Stability and Modal Conversion Phenomenon of Pipe-in-Pipe Structures with Arbitrary Boundary Conditions by Means of Green’s Functions

2021 ◽  
Author(s):  
Xueping Chang ◽  
Jinming Fan ◽  
Duzheng Han ◽  
Bo Chen ◽  
Yinghui Li
Keyword(s):  
Boundary Conditions ◽  
Flow Velocity ◽  
Volume Fraction ◽  
Frequency Equation ◽  
Stiffness Coefficient ◽  
Equivalent Stiffness ◽  
Critical Flow Velocity ◽  
Arbitrary Boundary ◽  
The Stability ◽  
Single Pipe

In this paper, a closed-form frequency equation of the pipe-in-pipe (PIP) structure with arbitrary boundaries is obtained. The frequency equation is derived from Green’s function of the transverse forced vibration of the PIP structure and takes into account the effects of internal two-phase flow and axial pressure. The reliability of the method in this paper is proved by comparison with the published literature. In the numerical discussion part, the PIP structures with clamped-clamped, clamped-free, and elastic boundary conditions are used as examples to discuss. The effects of equivalent stiffness coefficient, internal flow velocity, and gas volume fraction on the stability of PIP structure are studied. The results show that the stability of the PIP structure is better than that of the single-pipe structure, and the greater the equivalent stiffness coefficient of the elastic layer, the higher the critical flow velocity of the structure. In addition, a modal conversion phenomenon existing in the PIP structure is discovered. There are different forms of modal conversion for different boundary conditions, and the modal conversion makes the order of instability of the PIP structure different from that of a single-pipe. The conclusion of this paper has positive significance for the dynamic research of PIP structure.

Free vibration analysis of three-layer thin cylindrical shell with variable thickness two-dimensional FGM middle layer under arbitrary boundary conditions

2021 ◽  
pp. 109963622110204
Author(s):  
Xue-Yang Miao ◽  
Chao-Feng Li ◽  
Yu-Lin Jiang ◽  
Zi-Xuan Zhang
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Volume Fraction ◽  
Ritz Method ◽  
Admissible Function ◽  
Free Vibration Analysis ◽  
Middle Layer ◽  
Two Dimensional ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions

In this paper, a unified method is developed to analyze free vibrations of the three-layer functionally graded cylindrical shell with non-uniform thickness. The middle layer is composed of two-dimensional functionally gradient materials (2D-FGMs), whose thickness is set as a function of smooth continuity. Four sets of artificial springs are assigned at the ends of the shells to satisfy the arbitrary boundary conditions. The Sanders’ shell theory is used to obtain the strain and curvature-displacement relations. Furthermore, the Chebyshev polynomials are selected as the admissible function to improve computational efficiency, and the equation of motion is derived by the Rayleigh–Ritz method. The effects of spring stiffness, volume fraction indexes, configuration on of shell, and the change in thickness of the middle layer on the modal characteristics of the new structural shell are also analyzed.

scholarly journals Influence of Dry Friction on the Dynamics of Cantilevered Pipes Conveying Fluid

2022 ◽  
Vol 12 (2) ◽  
pp. 724
Author(s):  
Zilong Guo ◽  
Qiao Ni ◽  
Lin Wang ◽  
Kun Zhou ◽  
Xiangkai Meng
Keyword(s):  
Flow Velocity ◽  
Friction Force ◽  
Dry Friction ◽  
Critical Flow Velocity ◽  
Pipe System ◽  
Pipes Conveying Fluid ◽  
Cantilevered Pipe ◽  
The Stability ◽  
Friction Parameters ◽  
Conveying Fluid

A cantilevered pipe conveying fluid can lose stability via flutter when the flow velocity becomes sufficiently high. In this paper, a dry friction restraint is introduced for the first time, to evaluate the possibility of improving the stability of cantilevered pipes conveying fluid. First, a dynamical model of the cantilevered pipe system with dry friction is established based on the generalized Hamilton’s principle. Then the Galerkin method is utilized to discretize the model of the pipe and to obtain the nonlinear dynamic responses of the pipe. Finally, by changing the values of the friction force and the installation position of the dry friction restraint, the effect of dry friction parameters on the flutter instability of the pipe is evaluated. The results show that the critical flow velocity of the pipe increases with the increment of the friction force. Installing a dry friction restraint near the middle of the pipe can significantly improve the stability of the pipe system. The vibration of the pipe can also be suppressed to some extent by setting reasonable dry friction parameters.

