Showing papers in "Journal of Sound and Vibration in 2005"

An overview of modeling and experiments of vortex-induced vibration of circular cylinders

Abstract: This paper reviews the literature on the mathematical models used to investigate vortex-induced vibration (VIV) of circular cylinders. Wake-oscillator models, single-degree-of-freedom, force–decomposition models, and other approaches are discussed in detail. Brief overviews are also given of numerical methods used in solving the fully coupled fluid–structure interaction problem and of key experimental studies highlighting the nature of VIV.

Vibration serviceability of footbridges under human-induced excitation : a literature review

Abstract: Increasing strength of new structural materials and longer spans of new footbridges, accompanied with aesthetic requirements for greater slenderness, are resulting in more lively footbridge structures. In the past few years this issue attracted great public attention. The excessive lateral sway motion caused by crowd walking across the infamous Millennium Bridge in London is the prime example of the vibration serviceability problem of footbridges. In principle, consideration of footbridge vibration serviceability requires a characterisation of the vibration source, path and receiver. This paper is the most comprehensive review published to date of about 200 references which deal with these three key issues. The literature survey identified humans as the most important source of vibration for footbridges. However, modelling of the crowd-induced dynamic force is not clearly defined yet, despite some serious attempts to tackle this issue in the last few years. The vibration path is the mass, damping and stiffness of the footbridge. Of these, damping is the most uncertain but extremely important parameter as the resonant behaviour tends to govern vibration serviceability of footbridges. A typical receiver of footbridge vibrations is a pedestrian who is quite often the source of vibrations as well. Many scales for rating the human perception of vibrations have been found in the published literature. However, few are applicable to footbridges because a receiver is not stationary but is actually moving across the vibrating structure. During footbridge vibration, especially under crowd load, it seems that some form of human–structure interaction occurs. The problem of influence of walking people on footbridge vibration properties, such as the natural frequency and damping is not well understood, let alone quantified. Finally, there is not a single national or international design guidance which covers all aspects of the problem comprehensively and some form of their combination with other published information is prudent when designing major footbridge structures. The overdue update of the current codes to reflect the recent research achievements is a great challenge for the next 5–10 years.

A review of vibration-based techniques for helicopter transmission diagnostics

Abstract: Over the past 25 years, much research has been devoted to the development of Health and Usage Monitoring (HUM) systems for rotorcraft gearbox and drivetrain components. The promise of HUM systems is the ability to provide accurate information regarding the condition of various flight critical components. This paper reviews the state of the art in vibration-based helicopter transmission diagnostics. The development of various damage detection techniques is discussed from a historical perspective, and the ability of these techniques to detect damage in helicopter transmissions is reviewed. Emerging research trends suggest that improvements in signal processing, sensor development and individual-tooth mesh waveform modelling could improve the performance of current and future helicopter transmission diagnostics.

An improved Hilbert Huang transform and its application in vibration signal analysis

Abstract: The vibration generated by industrial machines always contains nonlinear and non-stationary signals. Recently, a number of new methods have been proposed to analyse these signals. One of the promising methods is the Hilbert–Huang Transform (HHT). The HHT is derived from the principals of empirical mode decomposition (EMD) and the Hilbert Transform. When applying the HHT, first, the EMD will decompose the acquired signal into a collection of intrinsic mode functions (IMF). The IMF is a kind of complete, adaptive and almost orthogonal representation for the analysed signal. Since the IMF is almost monocomponent, it can determine all the instantaneous frequencies from the nonlinear or non-stationary signal. Second, the local energy of each instantaneous frequency can be derived through the Hilbert Transform. Hence, the result is an energy–frequency–time distribution of the signal. Since applying the process of HHT is not computational intensive, the HHT becomes a promising method to extract the properties of nonlinear and non-stationary signal. However, after the completion of a thorough experiment, the result generated by the HHT has its deficiency. First, the EMD will generate undesirable IMFs at the low-frequency region that may cause misinterpretation to the result. Second, depends on the analysed signal, the first obtained IMF may cover too wide a frequency range such that the property of monocomponent cannot be achieved. Third, the EMD operation cannot separate signals that contain low-energy components. In this study, new techniques have been applied to improve the result of HHT. In the improved version of HHT, the wavelet packet transform (WPT) is used as preprocessing to decompose the signal into a set of narrow band signals prior to the application of EMD. With the help from WPT, each IMF derived from the EMD can truly become monocomponent. Then, a screening process is conducted to remove unrelated IMFs from the result. Both simulated and experimental vibration signals of having a rotary system with the fault of rubbing occurred have proven that the improved HHT does show the rubbing symptoms more clear and accurate than the original HHT. Hence, the improved HHT is a precise method for nonlinear and non-stationary signal analysis.

