Showing papers in "Journal of Pressure Vessel Technology-transactions of The Asme in 1999"

Modeling of Tuned Liquid Damper With Submerged Nets

Abstract: An analytical model for describing the effectiveness of tuned liquid damper (TLD) with submerged nets for suppressing horizontal vibration of structures is proposed. Dissipation energy due to the liquid motion under sinusoidal excitations is calculated based on nonlinear shallow water wave theory. In particular, the effects of hydraulic resistance produced by nets installed in a tank on the performance of TLDs are examined. The results of dissipation energy theoretically obtained are confirmed by experiments. To show the effectiveness of the proposed analytical model for TLD-structure interaction problems, the case in which TLD with nets is installed on top of a pylon of a cable-stayed bridge is described and the calculated results are compared with the actual experimental data. In the calculation, it is shown that the optimal damping factor, as is the case for tuned mass dampers (TMD), can be produced by the nets, and the effectiveness of TLD with nets are demonstrated.

Bauschinger Effect Design Procedures for Autofrettaged Tubes Including Material Removal and Sachs’ Method

Abstract: : Autofrettage is used to introduce advantageous residual stresses into pressure vessels and to enhance their fatigue lifetimes. The Bauschinger effect serves to reduce the yield strength in compression as a result of prior tensile plastic overload and can produce lower compressive residual hoop stresses near the bore than are predicted by ideal' autofrettage solutions (elastic/perfectly plastic without Bauschinger effect). A complete analysis procedure is presented which encompasses representation of elastic-plastic uniaxial loading material behavior and of reverse-loading material behavior as a function of plastic strain during loading. Such data are then combined with some yield criterion to accurately predict elastic-plastic residual stress fields within an autofrettaged thick cylinder. Pressure for subsequent re-yielding of the tube is calculated. The numerical procedure is further used to determine residual stress fields after removal of material from inside diameter (ID) and/or outside diameter (OD), including the effects of any further plasticity. A specific material removal sequence is recommended. It is shown that Sachs' experimental method, which involves removing material from the ID, may very significantly overestimate autofrettage residual stresses near the bore. Stress ranges and stress intensity factors for cracks within such stress fields are calculated together with the associated fatigue lifetimes as such cracks propagate under cyclic pressurization. The loss of fatigue lifetime resulting from the Bauschinger effect is shown to be extremely significant.

The structural response of cylindrical shells to internal shock loading

Abstract: The internal shock loading of cylindrical shells can be represented as a step load advancing at constant speed. Several analytical models are available to calculate the structural response of shells to this type of loading. These models show that the speed of the shock wave is an important parameter. In fact, for a linear model of a shell of infinite length, the amplitude of the radial deflection becomes unbounded when the speed of the shock wave is equal to a critical velocity. It is evident that simple (static) design formulas are no longer accurate in this case. The present paper deals with a numerical and experimental study on the structural response of a thin aluminum cylindrical shell to shock loading. Transient finite element calculations were carried out for a range of shock speeds. The results were compared to experimental results obtained with the GALCIT 6-in. shock tube facility. Both the experimental and the numerical results show an increase in amplitude near the critical velocity, as predicted by simple steady-state models for shells of infinite length. However, the finite length of the shell results in some transient phenomena. These phenomena are related to the reflection of structural waves and the development of the deflection profile when the shock wave enters the shell.

Limit Loads for Pipe Elbows Subjected to In-Plane Opening Moments and Internal Pressure

Abstract: The purpose of this study is to determine limit loads for pipe elbows subjected to in-plane bending moments that tend to open the elbow (i.e., increase its radius of curvature), and the influence of internal pressure on the value of the limit load. Load-deflection curves were obtained, and from these curves plastic collapse and instability loads at various values of internal pressure were determined. This was done for different pipe bend factors (h = Rt/r 2 ) using the nonlinear finite element analysis code (ABAQUS) with its special elbow element. A set of limit curves was generated from the results. These curves show the variation of collapse and instability loads with internal pressure for different elbows. Collapse loads were found to increase and then decrease with increasing pressure for all the elbow geometries studied. Instability loads were difficult to reach because of the large stiffening effect of the elbow cross-sectional deformation, and they were generally found to decrease with increasing pressure.

