussed. Specifically, their effects on the PDFs with amplitude and energy for dynamic characteristics, as well as on reliability and the first-passage time are analyzed. The results indicate that the increasing fluid speed leads to greater maximum displacement, larger total energy, decreased reliability, and earlier first-passage time for the pipe system. Conversely, an increase in the filter coefficient causes the greater maximum displacement, decreased total energy, improved dynamic reliability, and delayed first-passage time for the pipe system. These findings provide valuable insights into the design and operation of pipe systems under colored noise excitations.
AsnafiA (2017) Dynamic stability recognition of cylindrical shallow shells in Kelvin–Voigt viscoelastic medium under transverse white noise excitation. Nonlinear Dynamics90: 2125–2135.
2.
ChenLZhuW (2009) The first passage failure of SDOF strongly nonlinear stochastic system with fractional derivative damping. Journal of Vibration and Control15(8): 1247–1266.
3.
ChenLYuanZQianJ, et al. (2023a) Random vibration of hysteretic systems under Poisson white noise excitations. Applied Mathematics and Mechanics44(2): 207–220.
4.
ChenZHanKRenF, et al. (2023b) Influence of transverse vibration induced by fluid-structure interaction on pipeline strength. Nuclear Engineering and Design411: 112445.
5.
DengTCDingHMaoXY, et al. (2023) Natural vibration of pipes conveying high-velocity fluids with multiple distributed retaining clips. Nonlinear Dynamics111(20): 18819–18836.
6.
FezeuGFokouIMBuckjohnCND, et al. (2020) Resistance induced p-bifurcation and ghost-stochastic resonance of a hybrid energy harvester under colored noise. Physica A: Statistical Mechanics and its Applications557: 124857.
7.
FokouIMBuckjohnCNDSieweMS, et al. (2018) Probabilistic distribution and stochastic P-bifurcation of a hybrid energy harvester under colored noise. Communications in Nonlinear Science and Numerical Simulation56: 177–197.
8.
GeGXieN (2020) An approach dealing with inertia nonlinearity of a cantilever model subject to lateral basal Gaussian white noise excitation. Chaos, Solitons & Fractals131: 109469.
9.
GuXZhaoBDengZ, et al. (2023) Approximate analytical response of nonlinear functionally graded beams subjected to harmonic and random excitations. International Journal of Non-Linear Mechanics148: 104269.
10.
GuoSS (2018) Nonstationary solutions of nonlinear dynamical systems excited by Gaussian white noise. Nonlinear Dynamics92: 613–626.
11.
GuoXXiaoCGeH, et al. (2022) Dynamic modeling and experimental study of a complex fluid-conveying pipeline system with series and parallel structures. Applied Mathematical Modelling109: 186–208.
12.
HäunggiPJungP (1994) Colored noise in dynamical systems. Advances in Chemical Physics89: 239–326.
JungDChungJMazzoleniA (2008) Dynamic stability of a semi-circular pipe conveying harmonically oscillating fluid. Journal of Sound and Vibration315(1-2): 100–117.
KryskoVAwrejcewiczJKrylovaEY, et al. (2018) Non-symmetric forms of non-linear vibrations of flexible cylindrical panels and plates under longitudinal load and additive white noise. Journal of Sound and Vibration423: 212–229.
17.
LiJDengHJiangW (2019) Dynamic response and vibration suppression of a cantilevered pipe conveying fluid under periodic excitation. Journal of Vibration and Control25(11): 1695–1705.
18.
LiWZhangHQuW (2021) Stress response of a straight hydraulic pipe under random vibration. International Journal of Pressure Vessels and Piping194: 104502.
19.
LiXDingHChenLQ (2022) Effects of weights on vibration suppression via a nonlinear energy sink under vertical stochastic excitations. Mechanical Systems and Signal Processing173: 109073.
20.
LiJLiuDLiM (2023a) Probabilistic response analysis of nonlinear vibro-impact systems with two correlated Gaussian white noises. International Journal of Non-Linear Mechanics151: 104370.
21.
LiMLiuDLiJ (2023b) Stochastic analysis of vibro-impact bistable energy harvester system under colored noise. Nonlinear Dynamics111(18): 17007–17020.
22.
LiYDFengCBoS, et al. (2023c) Three-dimensional vibration analysis in extensible pipes conveying fluid with different initial geometrical configurations. Applied Mathematical Modelling115: 470–489.
23.
LiuFZhaoXFengJ (2016) Chaos and control in Josephson system subjected to combined bounded noise and harmonic excitation. Journal of Vibration and Control22(4): 1158–1167.
24.
LiuDXuYLiJ (2017) Probabilistic response analysis of nonlinear vibration energy harvesting system driven by Gaussian colored noise. Chaos, Solitons & Fractals104: 806–812.
25.
LiuMWangZZhouZ, et al. (2018) Vibration response of multi-span fluid-conveying pipe with multiple accessories under complex boundary conditions. European Journal of Mechanics - A: Solids72: 41–56.
26.
LiuDLiMLiJ, et al. (2022) Performance analysis of nonlinear vibration energy harvesting system with inelastic barrier under colored noise excitation. Applied Mathematical Modelling105: 243–257.
27.
MohammadRKotousovACodringtonJ, et al. (2011) Effect of flowing medium for a simply supported pipe subjected to impulse loading. Australian Journal of Mechanical Engineering8(2): 133–141.
28.