Uncertainties and dynamic problems of bolted joints and other fasteners

Abstract: This review article provides an overview of the problems pertaining to structural dynamics with bolted joints. These problems are complex in nature because every joint involves different sources of uncertainty and non-smooth non-linear characteristics. For example, the contact forces are not ideally plane due to manufacturing tolerances of contact surfaces. Furthermore, the initial forces will be redistributed non-uniformly in the presence of lateral loads. This is in addition to the prying loading, which is non-linear tension in the bolt and non-linear compression in the joint. Under environmental dynamic loading, the joint preload experiences some relaxation that results in time variation of the structure's dynamic properties. Most of the reported studies focused on the energy dissipation of bolted joints, linear and non-linear identification of the dynamic properties of the joints, parameter uncertainties and relaxation, and active control of the joint preload. Design issues of fully and partially restrained joints, sensitivity analysis to variations of joint parameters, and fatigue prediction for metallic and composite joints will be discussed.

Back-scattering correction and further extensions of amiet's trailing-edge noise model. Part 1: theory

Abstract: A previously published analytical formulation aimed at predicting broadband trailing-edge noise of subsonic airfoils is extended here to account for all the effects due to a limited chord length, and to infer the far-field radiation off the mid-span plane. Three-dimensional gusts are used to simulate the incident aerodynamic wall pressure that is scattered as acoustic waves. A leading-edge back-scattering correction is derived, based on the solution of an equivalent Schwarzschild problem, and added to the original formula. The full solution is found to agree very well with other analytical results based on a vanishing Mach number Green's function tailored to a finite-chord flat plate and sources close to the trailing edge. Furthermore, it is valid for any subsonic ambient mean flow velocity. The back-scattering correction is shown to have a significant effect at lower reduced frequencies, for which the airfoil chord is acoustically compact, and at the transition between supercritical and subcritical gusts. It may be important for small-size airfoils, such as automotive fan blades and similar technologies. The final far-field noise formula can be used to predict trailing-edge noise in an arbitrary configuration, provided that a minimum statistical description of the aerodynamic pressure fluctuations on the airfoil surface close to the trailing edge is available.

Vibro-acoustic analysis of complex systems

Abstract: A general method is presented for predicting the ensemble average steady-state response of complex vibro-acoustic systems that contain subsystems with uncertain, or random, properties. The method combines deterministic and statistical techniques to produce a non-iterative hybrid method that incorporates equations of dynamic equilibrium and power balance. The method is derived explicitly without reference to statistical energy analysis (SEA); however, it is seen that the wave approach to SEA can be viewed as a special case of the proposed method. The proposed method provides a flexible way to account for necessary deterministic details in a vibro-acoustic analysis without requiring that an entire system be modeled deterministically. The method therefore provides a potential solution to the mid-frequency problem (in which a system is neither entirely deterministic nor entirely statistical). The application of the method is illustrated with a numerical validation example.

Semi-active H∞ control of vehicle suspension with magneto-rheological dampers

Abstract: Semi-active H∞ control of vehicle suspension with magneto-rheological (MR) damper is studied in this paper. First, an experiment is conducted on an MR damper prototype subjected to cyclic excitation. Then, a polynomial model is adopted to characterize the dynamic response of the MR damper. Such a model has an advantage that it can represent the inverse dynamics of the MR damper analytically, so that the desired output in the open-loop control scheme can be realized easily. Finally, a static output feedback H∞ controller which utilizes the measurable suspension deflection and sprung mass velocity as feedback signals for active vehicle suspension is designed. The active control force is realized with the MR damper using the obtained polynomial model. A quarter-car suspension model is considered in this paper for analysis and simulation. The proposed scheme is further validated by numerical simulation under random excitation. Simulation results showed that the designed static output feedback H∞ controller realized by the MR damper can achieve good active suspension performance.