Modeling of Deepwater-Type Rectangular Tuned Liquid Damper With Submerged Nets

Abstract: An analytical model for describing the effectiveness of deepwater-type tuned liquid damper (TLD) with submerged nets for suppressing horizontal vibration of structures is proposed. TLD is a damping device for suppressing the vibration of long-period structures such as high-rise buildings, tall towers, the pylons of cable-stayed bridges, and so on. The damping force is created by the hydrodynamic force caused by the sloshing of water contained in rectangular tanks located on top of such structures. In this study, we proposed the dynamical model for analyzing deepwater-type TLD (DTLD) where the liquid depth is deep compared with the length of the rectangular tank. In particular, the effect of hydraulic resistance produced by submerged nets installed in the tank is examined intensively. In the analysis of DTLD, employing finite amplitude wave theory, we obtained the hydrodynamic force and the dissipation energy by using Galerkin method, taking the effect of submerged nets into account. The calculated results thus obtained are compared with experimental results, by which the validity of the modeling methodology is confirmed. Finally, the case in which DTLD with nets is installed on an actual structure is investigated both theoretically and experimentally and the the performance of DTLD is illustrated.

A High-Order Theory for Dynamic Buckling and Postbuckling Analysis of Laminated Cylindrical Shells

Abstract: Using a high-order Reisner-Mindlin-type shear deformation theory in a power series form, the general large deformation form of the Green strain tensor for imperfect cylindrical shells is introduced. Then, based on Hamilton`s principle, the equations of motion are derived for laminated composite shells. Related constitutive equations are also proposed. In this formulation, temperature dependency of material properties is considered, too. No simplifications are made in solving the coupled nonlinear equations of motion. Finally, few examples of the well-known references are reconsidered for comparison purposes.

Steam Generator Fretting-Wear Damage: A Summary of Recent Findings

Abstract: Flow-induced vibration of steam generator (SG) tubes may sometimes result in fretting-wear damage at the tube-to-support locations. Fretting-wear damage predictions are largely based on experimental data obtained at representative test conditions. Fretting-wear of SG materials has been studied at the Chalk River Laboratories for two decades. Tests are conducted in fretting-wear test machines that simulate SG environmental conditions and tube-to-support dynamic interactions. A new high-temperature force and displacement measuring system was developed to monitor tube-to-support interaction (i.e., work-rate) at operating conditions. This improvement in experimental fretting-wear technology was used to perform a comprehensive study of the effect of various environment and design parameters on SG tube wear damage. This paper summarizes the results of tests performed over the past 4 yr to study the effect of temperature, water chemistry, support geometry, and tube material on fretting-wear. The results show a significant effect of temperature on tube wear damage. Therefore, fretting-wear tests must be performed at operating temperatures in order to be relevant. No significant effect of the type of water treatment on tube wear damage was observed. For predominantly impacting motion, the wear of SG tubes in contact with 410 stainless steel is similar regardless of whether Alloy 690 ormore » Alloy 800 is used as tubing material or whether lattice bars or broached hole supports are used. Based on results presented in this paper, an average wear coefficient value is recommended that is used for the prediction of SG tube wear depth versus time.« less

Analysis of Thermal Stresses in a Boiler Drum During Start-Up

Abstract: The paper presents an analytical way of calculating thermal stress distributions in cylindrical vessels, nonuniformly heated on their circumference. In thick-walled vessel elements, simplified analytical formulas do not give satisfactory results. A new method for determining thermal stresses has been developed. On the basis of temperature history measurements at several points on the drum outer surface, a time-space temperature distribution in the component cross section is determined, and next, thermal stresses are calculated using the finite element method (FEM). The new method, proposed for the solution of the inverse heat conduction problem, is sufficiently accurate. Knowledge of the boundary conditions on the inner surface of the drum, i.e., fluid temperature and heat transfer coefficient, is not necessary because the transient temperature distribution in the component is obtained from the solution of the inverse heat conduction problem. Comparison of the thermal distributions from FEM versus the new method demonstrate the accuracy of the new method. An example application of the new method demonstrates its benefits over the solution of the boundary-initial problem obtained by FEM.

