Structural Response of Pipeline Free Spans Based on Beam Theory

2002 ◽  
Author(s):  
Olav Fyrileiv ◽  
Kim Mo̸rk
Keyword(s):  
Natural Frequencies ◽  
Structural Response ◽  
Beam Theory ◽  
Vertical Vibration ◽  
Mode Shapes ◽  
Ocean Current ◽  
Vibration Modes ◽  
Wave Loading ◽  
Vortex Induced Vibrations ◽  
Subsea Pipelines

One of the main risk factors for subsea pipelines exposed on the seabed is fatigue failure of free spans due to ocean current or wave loading. This paper describes how the structural response of a free span, as input to the fatigue analyses, can be assessed in a simple and still accurate way by using improved beam theory formulations. In connection with the release of the DNV Recommended Practice, DNV-RP-F105 “Free Spanning Pipelines”, the simplified structural response quantities have been improved compared to previous codes. The boundary condition coefficients for the beam theory formulations have been updated based an effective span length concept. This concept is partly based on theoretical studies and partly on a large number of FE analyses. The updated expressions are general and fit all types of soil and pipe dimensions for lower lateral and vertical vibration modes. The present paper focus on estimation of simplified response quantities such as lower natural frequencies and associated mode shapes. Hydrodynamical aspects of Vortex Induced Vibrations (VIV) are outside the scope of this paper.

scholarly journals NASTRAN Analysis of a Turbine Blade and Comparison With Test and Field Data

1975 ◽  
Author(s):  
J. M. Allen ◽  
L. B. Erickson
Keyword(s):  
Turbine Blade ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Mode Shapes ◽  
Stress Distributions ◽  
Free Standing ◽  
Element Analysis ◽  
Metallographic Examination ◽  
Stiffening Effect ◽  
Generalized Beam Theory

A NASTRAN finite element analysis of a free standing gas turbine blade is presented. The analysis entails calculation of the first four natural frequencies, mode shapes, and relative vibratory stresses, as well as deflections and stresses due to centrifugal loading. The stiffening effect of the centrifugal force field was accounted for by using NASTRAN’s differential stiffness option. Natural frequencies measured in a rotating test correlated well with computed results. Areas of maximum vibratory stress (fundamental mode) coincided with the three zones of crack initiation observed in a metallographic examination of a fatigue failure. Airfoil stress distributions were found to be significantly different from that predicted by generalized beam theory, especially near the airfoil-platform junction.

In-Plane Vibration Modes of Arbitrarily Thick Disks

1997 ◽  
Author(s):  
Kevin I. Tzou ◽  
Jonathan A. Wickert ◽  
Adnan Akay
Keyword(s):  
Natural Frequencies ◽  
Arbitrary Dimension ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Three Dimensional Model ◽  
Bending Vibration ◽  
Annular Disk ◽  
Out Of Plane ◽  
Plane Bending

Abstract The three-dimensional vibration of an arbitrarily thick annular disk is investigated for two classes of boundary conditions: all surfaces traction-free, and all free except for the clamped inner radius. These two models represent limiting cases of such common engineering components as automotive and aircraft disk brakes, for which existing models focus on out-of-plane bending vibration. For a disk of significant thickness, vibration modes in which motion occurs within the disk’s equilibrium plane can play a substantial role in setting its dynamic response. Laboratory experiments demonstrate that in-plane modes exist at frequencies comparable to those of out-of-plane bending even for thickness-to-diameter ratios as small as 10−1. The equations for three-dimensional motion are discretized through the Ritz technique, yielding natural frequencies and mode shapes for coupled axial, radial, and circumferential deformations. This treatment is applicable to “disks” of arbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings, and shells. The solutions so obtained converge in the limiting cases to the values expected from the classical theories, and to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the technologically-important range, the natural frequencies of certain in- and out-of-plane modes can be close to one another, or even identically repeated.

Positioning of bearings for curved continuous spread-box girder bridges

2002 ◽  
Vol 29 (5) ◽  
pp. 641-652 ◽  
Author(s):  
Magdy Samaan ◽  
Khaled Sennah ◽  
John B Kennedy
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Structural Response ◽  
Element Model ◽  
Extensive Study ◽  
Mode Shapes ◽  
Box Girder ◽  
Girder Bridges ◽  
Bridge Superstructure ◽  
Girder Bridge

The type and arrangement of bearings for a bridge superstructure are important considerations in bridge design. For a curved continuous spread-box girder bridge, the support conditions for the bridge superstructure may significantly influence the distribution factors for maximum stresses, reactions, and shear forces as well as the bridge natural frequencies and mode shapes. Current design practices in North America recommend very few guidelines for bearing arrangements and types. This paper describes an extensive study carried out using an experimentally calibrated finite element model, in which curved continuous prototype bridges were analyzed to determine their structural response. Six different types and arrangements of support bearings were studied to determine their effect on the maximum stress and reaction distributions as well as on the natural frequencies of such bridges. The results were used to suggest the most favourable bearing arrangement and type.Key words: bridge bearings, composite, continuous, curved bridges, design, distribution factors, finite element, spread-box.

