Bolted joints are widely used for the mechanical assembly of engineering structures. It has been widely observed that fasteners turn loose when subjected to dynamic loads in the form of vibration or cyclic loading. Preload relaxation of threaded fasteners is the main factor that influences the joint failure under normal cyclic loading, but it is difficult to monitor the energy dissipation between the interface of the bolted joint. This paper presents an energy dissipation model for the bolted joint based on two-degree-of-freedom vibration differential mathematical model. A non-uniform pressure at the interface is considered and the resulted distinct stick-slip transitions along the contact interface are presented. The parameters of the model is calculated by using the fractal theory and differential operator method. Experiments are conducted to verify the efficiency of the proposed model. The results show that the theoretical mode shapes are in good agreement with the experimental mode shapes. According to the change of cyclic load and vibration frequency, the vibration response and the law of energy dissipation under different factors can be obtained. The results show that the vibration frequency and cyclic load are the main factors affecting the energy dissipation between interfaces. The energy dissipation of the contact surface of the bolted joints account for the main part of the energy dissipation of the bolted structure. As the preload increases, its energy dissipation decrease gradually. The results provide a theoretical basis for reducing micro-slip at the bolted joints interface.

Simple approximate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using Vlasov assumptions and Fourier series for the circumferential direction, an exact solution in the axial direction is obtained. To improve the results assumptions of Vlasov’s semimomentless theory are enhanced, i.e. we have used only the hypothesis of middle surface inextensibility to obtain a solution in axial direction. Nonlinear characteristic equations and natural mode shapes, are derived for all type of boundary conditions. Good agreement with experimental data and FEM is shown and advantage over the existing formulas for a variety of boundary conditions is presented.

Scanning acoustic microscopy (SAM) has been a well-recognized tool for both visualization and quantitative evaluation of materials at the microscale since its invention in 1974. While there have been multiple advances in SAM over the past four decades, some issues still remain to be addressed. First, the measurement speed is limited by the mechanical movement of the acoustic lens. Second, a single element transducer acoustic lens only delivers a predetermined beam pattern for a fixed focal length and incident angle, thereby limiting control of the inspection beam. Here, we propose to develop a phased-array probe as an alternative to overcome these issues. Preliminary studies to design a practical high frequency phased-array acoustic microscope probe were explored. A linear phased-array, comprising 32 elements and operating at 5 MHz, was modeled using PZFlex, a finite-element method software. This phased-array system was characterized in terms of electrical input impedance response, pulse-echo and impulse response, surface displacement profiles, mode shapes, and beam profiles. The results are presented in this paper.

Flow-induced vibration analysis of the San Onofre Nuclear Generating Station (SONGS) Replacement Steam Generators is made using non-proprietary public data for these steam generators on the Nuclear Regulatory Commission public web site, www.NRC.com. The analysis uses the methodology of Appendix N Section III of the ASME Boiler and Pressure Vessel Code, Subarticle N-1300 Flow-Induced Vibration of Tubes and Tube Banks. First the tube geometry is assembled and overall flow and performance parameters are developed at 100% design flow, then analysis is made to determine the flow velocity in the gap between tubes and tube natural frequencies and mode shapes. Finally, the mass damping and reduced velocity for tubes on the U bend are assembled and plotted on the ASME code Figure N-11331-4 fluid elastic stability diagram.

The presence of air in piping systems is a major concern in the industry. Problems like flow disruption, reduction of hydraulic machinery efficiencies or a significant drop in pipe capacity are many times related to this fact. The present paper aims to find a simple and non-intrusive experimental method to detect air in piping systems. The method, based on the dynamic properties of fluid-structure systems and underpinned by a novel low computational cost numerical simulation, accurately predicts the volume of water present in a pipe. Good agreement between numerical and experimental solutions has been obtained using much less computational effort than traditional fully coupled Fluid Structure Interaction with CFD analysis. From the numerical and experimental data, two different mathematical expressions relating the system natural frequencies, both vertically and horizontally, and the area occupied by the water have been obtained. These expressions account for the pipe geometry which theoretically would make them suitable for other diameter and wall thickness values. The paper is combined with a preliminary study of the system’s mode shapes for the different volumes of water.