Vehicle–bridge interaction dynamics and potential applications

Abstract: The dynamic interaction between a moving vehicle and the sustaining bridge is studied. By the method of modal superposition, closed-form solutions are obtained for the vertical responses of both the bridge and moving vehicle, assuming the vehicle/bridge mass ratio to be small. For both the bridge and vehicle responses, it is confirmed that rather accurate solutions can be obtained by considering only the first mode. The displacement, velocity, and acceleration of the bridge are governed at different extents by two sets of frequencies, i.e., the driving frequency of the vehicle and natural frequencies of the bridge. From the spectrum for the bridge displacement, the vehicle speeds can be shown to be associated with some low-frequency pikes. On the other hand, the vehicle responses are governed by five distinct frequencies that appear as driving frequencies, vehicle frequency, and bridge frequencies with shift. From the vehicle's acceleration spectrum, the first bridge frequency (with shift) is shown to have rather high visibility and can be easily identified. The effects of damping of the vehicle and bridge are evaluated in the numerical studies. Potential applications of the present results, as well as further researches required, are also indicated in the paper.

Temperature dependent vibration analysis of functionally graded rectangular plates

Abstract: A theoretical method is developed to investigate vibration characteristics of initially stressed functionally graded rectangular plates made up of metal and ceramic in thermal environment. The temperature is assumed to be constant in the plane of the plate and to vary in the thickness direction only. Two types of thermal condition are considered. The first type is that one value of the temperature is imposed on the upper surface and the other (or same) value on the lower surface. The second is that the heat flows from the upper surface to the lower one held at a prescribed temperature. Material properties are assumed to be temperature dependent, and vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The third-order shear deformation plate theory to account for rotary inertia and transverse shear strains is adopted to formulate the theoretical model. The Rayleigh–Ritz procedure is applied to obtain the frequency equation. The analysis is based on an expansion of the displacements in the double Fourier series that satisfy the boundary conditions. The effect of material compositions, plate geometry, and temperature fields on the vibration characteristics is examined. The present theoretical results are verified by comparing with those in literature.

A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics

Abstract: In structural dynamics, a predictive model is constructed by developing a mathematical–mechanical model of a designed system in order to predict the response of the real system which is the manufactured system realized from the designed system. The mathematical–mechanical modelling process of the designed system introduces two fundamental types of uncertainties: the data uncertainties and the model uncertainties. Uncertainties have to be taken into account for improving the predictability of the model. Model uncertainties cannot be modelled by using the usual parametric probabilistic approach. Recently, a general non-parametric probabilistic approach of model uncertainties for dynamical systems has been proposed using the random matrix theory. This paper gives a comprehensive overview of this approach in developing its foundations in simple terms and in illustrating all the concepts and the tools introduced in the general theory, by using a simple example. This paper deals with (1) notions of designed systems, real systems, mean models as predictive models, errors and uncertainties; (2) the definition of a simple example in linear elastodynamics; (3) a comprehensive overview of the non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics; (4) a summary of the random matrix ensembles which are necessary for the non-parametric modelling of random uncertainties; (5) the estimation of the dispersion parameters of the non-parametric probabilistic model using experimental data; (6) the method to solve the stochastic equation of the dynamical system with non-parametric probabilistic model of random uncertainties; (7) a numerical simulation and the validation for the simple example.

The excitation of ground vibration by rail traffic: theory of vehicle–track–soil interaction and measurements on high-speed lines

Abstract: This article presents an integrated model for the computation of vehicle–track interaction and the ground vibrations of passing trains. A combined finite element and boundary element method is used to calculate the dynamic compliance of the track on realistic soil whereas multi-body models are used for the vehicle. The dynamic stiffness of the vehicle and that of the track are combined to calculate the dynamic axle loads due to the irregularities of the vehicle and the track as well as those due to sleeper passing excitation. These loads serve as input for the calculation of ground vibration near railway lines in the time and frequency domains. The theoretical methods and results have been proven by experiments in several respects and at several instances. First, on the occasion of the test and record runs of the Intercity Experimental, there was a very good quality of the vehicle and of the newly built track so that the deterministic parts of the excitation—the static load and the sleeper-passing component—could clearly be identified, the first being of minor importance apart from the track. Second, simultaneous measurements of the vehicle, the track and the soil at three different track situations were performed where we could verify the different parts of the stochastic excitation and their importance for the ground vibrations. The irregularities of the vehicle are dominant at high frequencies whereas the irregularities of the track are more important at lower frequencies. The comparison of the theory and the measurements also points to the phenomena of the vehicle–track resonance and the scattering of the quasi-static axle impulses by randomly varying soil.

