Article
Engineering, Mechanical
Yu-Fei Shao, Hu Ding
Summary: In this paper, the effect of gravity on the nonlinear vibration of a pipe conveying fluid is evaluated. The nonlinear vibration of the pipe with an intermediate elastic support is investigated, and the equilibrium configuration of the pipe caused by gravity is calculated. The influence of gravity on the vibration characteristics of the pipe is studied and the effects of gravity on the natural frequencies are illustrated.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2023)
Article
Mathematics, Applied
Bo Dou, Hu Ding, Xiaoye Mao, Sha Wei, Liqun Chen
Summary: In this study, a new dynamic model of a fluid-conveying pipe restrained by an intermediate clip is established by considering the clip width. By comparing it with a half pipe model, it is found that the half pipe model overestimates the critical velocity and may estimate the pipe's dynamical behavior incorrectly. The increase in clip stiffness shows the conversion processes of the first two modes of the pipe. Furthermore, the effect of flow velocity on the accuracy of a concentrated restraint clip model is presented by ignoring the width of the clip. When the flow velocity is close to the critical velocity, the accuracy of the concentrated restraint clip model significantly reduces, especially with a large clip width.
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
(2023)
Article
Engineering, Mechanical
Tian-Chang Deng, Hu Ding, Li-Qun Chen
Summary: This study investigates the influence of retaining clips on the supercritical vibration characteristics of fluid-conveying pipes. The governing equation for the pipe with retaining clip is derived, and the effects of clip stiffness and position on critical flow velocity, equilibrium configuration, and natural frequencies are emphasized. The study reveals that retaining clip stiffness can lead to different types of equilibrium configurations and the natural frequencies do not follow a monotonic pattern with increasing clip stiffness in supercritical flow.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2022)
Article
Engineering, Marine
Jia-Rui Yuan, Hu Ding
Summary: In this paper, a dynamic model for the out-of-plane vibration of in-plane curved pipes conveying fluid is established for the first time. The governing equations of the out-of-plane vibration are derived analytically based on force analysis and fluid analysis. The critical velocity, natural frequencies, and modes of the curved pipe are calculated using the Galerkin truncation method. It is found that pipes with larger in-plane curvature have lower critical velocity for out-of-plane motion, and there is a significant decrease in natural frequencies with increasing curvature and fluid velocity.
Article
Mechanics
Akintoye O. Oyelade, Ayo A. Oyediran
Summary: The study developed governing equations and boundary conditions for the motion of vibrating pipes conveying two-phase flow, showing that as the volume fraction of sand increases in the two-phase flow, the natural frequencies decrease. The nonlinear displacement of the pipe is influenced by the initial curvature and volume fraction.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2021)
Review
Engineering, Civil
Jie Zhou, Xueping Chang, Zijie Xiong, Yinghui Li
Summary: This paper investigates the stability and nonlinear vibration characteristics of fluid-conveying composite pipes considering geometric nonlinear deformation and elastic boundary conditions. Dynamic governing equations and elastic boundary conditions of composite pipe are established. Nonlinear vibration characteristics are solved using the Homotopy analysis method. The results show that the rotation spring improves stability, while the increase of viscoelastic coefficient and fiber orientation decreases nonlinear frequency and larger initial amplitude leads to larger nonlinear frequency.
THIN-WALLED STRUCTURES
(2022)
Article
Acoustics
Xiao-Ye Mao, Song Shu, Xin Fan, Hu Ding, Li-Qun Chen
Summary: An approximate method is proposed for the strong nonlinear and non-homogenous boundary value problem of a pipe conveying fluid, using modal correction and projection to treat the boundaries as generalized governing equations. The discussion on natural frequencies and harmonic convergence helps in judging the stability of the solution and the type of bifurcation, while revealing detailed information of the response. The proposed method shows advantages in dealing with strong boundaries compared to other existing methods.
JOURNAL OF SOUND AND VIBRATION
(2021)
Article
Engineering, Marine
Gang Liu, Yueshe Wang, Zongrui Hao, Yue Wang, Wanlong Ren
Summary: This study investigates the natural frequency characteristics of simply supported pipes conveying gas-liquid two-phase slug flow to uncover critical conditions leading to piping system instability. The intermittent features of local flow parameters are emphasized for dynamic analysis of the piping system. Correlations are introduced to reveal the inherent regularity of flow characteristics and vibration performances in slug flow piping systems.
Article
Engineering, Marine
M. Heshmati, F. Daneshmand, Y. Amini
Summary: The dynamic responses of corrugated clamped-clamped pipes conveying fluid are investigated in this study. The governing equations of the system are derived based on the Hamiltonian principle using the Euler-Bernoulli beam hypothesis. Non-uniformity of the flow velocity profile is considered and flow-profile-modification factor and space-dependent mean velocity are proposed. The finite element method is used for spatial discretization. The stability of the pipe system is examined with various parameters, showing significant effects of corrugation length and amplitude on system stability.
Article
Engineering, Marine
H. Q. Li, X. F. Zhang, W. A. Jiang, H. Ding, L. Q. Chen, Q. S. Bi
Summary: The main purpose of this article is to investigate the originality multiple-frequency bursting of simply-supported fluid-conveying pipes with initial micro-bending shape under different low-frequency excitation conditions. Through the use of Galerkin's method and the fast-slow dynamics analysis method, various vibration phenomena are observed under different excitation conditions, and the multi-valued characteristics are verified by the domain of attraction. The results demonstrate that low-frequency excitation can lead to complex dynamical phenomena of the fluid-conveying pipes.