A cylinder array vibrating in a fluid exhibits multiple coupled frequencies and coupled mode shapes. For a square array of four cylinders with a pitch-to-diameter ratio of 1.25, one cylinder was excited. In order to obtain the coupled modes of the whole array without the influence of exciters, a new method named noncontact-measurement image processing system was used in this paper. This system can guarantee the consistency of the frequencies quantificationally. Due to noncontact-measurement, the flow field around cylinder arrays will not be disturbed and can be measured precisely. Experimental results show that if we want to obtain all the coupled mode shapes, the consistency of cylinder frequencies (within 2%) must be insured and the vibrated cylinder should be chosen with larger amplitude in the coupled mode shapes. Distinct coupled frequencies correspond to symmetric mode shapes, while repeated coupled frequencies correspond to asymmetric ones. Besides, the acoustic fluid-solid interaction numerical method was used to calculate the vibration process of multi objects in still water. The numerical simulation results were in good agreement with experimental ones. It is found that for the same number of cylinders, the bandwidth of coupled frequencies increases with the decrease of pitch-to-diameter ratio, and that for the same pitch-to-diameter ratio, the bandwidth of coupled frequencies increases with the increase of the number of cylinders. Detuning of the cylinder frequencies leads to changes of coupled frequencies and coupled mode shapes.

Flow-induced vibrations of tubes in two-phase heat exchangers are a concern for the nuclear industry. EDF has developed a numerical tool, which allows one to evaluate safety margins and thereafter to optimize the exchanger maintenance policy. The software is based on a semi analytical model of fluid-dynamic forces and dimensionless fluid force coefficients which need to be evaluated by experiment. A test rig was presented in previous PVP conferences with the aim of assessing parallel triangular tube arrangement submitted to a two-phase vertical cross-flow: a kernel of nine flexible tubes is set in the middle of a rigid bundle. These tubes vibrate as solid bodies (in translation) both in the lift and drag directions. This paper presents some extended physical analysis applied to some selected points of the aforementioned experiment series: the response modes are identified by means of operational modal analysis (i.e. under unmeasured flow excitation) and presented in terms of frequency, damping and mode shapes. Among all the modes theoretically possible in the bundle, it was found that some of them have a higher response depending on the flow velocity and the void fraction. Mode shapes allow to argue if lock-in is present and to clarify the role of lift and drag forces close to the fluidelastic instability.

Damping is known to be a major parameter in the seismic design of nuclear facilities. Of special interest is the case of fuel assemblies in PWR plants, which, unlike other components, are submitted to axial flows: it has been known since the late 80s that their frequency response to lateral excitations was largely dependent on the flow velocity, and the issue raised by this observation is to determine a consistent fluid force model which could be used in seismic design. In the scientific literature, the standard model of fluid forces exerted upon an oscillating slender body was originally derived by Lighthill, and it involves a lift coefficient which, up to a reference frame shift, describes the force generated by a small angle of inclination of the body axis against the flow direction. Recent works by Divaret et al. have provided a value of this lift coefficient equal to 0.11 for a single cylinder, and to 0.18 for a square array of 5 by 8 cylinders, the Reynolds numbers being in the range of 10 4 . Sticking to the idea that the damping stems from the local angle of inclination of the structure against the flow direction, the present study revisits recent tests performed in the Hermes test rig of CEA Cadarache, where a fuel assembly was submitted to incipient flow velocities varying from 1.5 to 5m.s −1 , and to a lateral force exerted upon the middle grid, generating displacements in the ranges of a few mm and of a few Hz. Under the assumption that the fuel assembly behaves in an approximately linear manner and that it undergoes harmonic deformations close to its first natural mode shape, the dissipative fluid force can be expressed by an adequate combination of the hydraulic cylinder force and of the structure displacements. A lift coefficient equal to 0.3–0.4 is obtained with this procedure, which stands for the overall fuel bundle, rods and grids included.