An Exact Solution for the Natural Frequencies of Flexible Beams Undergoing Overall Motions

2003 ◽  
Vol 9 (11) ◽  
pp. 1221-1229 ◽  
Author(s):  
Ali H Nayfeh ◽  
S.A. Emam ◽  
Sergio Preidikman ◽  
D.T. Mook
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Bernoulli Beam ◽  
Flexible Beams ◽  
Euler Bernoulli Beam

We investigate the free vibrations of a flexible beam undergoing an overall two-dimensional motion. The beam is modeled using the Euler-Bernoulli beam theory. An exact solution for the natural frequencies and corresponding mode shapes of the beam is obtained. The model can be extended to beams undergoing three-dimensional motions.

Thermo-Electro-Mechanical Vibration Characteristics of Graphene/Piezoelectric/Graphene Sandwich Nanobeams

2017 ◽  
Vol 35 (1) ◽  
pp. 65-79 ◽  
Author(s):  
N. Kammoun ◽  
H. Jrad ◽  
S. Bouaziz ◽  
M. B. Amar ◽  
M. Soula ◽  
...  
Keyword(s):  
Nonlocal Elasticity ◽  
Natural Frequencies ◽  
Nonlocal Parameter ◽  
Mechanical Vibration ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Mode Shapes ◽  
Governing Equations ◽  
Numerical Examples ◽  
Generalized Differential

AbstractThis paper reports an investigation on thermo-electro-mechanical vibration of graphene/piezoelectric graphene/piezoelectric/graphene sandwich nanobeams. Based on the nonlocal elasticity theory, Timoshenko beam theory and Hamilton's principles, the governing equations are developed and solved using generalized differential quadrature (GDQ) method. The effects of the nonlocal parameter, external electrical voltage, temperature change and axial force on vibration of graphene/piezoelectric/graphene sandwich nanobeams are examined. The performance and the accuracy of the presented model are highlighted through numerical examples with different boundary conditions. This study reports that the nonlocal parameter and thermo-electro-mechanical loadings have important effect on the natural frequencies and the deflection mode shapes of the graphene/piezoelectric/graphene sandwich nanobeam. The present work can serve as guideline for the design of a nanoscale graphene/piezoelectric/graphene beams based electromechanical resonator sensors.

scholarly journals Natural Frequencies and Mode Shapes of Drill Pipe in Subsea Xmas Tree Installation

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Wensheng Xiao ◽  
Haozhi Qin ◽  
Jian Liu ◽  
Qi Liu ◽  
Junguo Cui ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Drill Pipe ◽  
Beam Theory ◽  
Transformation Method ◽  
Variable Coefficients ◽  
Mode Shapes ◽  
Order Partial Differential Equation ◽  
Lumped Mass ◽  
Acceleration Sensors

In this study, experimental and numerical investigations on the vibration characteristics of a drill pipe during the lowering of a subsea Xmas tree were presented. A fourth-order partial differential equation with variable coefficients was established based on Euler–Bernoulli beam theory. The natural frequencies and mode shapes are obtained by using the differential transformation method. Four drill pipe models of different sizes were used in the experiments which were measured using piezoelectric acceleration sensors and fiber Bragg grating sensors, respectively. The factors that affect the natural frequencies and mode shapes, such as length, diameter, lumped mass, and boundary conditions, were analyzed. The results show that all factors have remarkable effects on the natural frequency, but changes in the length and diameter of the pipe have little effect on the mode shapes; the main factors affecting the mode shape are the boundary conditions and lumped mass. The results of the numerical calculation were validated by a comparison with the experimental results and showed good agreement.

scholarly journals Free Vibrations of a Reddy-Bickford Multi-Span Beam Carrying Multiple Spring-Mass Systems

2011 ◽  
Vol 18 (5) ◽  
pp. 709-726 ◽  
Author(s):  
Yusuf Yesilce
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Structural Elements ◽  
Mass System ◽  
Assembly Technique

The structural elements supporting motors or engines are frequently seen in technological applications. The operation of machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko single-span beams carrying a number of spring-mass system and multi-span beams carrying multiple spring-mass systems are plenty, but the free vibration analysis of Reddy-Bickford multi-span beams carrying multiple spring-mass systems has not been investigated by any of the studies in open literature so far. This paper aims at determining the exact solutions for the natural frequencies and mode shapes of Reddy-Bickford beams. The model allows analyzing the influence of the shear effect and spring-mass systems on the dynamic behavior of the beams by using Reddy-Bickford Beam Theory (RBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1–4 span beams are studied. The natural frequencies of Reddy-Bickford single-span and multi-span beams calculated by using the numerical assembly technique and the secant method are compared with the natural frequencies of single-span and multi-span beams calculated by using Timoshenko Beam Theory (TBT); the mode shapes are presented in graphs.

