Dynamic Stress Analysis of Exposed Pipes Subjected to Moving In-Line Inspection Tool

2020 ◽  
Author(s):  
Hamid Mostaghimi ◽  
Mohsen Hassani ◽  
Deli Yu ◽  
Ron Hugo ◽  
Simon Park
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Stress ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Beam Theory ◽  
Assessment Method ◽  
Integrity Assessment ◽  
Defect Assessment ◽  
Proposed Model ◽  
Assessment And Monitoring

Abstract In-line inspection is a non-destructive assessment method commonly used for defect assessment and monitoring of pipelines. The passage of an ILI tool through an excavated or exposed section of a pipe during an integrity assessment can excite vibrations and exert substantial forces, stress, and deflections on the pipe due to the weight and speed of the ILI tool. When the excitation frequency due to the ILI tool movement is close to the natural frequency of the overall structure, the dynamic stress generated within the pipe can be large enough to the extent that it imposes integrity concern on the line. This research aims to study effects of the ILI tool passage through floating and partially supported pipes under a variety of boundary and loading conditions. A finite element method is used to model the pipe with moving ILI tool. The model is developed based on Timoshenko beam theory with planar degrees-of-freedom and the differential equations of motion are solved numerically to predict displacement, strain, stress, and frequency responses of the pipe. The model is further validated using a lab-scale experimental setup. The comparison of the simulation to experimental results show how the proposed model is capable of predicting pipe dynamics, effectively.

Dynamic Stress Analysis of Exposed Pipes Subjected to a Moving In-line Inspection Tool

2020 ◽  
pp. 1-35
Author(s):  
Hamid Mostaghimi ◽  
Mohsen Hassani ◽  
Deli Yu ◽  
Ronald J. Hugo ◽  
Simon S. Park
Keyword(s):  
Dynamic Stress ◽  
Excitation Frequency ◽  
Beam Theory ◽  
Element Model ◽  
Assessment Method ◽  
Integrity Assessment ◽  
Defect Assessment ◽  
Pipe Section ◽  
Proposed Model ◽  
Wide Range

Abstract In-line inspection (ILI) is a non-destructive assessment method commonly used for defect assessment and for pipeline monitoring. Passing an ILI tool through an excavated or exposed section of a pipe during an integrity assessment can excite vibrations. The ILI tool's weight and speed can exert substantial forces, stresses, and deflections on the pipe section. When the excitation frequency from the ILI tool's movement is close to the pipe's natural frequency, the dynamic stress generated within the pipe can become great enough that it creates integrity concerns on the pipeline. This research aims to study effects of an ILI tool's passage through exposed and partially supported pipes under a variety of boundary and loading conditions. A finite element model of an exposed pipe section is developed based on the Timoshenko beam theory to predict the pipe's displacement, strain, stress, and frequency responses under a wide range of excitation frequencies. The model is further validated using a lab-scale experimental setup with a mass that moves at different speeds. A comparison between the simulation and the experimental results shows that the proposed model can effectively predict the pipe's dynamics.

TSDT theory for free vibration of functionally graded plates with various material properties

2021 ◽  
Vol 8 (4) ◽  
pp. 691-704
Author(s):  
M. Janane Allah ◽  
◽  
Y. Belaasilia ◽  
A. Timesli ◽  
A. El Haouzi ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Implicit Algorithm ◽  
Proposed Model ◽  
Graded Material ◽  
Composite Modeling

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

Optimization of Nonlinear Unbalanced Flexible Rotating Shaft Passing Through Critical Speeds

2021 ◽  
Author(s):  
Sadegh Amirzadegan ◽  
Mohammad Rokn-Abadi ◽  
R. D. Firouz-Abadi
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Oscillations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Angular Acceleration ◽  
Beam Theory ◽  
Rotor System ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Applied Torque

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for this work. The shaft is modeled as a beam and the Euler–Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6 degrees of freedom. In order to solve these equations numerically, the finite element method (FEM) is used. Furthermore, for different bearing properties, rotor responses are examined and curves of passing through critical speeds with angular acceleration due to applied torque are plotted. Then the optimal values of bearing stiffness and damping are calculated to achieve the minimum vibration amplitude, which causes to pass easier through critical speeds. It is concluded that the value of damping and stiffness of bearing change the rotor critical speeds and also significantly affect the dynamic behavior of the rotor system. These effects are also presented graphically and discussed.

Member Initial Curvature Effects on the Elastic Slider-Crank Mechanism Response

1982 ◽  
Vol 104 (1) ◽  
pp. 159-167 ◽  
Author(s):  
M. Badlani ◽  
A. Midha
Keyword(s):  
Steady State ◽  
Natural Frequency ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Beam Theory ◽  
Connecting Rod ◽  
Initial Curvature ◽  
Curvature Effects ◽  
Transient Solutions ◽  
Crank Mechanism

Parametric vibration of initially curved columns loaded by axial-periodic loads has received considerable attention, concluding that regions of instability exist and that excitation frequencies less than the natural frequency of the principal resonance may occur. Recent publications have cautioned against the use of curved members in machines designed for precise operation, suggesting a detrimental coupling of the longitudinal and transverse deformations. In this work, the dynamic behavior of a slider-crank mechanism with an initially curved connecting rod is investigated. Governing equations of motion are developed using the Euler-Bernoulli beam theory. Both steady-state and transient solutions are determined, and compared with those obtained for the mechanism possessing a geometrically perfect (straight) connecting rod. A very small initial curvature is shown to cause a significantly greater steady-state response. The magnification in its transient response is shown to be even greater than that due to a straight connecting rod. Additionally, an excitation frequency less than the natural frequency is also shown to occur.

scholarly journals Vibration Analysis of Inclined Laminated Composite Beams under Moving Distributed Masses