A typical mainframe computer rack is narrow, tall and long. In certain installations, during its functional operation, the server can be subjected to earthquake events. The rack is a steel structure joined together with steel rivets. One of the rack’s functions is to protect the critical components such as the processor, input-output and storage drawers from excessive motion by minimizing the amount of deflection. The riveted joints pose a challenge in accurately representing more than three thousand joints in a finite element (FE) model. In the FE model, bonding together sheet metal regions around the rivet joints will lead to a significantly stiffer model than the actual structure. On the other hand, an accurate representation of the riveted joints will lead to a better representation of the dynamic response of the server rack under vertical and horizontal loadings. This paper presents a method of analyzing rivet joints. The rivet joints are represented by beam elements with cylindrical cross-sections in the FE model. This is accomplished by identifying two parallel or overlapping plates and inserting discrete beam elements at the riveted joint. This method will be used to predict the dynamics modes of the structure. To validate the FE model, a prototype server rack was subjected to side to side vibration tests. A sine sweep vibration test identifies dominant mode shapes and the transmissibility of the input vibration. The results of the tests on the prototype rack serve as input for FE model refinement. The test data show that representing the riveted joints with beams does provide results that closely match the actual test data. A validated FE model will be used to evaluate dominant vibration modes for several configurations of rack weight as well as configurations to stiffen the structure in the side to side direction. The dynamic mode shapes visualize the effect of stiffening brackets on dominant frequencies of the rack. The optimal stiffening design will be the one that results in the minimum deflection under the standard testing profile.

Fitness-for-service assessment of a pressurized component containing dents or other mechanical damage is important to ensure the operational safety and structural integrity of the damaged equipment. In the present study, the API 579 level 3 fitness-for-service analysis were performed for a column equipment containing dent defects, and the main difficulty is to determine the applied dynamic load, especially when considering wind load and earthquake load at high order mode shapes. To solve this problem, a simplified method combining the analytic calculation and finite element (FE) method were proposed in this study. At the first step, the wind load and earthquake load on different segments of the column without defect were calculated by analytic methods according to Chinese code GB4710. Then the critical load combination determined in step one were applied on a whole column FE model containing 6 dent defects with different dimensions. Based on the FE simulation, the stress linearization were performed for strength check, and buckling analysis were performed buckling collapse failure respectively. The results of strength check and critical buckling load showed that the column containing dents under static load and dynamic load conditions was acceptable for continued operation based on API 579 level 3 analysis. Thus, the methodology developed in this study provides an available fitness-for-service assessment for dents in column equipment and enables the consideration of dynamic loads.

A simplified method for estimating the vibrations of water pipes under the effect of unsteady fluid flows is proposed. The first natural frequencies of water pipes being about some 10 Hz due to standard design rules, and supports being arranged with spans of the order of 5 m, the fluid flow can reasonably be described as incompressible, so that acoustics do not play a significant role within this framework. Assuming for the sake of simplicity that the fluid velocity field is the gradient of a potential, it generates an inertial pressure field along the pipe. Simple equations are derived for describing the fluid flow associated with a given mode shape of the pipe, and coupled equations are provided which link the unsteady fluid flow to the vibrations. A simple test case is provided, which supports the idea that for water pipes, the vibration velocity of the structure and the unsteady fluid velocity are in the same order of magnitude.

The development of a theoretical model for fluidelastic instability in tubes arrays is presented. Based on the simple model of Lever and Weaver, it considers a group of 7 tubes which move in both the streamwise and transverse directions. The analysis does not constrain either tube frequency or relative mode shape so that the tubes’ behaviour evolves from a perturbation naturally. No additional empirical input is required. A particular case is used to evaluate the model’s performance and the ratio of streamwise to transverse natural frequency is varied. Both streamwise and transverse fluidelastic instability are predicted and the results agree well with experimental observations.

Flow over ducted cavities can lead to strong resonances of the trapped acoustic modes due to the presence of the cavity within the duct. Aly & Ziada [1–3] investigated the excitation mechanism of acoustic trapped modes in axisymmetric cavities. These trapped modes in axisymmetric cavities tend to spin because they do not have preferred orientation. The present paper investigates rectangular cross-sectional cavities as this cavity geometry introduces an orientation preference to the excited acoustic mode. Three cavities are investigated, one of which is square while the other two are rectangular. In each case, numerical simulations are performed to characterize the acoustic mode shapes and the associated acoustic particle velocity fields. The test results show the existence of stationary modes, being excited either consecutively or simultaneously, and a particular spinning mode for the cavity with square cross-section. The computed acoustic pressure and particle velocity fields of the excited modes suggest complex oscillation patterns of the cavity shear layer because it is excited, at the upstream corner, by periodic distributions of the particle velocity along the shear layer circumference.