Neural networks-based damage detection for bridges considering errors in baseline finite element models

Abstract: Structural health monitoring has become an important research topic in conjunction with damage assessment and safety evaluation of structures. The use of system identification approaches for damage detection has been expanded in recent years owing to the advancements in signal analysis and information processing techniques. Soft computing techniques such as neural networks and genetic algorithm have been utilized increasingly for this end due to their excellent pattern recognition capability. In this study, a neural networks-based damage detection method using the modal properties is presented, which can effectively consider the modelling errors in the baseline finite element model from which the training patterns are to be generated. The differences or the ratios of the mode shape components between before and after damage are used as the input to the neural networks in this method, since they are found to be less sensitive to the modelling errors than the mode shapes themselves. Two numerical example analyses on a simple beam and a multi-girder bridge are presented to demonstrate the effectiveness of the proposed method. Results of laboratory test on a simply supported bridge model and field test on a bridge with multiple girders confirm the applicability of the present method.

A comparison of semi-active damping control strategies for vibration isolation of harmonic disturbances

Abstract: Active vibration isolation systems are less commonly used than passive systems due to their associated cost and power requirements In principle, semi-active isolation systems can deliver the versatility, adaptability and higher performance of fully active systems for a fraction of the power consumption Various semi-active control algorithms have been suggested in the past, many of which are of the “on–off” variety This paper studies the vibration isolation characteristics of four established semi-active damping control strategies, which are based on skyhook control and balance control A semi-active damper is incorporated into a single-degree-of-freedom (sdof) system model subject to base excitation Its performance is evaluated in terms of the root-mean-square (rms) acceleration transmissibility, and is compared with those of a passive damper and an ideal skyhook damper The results show that the semi-active system always provides better isolation at higher frequencies than a conventional passively damped system

Concept and model of eddy current damper for vibration suppression of a beam

Abstract: Electromagnetic forces are generated by the movement of a conductor through a stationary magnetic field or a time varying magnetic field through a stationary conductor and can be used to suppress the vibrations of a flexible structure. In the present study, a new electromagnetic damping mechanism is introduced. This mechanism is different from previously developed electromagnetic braking systems and eddy current dampers because the system investigated in the subsequent manuscript uses the radial magnetic flux to generate the electromagnetic damping force rather than the flux perpendicular to the magnet's face as done in other studies. One important advantage of the proposed mechanism is that it is simple and easy to apply. Additionally, a single magnet can be used to damp the transverse vibrations that are present in many structures. Furthermore, it does not require any electronic devices or external power supplies, therefore functioning as a non-contacting passive damper. A theoretical model of the system is derived using electromagnetic theory enabling us to estimate the electromagnetic damping force induced on the structure. The proposed eddy current damper was constructed and experiments were performed to verify the precision of the theoretical model. It is found that the proposed eddy current damping mechanism could increase the damping ratio by up to 150 times and provide sufficient damping force to quickly suppress the beam's vibration.

The influence of cracks in rotating shafts

Abstract: In this paper, the influence of transverse cracks in a rotating shaft is analysed. The paper addresses the two distinct issues of the changes in modal properties and the influence of crack breathing on dynamic response during operation. Moreover, the evolution of the orbit of a cracked rotor near half of the first resonance frequency is investigated. The results provide a possible basis for an on-line monitoring system. In order to conduct this study, the dynamic response of a rotor with a breathing crack is evaluated by using the alternate frequency/time domain approach. It is shown that this method evaluates the nonlinear behaviour of the rotor system rapidly and efficiently by modelling the breathing crack with a truncated Fourier series. The dynamic response obtained by applying this method is compared with that evaluated through numerical integration. The resulting orbit during transient operation is presented and some distinguishing features of a cracked rotor are examined.

On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates

Abstract: Two independent state equations are established for transversely isotropic magneto-electro-elastic media by introducing proper stress and displacement functions. The free vibration problem of simply supported rectangular plates with general inhomogeneous (functionally graded) material properties along the thickness direction is then considered. An approximate laminate model is employed to transform the state equations with variable coefficients to the ones with constant coefficients. Two different classes of vibrations are found. In particular, the frequency of the first class is only related to the elastic property of the plate, while that of the second class is affected by the couplings among the elastic, electric and magnetic fields. Numerical results are presented and some important issues are discussed.