Vibration and Frequency Analysis of Non-Uniform Timoshenko Beams Subjected to Axial Forces

2003 ◽  
Author(s):  
A. R. Ohadi ◽  
H. Mehdigholi ◽  
E. Esmailzadeh
Keyword(s):  
Stability Analysis ◽  
Boundary Conditions ◽  
Axial Force ◽  
Frequency Equation ◽  
Axial Loads ◽  
Various Boundary Conditions ◽  
Axial Forces ◽  
First Case ◽  
The Stability ◽  
Elastically Supported

Dynamic and stability analysis of non-uniform Timoshenko beam under axial loads is carried out. In the first case of study, the axial force is assumed to be perpendicular to the shear force, while for the second case the axial force is tangent to the axis of the beam column. For each case, a pair of differential equations coupled in terms of the flexural displacement and the angle of rotation due to bending was obtained. The parameters of the frequency equation were determined for various boundary conditions. Several illustrative examples of uniform and non-uniform beams with different boundary conditions such as clamped supported, elastically supported, and free end mass have been presented. The stability analysis, for the variation of the natural frequencies of the uniform and non-uniform beams with the axial force, has also been investigated.

Nonlinear Planar Dynamics of Fluid-Conveying Cantilevered Extensible Pipes

2013 ◽  
Author(s):  
Mergen H. Ghayesh ◽  
Michael P. Païdoussis ◽  
Marco Amabili
Keyword(s):  
Flow Velocity ◽  
Trivial Solution ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Time Integration ◽  
Axial Direction ◽  
Transverse Displacement ◽  
Lagrange Equations ◽  
Critical Flow Velocity ◽  
The Stability

This paper for the first time investigates the nonlinear planar dynamics of a cantilevered extensible pipe conveying fluid; the centreline of the pipe is considered to be extensible resulting in coupled longitudinal and transverse equations of motion; specifically, the kinetic and potential energies are obtained in terms of longitudinal and transverse displacements and then the extended version of the Lagrange equations for systems containing non-material volumes is employed to derive the equations of motion. Direct time integration along with the pseudo-arclength continuation method are employed to solve the discretized equations of motion. Bifurcation diagrams of the system are constructed as the flow velocity is increased as the bifurcation parameter. As opposed to the case of an inextensible pipe, an extensible pipe elongates in the axial direction as the flow velocity is increased from zero. At the critical flow velocity, the stability of the system is lost via a supercritical Hopf bifurcation, emerging from the trivial solution for the transverse displacement and non-trivial solution for the longitudinal displacement and leading to a flutter.

scholarly journals Damage detection of beam by natural frequencies: General theory and procedure

2006 ◽  
Vol 28 (2) ◽  
pp. 120-132 ◽  
Author(s):  
Nguyen Tien Khiem
Keyword(s):  
Boundary Conditions ◽  
Damage Detection ◽  
Natural Frequencies ◽  
Model Updating ◽  
Measurement Data ◽  
Main Tool ◽  
Frequency Equation ◽  
Geometrical Parameters ◽  
Arbitrary Boundary ◽  
Updating Procedure

The frequency equation of single damaged beam has been established for arbitrary boundary conditions that is the main tool for analysis as well as identification of damaged beam by using measured natural frequencies. A procedure for damage detection problem presented in this paper consists of three steps. First, the modelling error is reduced by a model updating procedure, in which the material, geometrical parameters and boundary conditions are updated. Then, measurement data are corrected based on the updated model. Finally, the damage parameters are identified using updated model and corrected measurement data. Theoretical investigation is illustrated by an example.

Basic Study on Mitigation of Annular-Flow-Induced Vibration by Considering Variability in Parameters of Structure and Fluid

2013 ◽  
Author(s):  
Atsuhiko Shintani ◽  
Hirokazu Isono ◽  
Tomohiro Ito ◽  
Chihiro Nakagawa
Keyword(s):  
Flow Velocity ◽  
Annular Flow ◽  
Coupled System ◽  
Critical Flow ◽  
Control Input ◽  
Navier Stokes Equation ◽  
Critical Flow Velocity ◽  
Fluid Structure ◽  
The Stability ◽  
Coupled Equation

In this study, the stability of a structure and mitigation of the vibration of a structure subjected to annular flow are investigated when the parameters of the structure and fluid have variability or uncertainty. The equations of motion of the structure and fluid are given by the Euler-Bernoulli-type partial differential equation and the Navier–Stokes equation, respectively. Hence, the fluid–structure coupled system has variability. The fluid–structure coupled equation considering variability is derived from the above-mentioned equations. By drawing the root locus of the coupled equation, the stability of the coupled system with variability is investigated. Because the parameters of structure and fluid have variability, the critical flow velocity also varies. The effect of parameter variability on the critical flow velocity variability is investigated. Furthermore, to reduce the coupled vibration of the system with variability, a control input is used. Through adequate control, the coupled system with variability is stabilized.