The interaction between the cylinder motion and the wake is a complex feedback phenomenon in which the symmetry relationship between the wake and the cylinder motion plays a key role. Depending on the frequency of oscillation the symmetry relationship between the unforced von Karman wake and the imposed forced oscillations can induce a series of bifurcations. This detailed bifurcation behavior is the subject of study in the present work. 2D and 3D simulations are carried out for a Reynolds number Re=1000. As the inline cylinder forcing amplitude is increased, the wake undergoes a series of bifurcations and associated changes in the flow structure. Although the 2D analysis is clearly non-physical, it leads to a ‘simpler’ and more tractable model. Detailed comparison of the 2D and 3D POD modes provides insight into the forced wake dynamics. The 3D spatial mode shapes are significantly similar to those from 2D simulations. The relative modal energy distribution captures well the wake flow complexity. The first mode contains over 90% of the flow energy in the 2D simulations. This ratio drops significantly in the 3D case to around 45%. Clearly 3D effects are very important when it comes to energy distribution between the modes. However, the predominance of the first mode seems high enough to maintain the 2D-like dynamics. The wake flow is found to undergo two main transitions with increased forcing. The first is periodic shedding to chaotic shedding. The second is chaotic shedding to half-frequency shedding caused by a period-doubling bifurcation. The 2D simulations correctly predict these bifurcations — including the type and the number of bifurcations. The results suggest that the forced wake dynamics are primarily dominated by two-dimensional rather than 3D dynamics. However, 3D effects are important in determining the exact parameter values where bifurcations occur. A previously developed low order analytical model, based on 2D simulations, is also used to predict the wake bifurcation behavior. The relevance of the low order model has interesting implications for VIV control.

Flow-induced structural acoustics involves the study of the vibration of a structure induced by a fluid flow as well as the resulting sound generated and radiated by the motion of the structure. A thin rectangular, structure, non-fluid-loaded was excited by turbulent boundary layer flow. A method called magnitude-phase identification (MPI) is derived to measure modal information from a structure using only two-point measurements. Using MPI, the mode shapes and the auto-spectral density of vibration of each mode was measured and found to agree well with the theoretical values. When the non-fluid-loaded structure was excited with a spatially non-homogeneous wall pressure field or fluid-loaded structure was excited with a spatially homogeneous wall pressure field, the measured mode shapes were found to be the same as those predicted by theory. When a fluid-loaded structure was excited with a spatially non-homogeneous wall pressure field, the mode shapes were found to change. This suggests that standard modal analysis may not be sufficient to predict the vibration of fluid-loaded structures, as such theory assumes that the mode shapes of the structure are independent of the method by which the structure is excited.

This paper experimentally investigates the flow-sound interaction mechanisms in a T-junction combining the flow from its two co-axial side-branches into the central branch. The T-junction has a sudden area expansion at each side-branch entrance. Flow separation at these area expansions forms free shear layers which are shown to excite the acoustic mode(s) of the branches over several ranges of flow velocity, each of which results from the coupling of the acoustic mode with a different shear layer oscillation mode. Phase-locked particle image velocimetry is utilized to detail the unsteady flow field over the acoustic cycle for the oscillation mode which resulted in the strongest acoustic resonance. Finite element analysis is used to characterize the excited acoustic mode shape and its associated particle velocity field. In-depth analysis of the flow-sound interaction mechanism inside the T-junction is performed by means of Howe’s acoustic analogy. It is concluded that the flow-sound interaction mechanism in the entrance region of the T-junction produces a spatially alternating pattern of acoustic energy generation and absorption. This alternating pattern of energy exchange between the flow and sound fields results in a minimal amount of net acoustic power being generated in the entrance region . However, the increasing orthogonality between the acoustic particle streamlines and the flow streamlines near the exit of the T-junction at its center results in the majority of the generated sound power which sustains the acoustic resonance.