Development of NiCrAlY Alloys for Corrosion-Resistant Coatings and Thermal Barrier Coatings of Gas Turbine Components

Abstract: The demand for improved efficiency and power output of energy conversion systems has lead to an increase of gas inlet temperatures in modern land-based gas turbines. The resulting increase of component surface temperature leads to an enhanced oxidation attack of the blade coating, which, in stationary gas turbines, is usually of the MCrAlY (with M = Co and/or Ni) type. Considerable efforts have been made in the improvement of the high temperature properties of MCrAlY coatings by additions of minor alloying elements. In the present paper, the effect of systematic composition variations, especially yttrium, silicon, and titanium additions, on the protective properties of MCrAlY coatings are presented. The coatings were applied to a steel substrate by low-pressure plasma spraying. Then, free-standing MCrAlY-bodies were machines from the coating. Isothermal and cyclic oxidation tests were carried out in the temperature range 950 C--1,100 C. The effect of systematic variation of titanium and silicon contents on oxidation and microstructural stability was studied by characterization of the coating and the corrosion products using light and electron optical microscopy and by secondary neutrals mass spectrometry (SNMS).

Overview of Fatigue Crack Initiation in Carbon and Low-Alloy Steels in Light Water Reactor Environments

Abstract: Recent test data illustrate potentially significant effects of light water reactor (LWR) coolant environments on the fatigue resistance of carbon and low-alloy steels. The crack initiation and crack growth characteristics of carbon and low-alloy steels in LWR environments are presented. Decreases in fatigue lives of these steels in high-dissolved-oxygen water are caused primarily by the effect of environment on growth of short cracks <100 μm in depth. The material and loading parameters that influence fatigue life in LWR environments are defined. Statistical models have been developed to estimate the fatigue lives of these steels in LWR environments, and design fatigue curves have been developed for carbon and low-alloy steel components in LWR environments. The significance of environmental effect on the current Code design curve is evaluated.

On the Choice of Initial Geometric Imperfections in Externally Pressurized Shells

Abstract: Localized and global, of eigenmode type, initial geometric imperfections were superimposed on perfect torispherical, ellipsoidal, and toroidal shells of circular and elliptical cross section Reduction of the load-carrying capacity was then calculated numerically for various geometries and the yield point of material which was assumed to be mild steel Results show that the buckling strength of torispheres and ellipsoids could be strongly affected by imperfections, but reduction of its magnitude was dependent on the choice of imperfection shape and, more importantly, on the imperfection's location Calculations carried out for closed toroids of circular cross section show that these shells are not sensitive to eigenmode-type imperfections, while toroids with elliptical cross sections are sensitive to eigen-imperfections

Residual Stress Analysis by Simplified Inherent Strain at Welded Pipe Junctures in a Pressure Vessel

Abstract: We present a new and simplified method of estimating residual stress in welded structures by using inherent strain. The method makes use of elastic analysis by means of the finite element method and is used to calculate the residual stress in complicated three-dimensional structures efficiently. The inherent strain distribution in a welded joint of a small-diameter pipe penetrating a pressure vessel was assumed to be a simple distribution, and the residual stress was calculated, Inherent strain distributions were inferred from those of welded joints with simple shapes. The estimated residual stress using these inferred inherent strains agrees well with the measurements of a mock-up specimen. The proposed method is a simple way to estimate welding residual stress in three-dimensional structures of complicated shapes.

The Interaction of Two Parallel Semi-Elliptical Surface Cracks Under Tension and Bending

Abstract: Multiple cracks are often observed in engineering structures; and their interaction and coalescence may significantly affect their life. Knowledge of the behavior of interacting cracks is very limited. A major component of any linear fracture mechanics model for fatigue crack growth is the calculation of the crack-tip stress intensity factor, SIF. In this paper, a parametric study is presented for two parallel surface cracks in an infinite plate subjected to remote tension or to pure bending loads. The stress intensity factors for these cracks as a function of the crack-front position, depth, shape, and plate thickness are calculated using three-dimensional (3-D) finite element, (FE) analysis. The ratios of crack depth to plate thickness, a/t, and to crack length, a/c, range from 0. 1 to 0.62 and 0.1 to 1.0, respectively. Where possible, a comparison of 3-D with 2-D results is also considered.

Analytical Model for Self-Excited Vibration of an Overflow Flexible Plate Weir

Abstract: An analytical model for the self-excited vibration of an overflow flexible weir as observed in the French demonstration fast breeder reactor, Super Phenix-1, is proposed. The instability condition was derived for the case in which the plate vibrates at the frequency of the downstream tank sloshing. In this analysis, the flexible plate weir is modeled as a simply supported-free-simply supported-clamped rectangular plate. Eigenfunction expansions were applied for analyzing both plate vibrations and the downstream tank sloshing. The effect of an overflow liquid is formulated based on the assumption that the momentum change due to the collision of an overflow liquid partly transmitted to the pressure rise on the free surface. As a result, the characteristic equation of the system yielding the theoretical stability boundary was obtained. The stability boundary thus derived agreed well with experimental results.