scholarly journals Free and Forced Vibrations of an Axially-Loaded Timoshenko Multi-Span Beam Carrying a Number of Various Concentrated Elements

2012 ◽  
Vol 19 (4) ◽  
pp. 735-752 ◽  
Author(s):  
Yusuf Yesilce
Keyword(s):  
Axial Force ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Coefficient Matrix ◽  
Mode Shapes ◽  
Harmonic Force ◽  
Concentrated Force ◽  
Vibrating System ◽  
Assembly Technique ◽  
Vibrating Systems

In the existing reports regarding free and forced vibrations of the beams, most of them studied a uniform beam carrying various concentrated elements using Bernoulli-Euler Beam Theory (BET) but without axial force. The purpose of this paper is to utilize the numerical assembly technique to determine the exact frequency-response amplitudes of the axially-loaded Timoshenko multi-span beam carrying a number of various concentrated elements (including point masses, rotary inertias, linear springs and rotational springs) and subjected to a harmonic concentrated force and the exact natural frequencies and mode shapes of the beam for the free vibration analysis. The model allows analyzing the influence of the shear and axial force and harmonic concentrated force effects and intermediate concentrated elements on the dynamic behavior of the beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate concentrated elements, an intermediate pinned support, applied harmonic force, left-end support and right-end support of Timoshenko beam are derived. After the derivation of the coefficient matrices, the numerical assembly technique is used to establish the overall coefficient matrix for the whole vibrating system. Finally, solving the equations associated with the last overall coefficient matrix one determines the exact dynamic response amplitudes of the forced vibrating system corresponding to each specified exciting frequency of the harmonic force. Equating the determinant of the overall coefficient matrix to zero one determines the natural frequencies of the free vibrating system (the case of zero harmonic force) and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. The calculated vibration amplitudes of the forced vibrating systems and the natural frequencies of the free vibrating systems are given in tables for different values of the axial force. The dynamic response amplitudes and the mode shapes are presented in graphs. The effects of axial force and harmonic concentrated force on the vibration analysis of Timoshenko multi-span beam are also investigated.

Transverse Vibration of Two Axially Moving Beams Connected by an Elastic Foundation

2005 ◽  
Author(s):  
Mohamed Gaith ◽  
Sinan Mu¨ftu¨
Keyword(s):  
Elastic Foundation ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Flexural Rigidity ◽  
Beam Theory ◽  
Mode Shapes ◽  
Winkler Elastic Foundation ◽  
Canonical State ◽  
Axially Moving Beams ◽  
Axially Moving

Transverse vibration of two axially moving beams connected by a Winkler elastic foundation is analyzed analytically. The system is a model of paper and paper-cloth (wire-screen) used in paper making. The two beams are tensioned, translating axially with a common constant velocity, simply supported at their ends, and of different materials and geometry. Due to the effect of translation, the dynamics of the system displays gyroscopic motion. The Euler-Bernoulli beam theory is used to model the deflections, and the governing equations are expressed in the canonical state form. The natural frequencies and associated mode shapes are obtained. It is found that the natural frequencies of the system are composed of two infinite sets describing in-phase and out-of-phase vibrations. In case the beams are identical, these modes become synchronous and asynchronous, respectively. Divergence instability occurs at the critical velocity; and, the frequency-velocity relationship is similar to that of a single traveling beam. The effects of the mass, flexural rigidity, and axial tension ratios of the two beams, as well as the effects of the elastic foundation stiffness are investigated.

Simultaneous Wake- and Vortex-Induced Vibrations of a Cylinder With Two Degrees of Freedom in Each Direction

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
J. R. Chaplin ◽  
W. M. J. Batten
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Elastic System ◽  
Cross Flow ◽  
Structural Response ◽  
Flow Induced Vibration ◽  
Vortex Induced Vibrations ◽  
Complicated Process ◽  
The Subject ◽  
Flow Directions

The flow-induced vibration of one cylinder in the wake of another is the subject of continuing interest in connection with interactions between vertical tension risers in deep water. When one riser is downstream of another, it is likely to be subject to wake-induced and vortex-induced excitations at different frequencies simultaneously. Both are complex mechanisms, and it is reasonable to assume that they interact. To begin to understand this complicated process, it is desirable that any modeling should incorporate some features of a multidegree-of-freedom structural response. With this aim, this paper describes experiments in which one cylinder was free to undergo simultaneous wake- and vortex-induced vibrations downstream of a similar but stationary cylinder in a steady flow. The downstream cylinder was mounted on an elastic system that had two natural frequencies in both the in-line and cross-flow directions. Mass ratios were almost the same in all four modes. Measurements are presented of simultaneous wake- and vortex-induced vibrations for cylinder separations of 5 and 10 diameters in the in-line direction, and up to 4 diameters transversely. At a reduced velocity of 83 (based on the cylinder's lower submerged natural frequency) and a separation of 5 diameters, excursions of wake-induced vibrations peaked at almost 5 diameters, when the downstream cylinder was near the edge of the upstream cylinder's wake.

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