Many technologies based on fluid-structure interaction mechanisms are being developed to harvest energy from geo-physical flows. The velocity of such flows is low, and so is their energy density. Large systems are therefore required to extract a significant amount of energy. The question of the efficiency of energy harvesting using VIV of cables is addressed in this paper, through the case of a hanging cable with a harvester at its upper extremity. An experimental analysis of the vortex-induced vibrations of a hanging cable with variable tension along its length is first presented. It is shown that standing waves develop and that the extracted mode shapes are self-similar. This self-similar behaviour of the spatial distribution of the vibrations along the hanging string is explained theoretically by performing a linear stability analysis of an adapted wake-oscillator model. The hanging cable is then combined with a localized harvester and its dynamics is measured. An appropriate reduced-order wake-oscillator model is also used to perform parametric studies of the impact of the harvesting parameters on the efficiency. An optimal set of parameters is identified and it is shown that the maximum efficiency is close to the value reached with an elastically-mounted rigid cylinder. The efficiency is found to be essentially driven by the occurrence of traveling wave vibrations.

While finite element modeling analysis is becoming more frequent for analyzing AIV problems, in the absence of experimental data in large diameter pipe, there is no industry wide accepted methodology for representing the pressure excitation for the pipe so accurate cycles to failure may be predicted. The assumptions involved in determining the actual amplitude of the acoustic excitation, which modes may develop and how they couple with the structure all contribute to the overall uncertainty of the problem. Depending on the degree of correlation assumed between the structural and acoustical mode shapes the results vary dramatically. There are also variations based on the number of participating modes assumed. Relative strengths of a Weldolet®, an Insert Weldolet® that is a variation of Sweepolet® and a Reducing Tee connection were analyzed for a 24×6 inch Sch. 10S and STD connection assuming various degrees of correlation and mode participation. Wide fluctuations in the cycles to failure were observed based on the assumptions; however, the stress ratios between the connections are relatively stable. This suggests the use of an acoustic Stress Intensification Factor (SIF) in conjunction with Fatigue Strength Reduction Factors (FSRF) to determine suitability of connections in AIV service rather than an absolute value of cycles to failure. Further investigation of the trends in the value of SIF as the D/d (branch to header diameter) and D/t (diameter to thickness) ratios over a range of pipe diameter are required before these SIF’s could be put into use. Experimental data for a few controlled failure cases are required to ground the finite element prediction in reality. As the experiment is more likely to be conducted with air the possible pitfalls in extending the results from air to commonly used process fluid are also discussed.

In this paper, the phenomenon of self-sustained pressure oscillations due to the flow past a deep, circular, axisymmetric cavity is investigated. In many engineering applications, such as flows through open gate valves, there exists potential for coupling between the vortex shedding from the upstream edge of the cavity and a diametral mode of the acoustic pressure fluctuations. In the present study, the unsteady pressure was measured at several azimuthal locations at the bottom of the cavity walls, and the associated acoustic mode shapes were calculated numerically for the four representative cases of the internal cavity geometry, which involved a reference case with sharp, 90°edges as well as several modifications that involved chamfers of various length of the upstream and the downstream edges of the cavity. In addition, the flow velocity in the vicinity of the cavity opening in selected cases was measured using digital particle image velocimetry (PIV). The optical access to the highly confined internal flow was provided by implementing an endoscope attached to the camera. This global, quantitative imaging approach yielded patterns of velocity, streamlines and out-of-plane vorticity component. Instantaneous and time-averaged flow patterns provided insight into the mechanism of the flow tone generation. Among the considered cavity geometries, the configuration that corresponded to the most efficient noise suppression was identified.

The stability of a finite flexible wall occupying part of a rigid wall that separates two inviscid channel flows is investigated. The two-dimensional system is solved using a boundary-element method coupled with a finite-difference method. The motion of the wall is driven by the transmural pressure while the no-flux condition at the wall provides the kinematic boundary condition for each of the flows. Flows and structure are fully coupled to yield a system equation that is then transformed into state-space form so that its eigenvalues can be analysed. The flow velocities at which divergence and modal-coalescence flutter of the flexible wall occur are then determined as are mode shapes. We show that decreasing the channel heights and increasing the fluid density causes instabilities to occur at lower flow velocities. When the channels flow in opposite directions it is possible to suppress modal-coalescence of the first two modes.