Applications of Iterative Elastic Techniques for Elastic-Plastic Analysis of Pressure Vessels

Abstract: The paper presents an application of iterative elastic techniques for the determination of elasto-plastic stress-strain fields, limit and shakedown loads The iterative elastic method relies on iterative modification of elastic modulus in regions at which elastically calculated effective stress exceeds material yield strength The technique is applied first to thick spherical and cylindrical shells under combined pressure and thermal gradient Results showed good correlation with analytical elasto-plastic solutions The elastic compensation technique is then applied to predict elasto-plastic stresses and shakedown loads of thin spherical shell with cylindrical nozzle subjected to internal pressure or end-thrust loading Predicted shakedown loads were found to be in good agreement with the well-known Leckie and Penny results adopted in pressure vessel codes

Effective Stress Factor Correlation Equations for Piping Branch Junctions Under Internal Pressure Loading

Abstract: The results from a previous finite element parametric study by the authors on the effective stress factors (ESFs) occurring in piping branch junctions under internal pressure loading are used to produce an ESF correlation equation for use in design. This is compared with some experimental data and also with other finite element data. Results suggest that ESFs can be predicted with some confidence using the correlation equation.

Effect of Internal Pressure on Elastic-Plastic Behavior of Pipe Elbows Under In-Plane Bending Moments

Abstract: The purpose of this study is to investigate the effect of pressure on the strain and stress analysis of pipe elbows subjected to in-plane bending moments. A finite element model for the bend was constructed and loaded with a pressure of 1200 psi and end moments taking geometric and material nonlinearities into account using (ABAQUS) nonlinear finite element code. The pressure changes the effective stress distribution and location of the initial yielding from the inside surface of the elbow crown to the outside surface for the closing moment case and increases the moment of yielding. For the opening moment case, yielding starts at the inside surface of the elbow crown with and without pressure. The pressure changes the location of the maximum axial strain at instability for the closing and opening cases, and it also changes the ovality of the cross section in both cases.

Further evaluation of creep-fatigue life prediction methods for low-carbon nitrogen-added 316 stainless steel

Abstract: Low-carbon, medium-nitrogen 316 stainless steel is a principal candidate for a main structural material of a demonstration fast breeder reactor plant in Japan. A number of long-term creep tests and creep-fatigue tests have been conducted for four products of this steel. Two representative creep-fatigue life prediction methods, i.e., time fraction rule and ductility exhaustion method were applied. Total stress relaxation behavior was simulated well by an addition of a viscous strain term to the conventional (primary plus secondary) creep strain, but only the letter was assumed to contribute to creep damage in the ductility exhaustion method. The present ductility exhaustion approach was found to have very good accuracy in creep-fatigue life prediction for all materials tested, while the time fraction rule tended to overpredict failure life as large as a factor of 30. Discussion was made on the reason for this notable difference.

Experimental, Analytical, and Regulatory Evaluation of Seismic Behavior of Piping Systems

Abstract: Based on an experimental program, including both individual components and piping system, CEA has evaluated the margins coming from present design procedures and has developed sound analytical methods that allow for a modelization, in the linear or nonlinear domain. For industrial purposes, simplified methods are proposed that are much less time-consuming than nonlinear time-history calculations, but much more accurate than linear methods. They are devoted to a better evaluation of the global behavior (internal moments in the piping system or reactions in supports, displacements, rotations).