Sound transmission through lightweight double-leaf partitions: theoretical modelling

Abstract: This paper presents theoretical modelling of the sound transmission loss through double-leaf lightweight partitions stiffened with periodically placed studs. First, by assuming that the effect of the studs can be replaced with elastic springs uniformly distributed between the sheathing panels, a simple smeared model is established. Second, periodic structure theory is used to develop a more accurate model taking account of the discrete placing of the studs. Both models treat incident sound waves in the horizontal plane only, for simplicity. The predictions of the two models are compared, to reveal the physical mechanisms determining sound transmission. The smeared model predicts relatively simple behaviour, in which the only conspicuous features are associated with coincidence effects with the two types of structural wave allowed by the partition model, and internal resonances of the air between the panels. In the periodic model, many more features are evident, associated with the structure of pass- and stop-bands for structural waves in the partition. The models are used to explain the effects of incidence angle and of the various system parameters. The predictions are compared with existing test data for steel plates with wooden stiffeners, and good agreement is obtained.

Nonlinear modal models for sonic fatigue response prediction: a comparison of methods

Abstract: Accurate prediction of sonic fatigue response is important in designing aircraft structures for long life. Early prediction methods were based on single-mode, linear models which were not accurate for complex structures or large-amplitude response levels. Direct time integration of full, nonlinear, finite element models can provide accurate results, but at a prohibitive computational expense. Recent methods reduce the finite element model to a low-order system of nonlinear modal equations. The modal equations can then be integrated in the time domain. The computational burden is greatly reduced and an accurate response prediction can be accomplished. In this paper, several methods used to construct the nonlinear modal models are compared using a clamped–clamped beam as an example problem.

On the selection of acoustic/vibration sensors for leak detection in plastic water pipes

Abstract: Leaks from buried water distribution pipes are commonly located by applying the correlation technique to two measured acoustic/vibration signals on either side of a leak. The effectiveness of the correlation technique for locating leaks in plastic pipes depends on the type of sensors used and their sensitivities. Based on an analytical model of the cross-correlation of pressure responses established in an earlier study, this paper investigates the behaviour of the cross-correlation coefficient for leak signals measured using pressure, velocity and acceleration sensors. Theoretical predictions show that a measure of pressure responses using hydrophones is effective for measurements where there is a small signal-to-noise ratio (SNR), but a sharper peak correlation coefficient can be achieved if accelerometers are used. The theoretical work is validated to some extent with test data from actual water pipes on a test site in Canada.

Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: sub-harmonic motions

Abstract: In this study, a non-linear time-varying dynamic model is used to investigate sub-harmonic and chaotic motions exhibited by a typical multi-mesh gear train. The purely torsional system is formed by three rigid shafts connected to each other by two spur gear pairs. The lumped parameter dynamic model includes both gear backlash clearances and parametric gear mesh stiffness fluctuations. Steady state period-one motions of the same system were studied in another by using a multi-term harmonic balance method in conjunction with discrete Fourier transforms. This study expands the same solution technique for an investigation of sub-harmonic resonances of the forced response. The accuracy of the predictions is demonstrated by comparing them to the direct numerical integration results. Effect of several system parameters such as alternating mesh stiffness amplitudes, gear mesh damping and static torque transmitted on sub-harmonic motions are described. It is shown that stable sub-harmonic motions mostly in the form of softening type resonances dictate the frequency ranges in which the period-one motions are unstable due to parametric excitations. Other non-linear phenomena including long sub-harmonic motions and period-doubling bifurcations leading to chaotic behavior are also predicted.