MuscolinoGRicciardiGCacciolaP (2003) Monte Carlo simulation in the stochastic analysis of non-linear systems under external stationary Poisson white noise input. International Journal of Non-Linear Mechanics38(8): 1269–1283.
29.
ParkJHChoYKKimSH, et al. (2015) Estimation of leak rate through circumferential cracks in pipes in nuclear power plants. Nuclear Engineering and Technology47(3): 332–339.
30.
PichlerLMasudABergmanLA (2013) Numerical solution of the Fokker–Planck equation by finite difference and finite element methods—a comparative study. Computational Methods in Stochastic Dynamics2: 69–85.
31.
QuWZhangHLiW, et al. (2021) Dynamic characteristics of a hydraulic curved pipe subjected to random vibration. International Journal of Pressure Vessels and Piping193: 104442.
32.
SazeshSShamsS (2019) Vibration analysis of cantilever pipe conveying fluid under distributed random excitation. Journal of Fluids and Structures87: 84–101.
33.
SuMXuWZhangY, et al. (2021) Response of a vibro-impact energy harvesting system with bilateral rigid stoppers under Gaussian white noise. Applied Mathematical Modelling89: 991–1003.
34.
TangBWangSBrennanMJ, et al. (2020) Identifying the stiffness and damping of a nonlinear system using its free response perturbed with Gaussian white noise. Journal of Vibration and Control26(9-10): 830–839.
35.
VictorovnaML (2018) Vibration strength of pipelines. In: System of System Failures. London: IntechOpen, 23–36.
36.
WangDXuWGuX, et al. (2016) Response analysis of nonlinear vibro-impact system coupled with viscoelastic force under colored noise excitations. International Journal of Non-Linear Mechanics86: 55–65.
37.
WangLXueLXuW, et al. (2017) Stochastic P-bifurcation analysis of a fractional smooth and discontinuous oscillator via the generalized cell mapping method. International Journal of Non-Linear Mechanics96: 56–63.
38.
WeiSSunYDingH, et al. (2023) Random vibration and reliability analysis of fluid-conveying pipe under white noise excitations. Applied Mathematical Modelling123: 259–273.
39.
XuYGuRZhangH, et al. (2011) Stochastic bifurcations in a bistable Duffing--Van der Pol oscillator with colored noise. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics83(5): 056215.
40.
XuYMaJWangH, et al. (2017) Effects of combined harmonic and random excitations on a Brusselator model. The European Physical Journal B90: 1–7.
41.
XuYZanWJiaW, et al. (2019) Path integral solutions of the governing equation of SDEs excited by Lévy white noise. Journal of Computational Physics394: 41–55.
42.
YangSPLiuZC (2024) Reliability analysis for product package via probability density function of acceleration random response. Journal of Vibration and Control30(7-8): 1841–1854.
43.
YeWChenLSunJQ (2023) Semi-analytical solutions for stationary response of a stay cable under combined Gaussian and Poisson excitations. Journal of Sound and Vibration566: 117923.
44.
YounesianDAskariHSaadatniaZ, et al. (2010) Frequency analysis of strongly nonlinear generalized duffing oscillators using He’s frequency–amplitude formulation and He’s energy balance method. Computers & Mathematics with Applications59(9): 3222–3228.
45.
YuJLinY (2004) Numerical path integration of a non-homogeneous Markov process. International Journal of Non-Linear Mechanics39(9): 1493–1500.
46.
YueXYuBLiY, et al. (2022) Dynamic response and bifurcation for Rayleigh-Liénard oscillator under multiplicative colored noise. Chaos, Solitons & Fractals155: 111744.
47.
ZhaiHWuZLiuY, et al. (2011) Dynamic response of pipeline conveying fluid to random excitation. Nuclear Engineering and Design241(8): 2744–2749.
48.
ZhangWGLinGMShangM, et al. (2014) Fracture analysis of hydraulic pipe of airplane. Advanced Materials Research971: 485–488.
49.
ZhangYLiYKennedyD (2019) An uncertain computational model for random vibration analysis of subsea pipelines subjected to spatially varying ground motions. Engineering Structures183: 550–561.
50.
ZhangYJinYXuP, et al. (2020) Stochastic bifurcations in a nonlinear tri-stable energy harvester under colored noise. Nonlinear Dynamics99: 879–897.
51.
ZhangYJiaoZDuanX, et al. (2021) Stochastic dynamics of a piezoelectric energy harvester with fractional damping under Gaussian colored noise excitation. Applied Mathematical Modelling97: 268–280.
52.
ZhuW (2006) Nonlinear stochastic dynamics and control in Hamiltonian formulation. Applied Mechanics Reviews59(4): 230–248.
53.
ZhuWLinY (1991) Stochastic averaging of energy envelope. Journal of Engineering Mechanics117(8): 1890–1905.
54.
ZhuWHuangZSuzukiY (2001) Response and stability of strongly non-linear oscillators under wide-band random excitation. International Journal of Non-Linear Mechanics36(8): 1235–1250.
55.
ZhuWHuangZDengM (2002) Feedback minimization of first-passage failure of quasi non-integrable Hamiltonian systems. International Journal of Non-Linear Mechanics37(6): 1057–1071.
56.
ZhuHGengGYuY, et al. (2020) Probabilistic analysis on parametric random vibration of a marine riser excited by correlated Gaussian white noises. International Journal of Non-Linear Mechanics126: 103578.