SHIPS AND OFFSHORE STRUCTURES
(2023)
Article
Acoustics
Yun-Long Zhou, Lie-Dong Mi, Mei Yang
Summary: This paper investigates the free vibration and stability of inclined pipes conveying gas-liquid slug flow, taking into account the intermittency of slug flow and gravity effects. A new lateral motion model is established based on stable slug flow dynamics and Euler-Bernoulli beam vibration models. The study comprehensively explores the natural frequencies, critical gas velocities, and responses to flow conditions, shedding light on the dynamic characteristics of inclined pipes. The results show that the gravity effects caused by the inclined angle significantly influence the vibration characteristics. The study contributes to understanding the complex dynamic behavior of inclined pipes conveying slug flow and promoting pipeline safety.
JOURNAL OF SOUND AND VIBRATION
(2022)
Article
Mathematics, Applied
Yongqi Ma, Yunxiang You, Ke Chen, Lili Hu, Aichun Feng
Summary: Harmonic differential quadrature (HDQ) method is an effective approach for analyzing the vibration problem of pipes conveying fluid, applicable to various boundary conditions and internal flow scenarios. Comparison with other methods demonstrates the superior computational efficiency and accuracy of HDQ method.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Engineering, Mechanical
Xiao-Ye Mao, Jie Jing, Hu Ding, Li-Qun Chen
Summary: This study investigates the effects of gradient Young's modulus on the dynamics of pipes conveying fluid. A model is established to analyze the influence of Young's modulus gradient on the natural characteristics and the non-trivial equilibrium configuration. The results show that the gradually varied Young's modulus leads to an asymmetric non-trivial equilibrium configuration, and increasing gradient can raise the critical fluid velocity and weaken the vibration.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Michael P. Paidoussis
Summary: Early studies have revealed the fundamental dynamics of pipes conveying fluid, and subsequent research has focused on various variants of the system. The publication rate of related papers has exponentially increased over time.
JOURNAL OF FLUIDS AND STRUCTURES
(2022)
Article
Acoustics
Andrzej Czerwinski, Jan Luczko
Summary: The study investigated the dynamic behavior of curved pipes conveying fluid, comparing experimental results with theoretical predictions and considering the vibration caused by pulsating flow and nonlinear factors. The results showed the effects of curvature, flow velocity, pulsation frequency, and amplitude on parametric vibration.
JOURNAL OF SOUND AND VIBRATION
(2021)
Article
Mathematics, Applied
Junfeng Cao, Ke Chen, Huan Han
Summary: This paper proposes a two-stage image segmentation model based on structure tensor and fractional-order regularization. In the first stage, fractional-order regularization is used to approximate the Hausdorff measure of the MS model. The solution is found using the ADI scheme. In the second stage, thresholding is used for target segmentation. The proposed model demonstrates superior performance compared to state-of-the-art methods.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Dylan J. Oliver, Ian W. Turner, Elliot J. Carr
Summary: This paper discusses a projection-based framework for numerical computation of advection-diffusion-reaction (ADR) equations in heterogeneous media with multiple layers or complex geometric structures. By obtaining approximate solutions on a coarse grid and reconstructing solutions on a fine grid, the computational cost is significantly reduced while accurately approximating complex solutions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Nathan V. Roberts, Sean T. Miller, Stephen D. Bond, Eric C. Cyr
Summary: In this study, the time-marching discontinuous Petrov-Galerkin (DPG) method is applied to the Vlasov equation for the first time, using backward Euler for a Vlasov-Poisson discretization. Adaptive mesh refinement is demonstrated on two problems: the two-stream instability problem and a cold diode problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Yizhi Sun, Zhilin Sun
Summary: This work investigates the convexity of a specific class of positive definite probability measures and demonstrates the preservation of convexity under multiplication and intertwining product. The study reveals that any integrable function on an interval with a polynomial expansion of fast absolute convergence can be decomposed into a pair of positive convex interval probabilities, simplifying the study of interval distributions and discontinuous probabilistic Galerkin schemes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Bhagwan Singh, Komal Jangid, Santwana Mukhopadhyay
Summary: This paper examines the prediction of bending characteristics of nanoscale materials using the Moore-Gibson-Thompson thermoelasticity theory in conjunction with the nonlocal strain gradient theory. The study finds that the stiffness of the materials can be affected by nonlocal and length-scale parameters, and the aspect ratios of the beam structure play a significant role in bending simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Guoliang Wang, Bo Zheng, Yueqiang Shang
Summary: This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method, and the post-processing technique. The algorithm generates a global continuous approximate solution using the partition of unity method and improves the smoothness of the solution by adding an extra coarse grid correction step. It has good parallel performance and is validated through theoretical error estimates and numerical test examples.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Hao Xu, Zeng-Qi Wang
Summary: Fluid flow control problems are crucial in industrial applications, and solving the optimal control of Navier-Stokes equations is challenging. By using Oseen's approximation and matrix splitting preconditioners, we can efficiently solve the linear systems and improve convergence.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhengya Yang, Xuejuan Chen, Yanping Chen, Jing Wang
Summary: This paper focuses on the high-order stable numerical solutions of the time-space fractional diffusion equation. The Fourier spectral method is used for spatial discretization and the Spectral Deferred Correction (SDC) method is used for numerical solutions in time. As a result, a high-precision numerical discretization scheme for solving the fractional diffusion equation is obtained, and the convergence and stability of the scheme are proved. Several numerical examples are presented to demonstrate the effectiveness and feasibility of the proposed numerical scheme.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)