Compressive Thermal Yielding Leading to Hydrogen Cracking in a Fired Cannon

Abstract: Investigation of environmental cracking of a 1100-MPa yield strength A723 steel cannon tube subjected to prototype firings is described. Metallographic results show cracking of the steel beneath a 0.12-mm protective layer of chromium. Cracks undermine and remove sections of chromium and lead to localized erosion that ruins the cannon. Key features of the firing thermal damage and cracking are: (i ) recrystalization of the chromium to a depth of up to 0.08 mm; (ii ) steel transformation to 0.19 mm below the chrome surface; (iii ) two different periodic arrays of cracks normal to the hoop and axial directions, with mean depths of 0.23 and 0.46 mm, respectively. Time-temperature-depth profiles for the firing cycle were derived via bi-material finite difference analysis of a semi-infinite solid which incorporated cannon combustion gas temperatures and material properties that vary as a function of temperature. The temperature and depth associated with the steel transformation were used to solve iteratively for the convective heat transfer coefficient. This value was further confirmed by the depths of chromium recrystalization and of the crack arrays in the two orientations. A profile of maximum temperature versus depth is used to determine the near-bore applied and residual stress distributions within the tube. The measured volume change of steel transformation is used to determine an upper limit on applied and residual stresses. These stresses are used to determine crack-tip stress intensity factors for the observed crack arrays, and hence provide some explanation for the differential depths of cracking. The near-bore temperature and residual stress distributions are used to help determine the cause of hydrogen cracking and measures to prevent cracking. Compressive yielding due to thermal loading produces near-bore tensile residual stresses, and thereby causes hydrogen cracking. Prevention of cracking is discussed in relationship to hydrogen crack growth rate tests of alternative alloys and coatings.

Elastic-plastic failure analysis of pressure burst tests of thin toroidal shells

Abstract: This paper provides a comparison between test and analysis results for bursting of thin toroidal shells. Testing was done by pressurizing two toroidal shells until failure by bursting. An analytical criterion for bursting is developed based on good agreement between structural instability predicted by large strain-large displacement elastic-plastic finite element analysis and observed burst pressure obtained from test. The failures were characterized by loss of local stability of the membrane section of the shells consistent with the predictions from the finite element analysis. Good agreement between measured and predicted burst pressure suggests that incipient structural instability as calculated by an elastic-plastic finite element analysis is a reasonable way to calculate the bursting pressure of thin membrane structures.

Numerical analysis of nonstationary thermal response characteristics for a fluid-structure interaction system

Abstract: Nonstationary thermal response analysis for a fundamental sodium experiment simulating thermal striping phenomena was carried out using a quasi-direct numerical thermohydraulics simulation code with a third-order upwind scheme for convection terms and a boundary element method code for thermal response evaluation of structures due to random sodium temperature fluctuations developed at Power Reactor and Nuclear Fuel Development Corporation (PNC) Discussions centered on an applicability of the numerical method for the damping effects of the temperature fluctuations in the course of heat transfer to the inside of structures from the fully turbulent region of sodium flows through the comparisons with the experiment From these comparisons, it was confirmed that the numerical method has a sufficiently high potential in accuracy to predict the damping effects of the temperature fluctuations related to the thermal striping phenomena Consequently, it is concluded that the numerical prediction by the method developed in this study can replace conventional experimental approaches using 1:1 or other scale model aiming at the simulation of the thermal striping phenomena in actual liquid metal fast breeder reactor (LMFBR) plants Furthermore, economical improvements in the FBR plants can be carried out based on the discussions of optimization and rationalization of the structural design using the numerical methods

Linearization Techniques for Seismic Analysis of Piping System on Friction Support

Abstract: Generally, industrial piping systems are supported on hangers, snubbers, friction supports, etc. Friction supports are used for free thermal expansion of the piping systems. They also have the property to absorb energy from earthquake excitation. In this paper, equivalent linearization techniques such as the Caughey method for bilinear system and the energy method are used to calculate equivalent damping of typical industrial piping system on friction support. These methods are compared in terms of the equivalent damping. An iterative response spectrum method is tried for evaluating response of the piping system using equivalent damping obtained by linearization techniques. Maximum response displacement obtained at friction support is compared with the experimental values. At the end it is concluded that the Caughey method and the energy method evaluate similar damping for the piping on friction support and also concluded that the iterative response spectrum method is easy and reasonable for use in design.

The Measurement of Fluidelastic Effects at Low Reduced Velocities Using Piezoelectric Actuators

Abstract: Fluidelastic effects which are responsible for fluidelastic instabilities may be indirectly measured through the analysis of the vibrating motion of system under flow. In this paper, piezoelectric actuators are used to increase the vibratory level when buffeting forces which excite tube vibration are low, and to improve the measurement of fluidelastic forces. The proposed method based on an added excitation allows the study of the added mass and provides a better accuracy on the measurement of the vibrating characteristics and, thereby, of the fluidelastic forces. This added excitation method is compared with a standard indirect approach on a tube underwater crossflow. The influence of the level of piezoelectric excitation forces is discussed, as well as the range of application of this technique.