Local damage detection using the two-dimensional gapped smoothing method

Abstract: This paper presents a procedure for locating variability in structural stiffness. For some types of structure, this variability is directly related to manufacturing defects and/or in-service damage. Unlike many published damage detection methods, the procedure presented here uses only data obtained from the damaged structure. Baseline data and theoretical models of the undamaged structure are not used during the analysis presented here. The procedure locates regions in a structure where the stiffness varies. Providing it is known that the structure, in its undamaged state, is homogeneous with respect to stiffness, the procedure will detect the areas of inhomogeneity that are caused by the incipient damage. For non-homogeneous structures, some knowledge of the structural details (for example, engineering drawings or a baseline test) is required in order to discriminate damage. The procedure is a two-dimensional generalization of a previously published one-dimensional gapped smoothing method, whereby local features in vibration curvature shapes are extracted using a localized curve fit (i.e., smoothing). A variability index is generated for each test point on the structure. Increased variability is due either to structural stiffness features or damage. A statistical treatment of the indices enables discrimination of areas with significant stiffness variability. Providing the damaged areas are sufficiently small compared to the total surface area, their indices will be statistical outliers. The procedure can either analyze mode shape data, or frequency dependent operating displacement shape data. The procedure is demonstrated with a finite element model of a plate, and experiments on composite plates with deliberately induced multiple delaminations. Finally, the method is demonstrated on data taken from a large composite hull structure. In all cases the procedure successfully located the damaged regions.

Experimental observation of nonlinear vibrations in a rub-impact rotor system

Abstract: An experimental setup is installed to simulate the rotor-to-stator rub of the rotor system. A special structure of stator is designed that can simulate the condition of the full rub. The vibration waveforms, spectra, orbits and Poincare's maps are used to analyze nonlinear responses and bifurcation characteristics of the system when the rub-impact occurs. Experiments with different conditions, including one and two rotor with single- and multi-disks, are performed. Very rich forms of periodic and chaotic vibrations were observed. The experiments show that the system motion generally contains the multiple harmonic components such as 2X, 3X, etc. and the 1/2 fractional harmonic components such as 1/2X, 3/2X, etc. Under some special conditions, the 1/3 fractional harmonic components such as 1/3X, 2/3X, etc. can be observed as well.

Freefield vibrations due to dynamic loading on a tunnel embedded in a stratified medium

Abstract: An efficient and modular numerical prediction model is developed to predict vibration and re-radiated noise in adjacent buildings from excitation due to metro trains in tunnels for both newly built and existing situations. The three-dimensional dynamic tunnel–soil interaction problem is solved with a subdomain formulation, using a finite element formulation for the tunnel and a boundary element method for the soil. The periodicity of the tunnel and the soil in the longitudinal direction is exploited using the Floquet transform, limiting the discretization effort to a single bounded reference cell. It is demonstrated in the paper how the boundary element method can efficiently be extended to deal with periodic media, reusing the available three-dimensional Green's tensors for layered media. The efficiency of the method is demonstrated with a numerical example, where the case of harmonic and transient point loading on the invert of a shallow cut-and-cover masonry tunnel in Paris is considered. The work described here was carried out under the auspices of the CONVURT project sponsored by the European Community.

The historical bases of the Rayleigh and Ritz methods

Abstract: Rayleigh's classical book Theory of Sound was first published in 1877. In it are many examples of calculating fundamental natural frequencies of free vibration of continuum systems (strings, bars, beams, membranes, plates) by assuming the mode shape, and setting the maximum values of potential and kinetic energy in a cycle of motion equal to each other. This procedure is well known as “Rayleigh's Method.” In 1908, Ritz laid out his famous method for determining frequencies and mode shapes, choosing multiple admissible displacement functions, and minimizing a functional involving both potential and kinetic energies. He then demonstrated it in detail in 1909 for the completely free square plate. In 1911, Rayleigh wrote a paper congratulating Ritz on his work, but stating that he himself had used Ritz's method in many places in his book and in another publication. Subsequently, hundreds of research articles and many books have appeared which use the method, some calling it the “Ritz method” and others the “Rayleigh–Ritz method.” The present article examines the method in detail, as Ritz presented it, and as Rayleigh claimed to have used it. It concludes that, although Rayleigh did solve a few problems which involved minimization of a frequency, these solutions were not by the straightforward, direct method presented by Ritz and used subsequently by others. Therefore, Rayleigh's name should not be attached to the method.

Leak location using the pattern of the frequency response diagram in pipelines: a numerical study

Abstract: This paper presents a method of leak detection in a single pipe where the behaviour of the system frequency response diagram (FRD) is used as an indicator of the pipe integrity. The presence of a leak in a pipe imposes a pattern on the resonance peaks of the FRD that can be used as a clear indication of leakage. Analytical expressions describing the pattern of the resonance peaks are derived. Illustrations of how this pattern can be used to individually locate and size multiple leaks within the system are presented. Practical issues with the technique, such as the procedure for frequency response extraction, the impact of measurement position, noise- and frequency-dependent friction are also discussed.