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
E. Bahmyari ◽  
S. R. Mohebpour ◽  
P. Malekzadeh
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Beam Theory ◽  
Composite Beams ◽  
Incline Angle ◽  
Centrifugal Forces ◽  
Coriolis And Centrifugal Forces ◽  
Laminated Composite Beams

The dynamic response of laminated composite beams subjected to distributed moving masses is investigated using the finite element method (FEM) based on the both first-order shear deformation theory (FSDT) and the classical beam theory (CLT). Six and ten degrees of freedom beam elements are used to discretize the CLT and FSDT equations of motion, respectively. The resulting spatially discretized beam governing equations including the effect of inertial, Coriolis, and centrifugal forces due to moving distributed mass are evaluated in time domain by applying Newmark’s scheme. The presented approach is first validated by studying its convergence behavior and comparing the results with those of existing solutions in the literature. Then, the effect of incline angle, mass, and velocity of moving body, layer orientation, load length, and inertial, Coriolis, and centrifugal forces due to the moving distributed mass and friction force between the beam and the moving distributed mass on the dynamic behavior of inclined laminated composite beams are investigated.

Non-Ideal System With Quadratic Nonlinearities Containing a Two-to-One Internal Resonance

2016 ◽  
Author(s):  
Rodrigo T. Rocha ◽  
Jose M. Balthazar ◽  
D. Dane Quinn ◽  
Angelo M. Tusset ◽  
Jorge L. P. Felix
Keyword(s):  
Internal Resonance ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Coupled System ◽  
Dynamical Behaviour ◽  
Main System ◽  
Weakly Coupled System ◽  
Ideal System ◽  
Quadratic Nonlinearities

The dynamical behaviour of a non-ideal three-degrees-of-freedom weakly coupled system associated with the quadratic nonlinearities in the equations of motion is investigated. The main system consists of two nonlinear mechanical oscillators coupling with quadratic nonlinearities and in which possess a 2:1 internal resonance between their translational movements. Under these conditions, we analyzed the response when a DC unbalanced motor with limited power supply (non-ideal system) excites the main system. When the excitation frequency is near to second natural frequency of the main system, saturation and jump phenomena are presented. Then, this work will analyze some torques of the motor, which causes the phenomena, and due to high amplitudes of motion will be possible to look for a way to harvest energy in a future work.

Research on Fluctuating Forces Occurred in Components of Reciprocating Hydrogen Compressors

2012 ◽  
Author(s):  
Yoshifumi Mori ◽  
Takashi Saito ◽  
Takehisa Aoki ◽  
Katsuhide Fujita
Keyword(s):  
Degrees Of Freedom ◽  
Beam Theory ◽  
Contact Theory ◽  
Model Parameters ◽  
Petrochemical Plant ◽  
Term Operation ◽  
Proposed Model ◽  
Rigid Body Model ◽  
System 1

This paper treats dynamic analysis about reciprocating compressors used in a petroleum refining plant and a petrochemical plant. In order to clarify the cause of damage occurred as a result of long-term operation, we investigated the effects of deterioration around the connecting parts and the sliding parts on the dynamics of the system. Introducing the rigid body model with eleven degrees of freedom, we have determined the model parameters based on beam theory and the Hertz contact theory. By comparison with experimental results, we showed validity of the proposed model. Thus, changes in the characteristics of the middle spring piston rod were found to be a major impact on the dynamics of the system [1].

Forced Vibration of Overhead Transmission Line: Analytical and Experimental Investigation

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
O. Barry ◽  
J. W. Zu ◽  
D. C. D. Oguamanam
Keyword(s):  
Transmission Line ◽  
Damping Ratio ◽  
Excitation Frequency ◽  
Beam Theory ◽  
Overhead Transmission Line ◽  
Proposed Model ◽  
Parametric Studies ◽  
Tip Mass ◽  
Euler Bernoulli Beam ◽  
Stockbridge Damper

An analytical model of a single line transmission line carrying a Stockbridge damper is developed based on the Euler–Bernoulli beam theory. The conductor is modeled as an axially loaded beam and the messenger is represented as a beam with a tip mass at each end. Experiments are conducted to validate the proposed model. An explicit expression is presented for the damping ratio of the conductor. Numerical examples show that the proposed model is more accurate than the models found in the literature. Parametric studies indicate that the response of the conductor significantly depends on the excitation frequency, the location of the damper, and the damper parameters.

Stability Analysis of Composite Shafts Considering Internal Damping and Coupling Effect

2020 ◽  
Vol 20 (11) ◽  
pp. 2050118
Author(s):  
Kwangchol Ri ◽  
Poknam Han ◽  
Inchol Kim ◽  
Wonchol Kim ◽  
Hyonbok Cha
Keyword(s):  
Degrees Of Freedom ◽  
Coupling Effect ◽  
Lagrange Equation ◽  
Nodal Point ◽  
Single Layer ◽  
Beam Theory ◽  
Weak Form ◽  
Internal Damping ◽  
Proposed Model ◽  
Equivalent Modulus

A mathematical model is proposed to analyze the stability of composite shafts, considering the internal damping, transverse shear deformation and Poisson’s coupling effect at the same time. The strain–displacement relations are described using the Timoshenko beam theory, and the strain energy and kinetic energy are expressed using the weak form quadrature element method (QEM), for which each nodal point has 4 degrees of freedom. Then, the motion equation of the system is established using the Lagrange equation. The instability thresholds of the composite shaft are determined using the proposed model. The results were compared with those calculated by the equivalent modulus beam theory (EMBT), equivalent single layer theory (ESLT) and simplified homogenized beam theory (SHBT). Good agreement has been achieved. Therefore, the proposed model can be effectively used for the dynamic analysis of composite shafts.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Sign in / Sign up

Export Citation Format

Share Document