Acoustically induced structural fatigue of piping systems

Abstract: Piping systems handling high-pressure and high-velocity steam and various process and hydrocarbon gases through a pressure-reducing device can produce severe acoustic vibration and metal fatigue in the system It has been previously shown that the acoustic fatigue of the piping system is governed by the relationship between fluid pressure drop and downstream Mach number, and the dimensionless pipe diameter/wall thickness geometry parameter In this paper, the devised relationship is extended to cover acoustic fatigue considerations of medium and smaller-diameter piping systems

Residual Stress Estimation in Crossbores With Bauschinger Effect Inclusion Using FEM and Strain Energy Density

Abstract: Crossbore intersections in liquid ends of positive displacement pumps (PDPs) have regions with high stress concentration. Due to the cyclic loading that occurs in most PDPs, these stress concentration points are susceptible to fatigue cracking. In order to prolong their life, the liquid ends are often overpressurized (autofrettaged), thus inducing beneficial compressive hoop stresses in these critical regions upon removal of the autofrettage pressure. This autofrettage process drives the region of high stress concentration beyond the elastic limit and well into the elastic-plastic region. Elastic-plastic stresses and strains due to loading and unloading were analyzed in crossbore geometries, with Bauschinger effect included, using 3-D finite element analysis of the liquid end. For comparison, an analytical approach was developed, based on the strain energy density criterion first proposed by Glinka. The approach was modified to include the Bauschinger effect for precise estimation of such stresses and strains. Good correlation was observed between elastic-plastic crossbore stresses and strains predicted by the analytical approach and the finite element analysis.

Experimental Study of the Flow in the Suction Pipe of a Centrifugal Pump at Partial Flow Rates in Unsteady Conditions

Abstract: The operational range and the performances of pumps are limited by the occurrence of backflow and prerotation in the suction pipe as the flow rate is reduced. This paper presents the study of static pressure measurements and visualizations in the suction pipe, near the inlet of centrifugal pump, at partial flow rates, in steady conditions, and during a fast start-up of the pump. The tests were carried out in water on the DERAP© test loop of the ENSAM Lille laboratory. Standard methods allowed to determine the recirculation critical flow rate. A visualization method showed that the axial extent of the recirculation and the prerotation with the flow rate is considerably reduced during a fast start-up compared to steady conditions.

Notch and Temperature Effects on Crack Propagation in SS 304 Under LCF Conditions

Abstract: Crack growth behavior at room temperature and at 600 C of SS 304 plates with a central circular hole is studied using linear elastic and elastic-plastic fracture mechanics concepts. Due to large local plastic zone at the hole edge, short fatigue crack propagation is strongly affected by closure phenomena; and the extension rate of a short crack could not be adequately expressed in terms of stress intensity factor {Delta}K. However, the parameter {Delta}K would be appropriate for investigating the behavior of long cracks. Crack acceleration due to temperature increase is discussed and a strain-based normalization factor for {Delta}K is suggested for long cracks. The J-integral obtained from a finite element analysis is successful in establishing the propagation rate of both short and long cracks; simple power relations exist between da/dN and cyclic J-integral ({Delta}J{sub f}) at room temperature and at 600 C. With the modified J-integral, using the actual flow strain, the temperature effect could be incorporated in the correlation between da/dN and {Delta}J{sub f}.

Fatigue Behavior of Line Pipes Subjected to Severe Mechanical Damage

Abstract: Fatigue behavior of electrically resistance welded (ERW) line pipes with a gouge in a dent was experimentally investigated. After denting and machining a gouge, fluctuating internal pressure was applied to line pipes. The fatigue behavior differed above and below the threshold Q(Q{sub th}), as a function of defect size and fracture toughness. When Q {lt} Q{sub th}, ductile crack growth was observed with a consequent decrease in fatigue life. On the contrary, fatigue crack growth was observed when Q {ge} Q{sub th}. Fatigue life was predictable with an experimentally based power law equation incorporating dent depth, gouge depth, and hoop stress amplitude when Q {ge} Q{sub th}.

Added Fluid Mass for Bellows Expansion Joints in Axial Vibrations

Abstract: This paper presents the results of an analysis of fluid added mass in bellows expansion joints during bending vibrations. The added mass is shown to consist of two parts, one due to transverse rigid body motion and the other due to distortion of the convolution during bending. The latter component, neglected in previous analyses, is shown to be important for relatively short bellows, as are commonly used for expansion joints, and to become increasingly important for higher vibration modes. The distortion component has been determined using finite element analysis and the results are presented in graphical form for a typical range of bellows geometries. The total added mass is given in a form suitable for hand calculations.