Sound absorption of a finite flexible micro-perforated panel backed by an air cavity

Abstract: Micro-perforated absorbers have been studied for decades. In the experimental results of some previous works, an unexpected peak due to the flexible panel vibration effect was found on the absorption coefficient curve. In this paper, the acoustic absorption of a finite flexible micro-perforated panel backed by an air cavity is studied in detail. The absorption formula that is developed for the micro-perforated absorber is based on the modal analysis solution of the classical plate equation coupled with the acoustic wave equation. Another approach to derive a simpler absorption formula is also developed. The predictions from the two formulas are very close, except for those at the resonant frequencies of the higher structural modes and acoustic modes parallel to the panel surface. The theoretical results show good agreement with the measurements. It can be concluded that (1) as the panel vibration effect can dissipate more energy, the corresponding absorption peaks can widen the absorption bandwidth of a micro-perforated absorber by appropriately selecting the parameters such as panel thickness, perforation diameter, and perforation spacing, etc., such that the structural resonant frequency is higher than the absorption peak frequency caused by the perforations; (2) the comparison of the cases of different panel mode shapes does not show a significant difference in the absorption performance; and (3) the structural damping effect can improve the absorption performance at the frequencies between the structural resonant frequencies and the peak frequency of the micro-perforation effect, and decrease the peak absorption values of the structural resonances.

Free vibration analysis of conical shells via the element-free kp-Ritz method

Abstract: In this paper, we consider the free vibration analysis of thin conical shells under different boundary conditions. The analysis is carried out using the element-free kp-Ritz method. The present study is based on the classical thin-shell theory. The kernel particle (kp) functions are employed in hybridized form with harmonic functions to approximate the two-dimensional displacement field. In order to examine the numerical stability of the present approach, convergence studies are performed based on the influences of the support size and the number of nodes. To verify the accuracy of this method, comparisons of the present results are made with results available in the open literature. This study also examines in detail the effects of semi-vertex angles and boundary conditions on the frequency characteristics of the conical shells.

The damped dynamic vibration absorbers: revisited and new result

Abstract: The dynamic vibration absorber (DVA) or tuned-mass damper (TMD) is a widely used passive vibration control device. A simple DVA consists of a mass and a spring. When a mass–spring system or a primary system is excited by a harmonic force, its vibration can be suppressed by attaching a DVA as shown in Fig. 1(a). However, adding a DVA to a one-degree-of-freedom (dof) system results in a new 2-dof system. If the exciting frequency coincides one of the two natural frequencies of the new system, the system will be at resonance. To overcome this problem, a damper is added to DVA. Fig. 1(b) shows a primary system attached by a damped DVA. Equations of motion of the system are given as

Dynamic force identification based on enhanced least squares and total least-squares schemes in the frequency domain

Abstract: Identifying dynamic forces from structural responses is necessary when direct measurement of those dynamic forces is impossible using conventional means. A common approach to address this problem is to determine the frequency response function (FRF) matrix, measure the structural responses, and calculate the dynamic forces based on least-squares (LS) scheme. This approach has been proven to be effective in reducing the random errors that occur in structural response signals. Unfortunately, the accuracy of this approach is often hindered by the inversion of an ill-conditioned FRF matrix at frequencies near the structural resonances. To overcome this inversion instability, two regularization filters, namely the truncated singular value decomposition (TSVD) filter and the Tikhonov filter, are used in conjunction with the conventional LS scheme at specific frequencies. Here a criterion for applying these enhanced LS schemes is proposed to aid in determining when the increase in computational effort is better utilized. Furthermore, a new LS form of the Morozov's discrepancy principle is formulated to aid in selecting the optimum regularization parameter for these filters at each frequency. The accuracy in using conventional LS, TSVD-based LS, and Tikhonov filter-based LS schemes are compared analytically and numerically in this paper. It is found that for small-sized FRF matrices, the Tikhonov filter-based LS scheme tends to work better than the TSVD filter-based LS scheme. Since these approaches can only deal with the random errors in the measured structural responses, a total least-squares (TLS) scheme that can also address errors associated with the FRF matrix is proposed in this research. Numerical simulations demonstrate that under certain conditions, the TLS scheme is more effective in reducing the impact of these errors.