The effect of two cases of temperature distributions on vibration of fluid-conveying functionally graded thin-walled pipes

2018 ◽  
Vol 53 (5) ◽  
pp. 324-331 ◽  
Author(s):  
Jianhua Cao ◽  
Yongshou Liu ◽  
Wei Liu
Keyword(s):  
Flow Velocity ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Critical Flow ◽  
Physical Parameters ◽  
Temperature Dependent ◽  
Critical Flow Velocity ◽  
Temperature Distributions ◽  
The Difference

The dynamic analysis of fluid-conveying functionally graded pipes under two cases of temperature distributions is investigated in this study. Two cases of temperature distribution of functionally graded pipes are considered: warmer outside than inside in Case 1 and warmer inside than outside in Case 2. The purpose is to determine the effect of two cases of temperature distributions on the natural frequencies and the critical flow velocity by applying a conventional finite element of functionally graded pipes neglecting shear deformation. The numerical results show that the difference in the natural frequencies or the critical flow velocity between two cases of temperature distributions is not monotonic, and not always greater than 0, which is conditional on the volume fraction index and temperature gradient. The article indicates that the physical parameters of temperature-dependent functionally graded pipes should be selected to adapt for Case 1 and Case 2, respectively.

Flexural vibration analysis of functionally graded sandwich plates resting on elastic foundation with arbitrary boundary conditions: Chebyshev collocation technique

2017 ◽  
Vol 22 (2) ◽  
pp. 156-189 ◽  
Author(s):  
Prapot Tossapanon ◽  
Nuttawit Wattanasakulpong
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Flexural Vibration ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Arbitrary Boundary ◽  
Chebyshev Collocation ◽  
Spring Constants

This paper aims to present accurate solutions for flexural vibration of functionally graded sandwich plates resting on two-parameter elastic foundation with any combined boundary conditions. The governing equations of free vibration problem are derived from the first-order shear deformation theory that covers the important effects of shear deformation and rotary inertia. To solve the coupled differential equations governing vibration behavior of the plates with various boundary conditions, an effective tool, namely Chebyshev collocation method, is implemented to obtain the accurate solutions with several parametric studies. The influences of material volume fraction index, layer thickness ratio, side-to-height ratio, boundary conditions, etc., on natural frequencies of the plates are taken into investigation and discussed in details. Our numerical experiments reveal that the proposed method can offer the accurate frequency results of the plates as compared to those available in the literature. Additionally, the spring constants of elastic foundation have a significant impact on frequency changes of the plates. Increasing the values of spring constants leads to considerable increases of the frequencies.

A Model for the Nonlinear Buckling of Human Aorta

2012 ◽  
Author(s):  
Marco Amabili ◽  
Kostas Karazis ◽  
Rosaire Mongrain ◽  
Nastaran Shahmansouri
Keyword(s):  
Blood Flow ◽  
Flow Velocity ◽  
Stokes Equations ◽  
Surrounding Tissue ◽  
Human Aorta ◽  
Critical Flow ◽  
Linear Potential ◽  
Critical Flow Velocity ◽  
Aortic Segment ◽  
The Stability

Human aortas are subjected to large mechanical stresses due to blood flow pressurization and through contact with the surrounding tissue. It is essential that the aorta does not lose stability by buckling for its proper functioning to ensure proper blood flow. A refined reduced-order bifurcation analysis model is employed to examine the stability of an aortic segment subjected to internal blood flow. The structural model is based on a nonlinear cylindrical orthotropic laminated composite shell theory that assumes three aortic wall layers representing the tunica intima, media and adventitia. The fluid model contains the unsteady effects obtained from linear potential flow theory and the steady viscous effects obtained from the time-averaged Navier-Stokes equations. Residual stresses due to pressurization are evaluated and included in the model. The aortic segment loses stability by divergence with deformation of the cross-section at a critical flow velocity for a given static pressure, exhibiting a strong subcritical behaviour with partial or total collapse of the inner wall. Subsequent analyses including the effect of geometric wall imperfections indicate that imperfections in the axial direction have a more profound effect on the stability of the aorta decreasing the critical flow velocity for buckling.

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