Showing papers in "Journal of Sound and Vibration in 2004"

Three-dimensional exact solution for the vibration of functionally graded rectangular plates

Abstract: A three-dimensional exact solution is presented for free and forced vibrations of simply supported functionally graded rectangular plates. Suitable displacement functions that identically satisfy boundary conditions are used to reduce equations governing steady state vibrations of a plate to a set of coupled ordinary differential equations, which are then solved by employing the power series method. The exact solution is valid for thick and thin plates, and for arbitrary variation of material properties in the thickness direction. Results are presented for two-constituent metal–ceramic functionally graded rectangular plates that have a power-law through-the-thickness variation of the volume fractions of the constituents. The effective material properties at a point are estimated by either the Mori–Tanaka or the self-consistent schemes. Exact natural frequencies, displacements and stresses are used to assess the accuracy of the classical plate theory, the first order shear deformation theory and a third order shear deformation theory for functionally graded plates. Parametric studies are performed for varying ceramic volume fractions, volume fraction profiles and length-to-thickness ratios. Results are also computed for a functionally graded plate that has a varying microstructure in the thickness direction using a combination of the Mori–Tanaka and the self-consistent methods. Forced vibrations of a plate with a sinusoidal spatial variation of the pressure applied on its top surface are scrutinized.

Extracting bridge frequencies from the dynamic response of a passing vehicle

Abstract: The frequencies of vibration of bridges represent a kind of information that is most useful for many purposes. Traditional vibration tests aimed at measuring the bridge frequencies often require on-site installation of the measurement equipment, which is not only costly, but also inconvenient. As a first attempt, the idea of using a vehicle moving over a bridge as a message carrier of the dynamic properties of the bridge is theoretically explored in this paper. In order to identify the key parameters dominating the vehicle–bridge interaction response, while illustrating the key phenomena involved, assumptions that lead to closed-form solutions are adopted in the analytical study. For instance, a vehicle is modelled as a sprung mass, and a bridge as a simply supported beam considering only the first mode of vibration. The concept of extracting bridge frequencies from a passing vehicle, however, is not restricted by the aforementioned assumptions, as will be demonstrated in an independent finite element study, which do not rely on any particular assumptions. Concluding remarks are given concerning the feasibility of extracting the bridge frequencies from the dynamic response of a passing vehicle, along with directions for future research identified.

Optimal sensor placement methodology for parametric identification of structural systems

Abstract: Theoretical and computational issues arising in the selection of the optimal sensor configuration for parameter estimation in structural dynamics are addressed. The information entropy, measuring the uncertainty in the system parameters, is used as the performance measure of a sensor configuration. A useful asymptotic approximation for the information entropy, valid for a large number of measured data, is derived. The asymptotic estimate is then used to rigorously justify that selections of the optimal sensor configuration can be based solely on a nominal structural model, ignoring the time history details of the measured data which are not available in the experimental design stage. It is further shown that the lower and upper bounds of the information entropy are decreasing functions of the number of sensors. Based on this result, two algorithms are proposed for constructing effective sensor configurations that are superior, in terms of computational efficiency and accuracy, to the sensor configurations provided by genetic algorithms. The theoretical developments and the effectiveness of the proposed algorithms are illustrated by designing the optimal configuration for a 10-degree-of-freedom (d.o.f.) chain-like spring–mass model and a 240-d.o.f. three-dimensional truss structure.

Damping as a result of piezoelectric energy harvesting

Abstract: Systems that harvest or scavenge energy from their environments are of considerable interest for use in remote power supplies. A class of such systems exploits the motion or deformation associated with vibration, converting the mechanical energy to electrical, and storing it for later use; some of these systems use piezoelectric materials for the direct conversion of strain energy to electrical energy. The removal of mechanical energy from a vibrating structure necessarily results in damping. This research addresses the damping associated with a piezoelectric energy harvesting system that consists of a full-bridge rectifier, a filter capacitor, a switching DC–DC step-down converter, and a battery. Under conditions of harmonic forcing, the effective modal loss factor depends on: (1) the electromechanical coupling coefficient of the piezoelectric system; and (2) the ratio of the rectifier output voltage during operation to its maximum open-circuit value. When the DC–DC converter is maximizing power flow to the battery, this voltage ratio is very nearly 1/2, and the loss factor depends only on the coupling coefficient. Experiments on a base-driven piezoelectric cantilever, having a system coupling coefficient of 26%, yielded an effective loss factor for the fundamental vibration mode of 2.2%, in excellent agreement with theory.

Acoustic ‘black holes’ for flexural waves as effective vibration dampers

Abstract: Elastic plates of variable thickness gradually decreasing to zero (elastic wedges) can support a variety of unusual effects for flexural waves propagating towards sharp edges of such structures and reflecting back. Especially interesting phenomena may take place in the case of plate edges having cross-sections described by a power law relationship between the local thickness h and the distance from the edge x : h ( x )= ex m , where m is a positive rational number and e is a constant. In particular, for m ⩾2—in free wedges, and for m ⩾5/3—in immersed wedges, the incident flexural waves become trapped near the edge and do not reflect back, i.e., the above structures represent acoustic ‘black holes’ for flexural waves. However, because of the ever-present edge truncations in real manufactured wedges, the corresponding reflection coefficients are always far from zero. The present paper shows that the deposition of absorbing thin layers on the plate surfaces can dramatically reduce the reflection coefficients. Thus, the combined effect of the specific wedge geometry and of thin absorbing layers can result in very efficient damping systems for flexural vibrations.

Structural damage identification of the highway bridge Z24 by FE model updating

Abstract: The development of a methodology for accurate and reliable condition assessment of civil structures has become very important. The finite element (FE) model updating method provides an efficient, non-destructive, global damage identification technique, which is based on the fact that the modal parameters (eigenfrequencies and mode shapes) of the structure are affected by structural damage. In the FE model the damage is represented by a reduction of the stiffness properties of the elements and can be identified by tuning the FE model to the measured modal parameters. This paper describes an iterative sensitivity based FE model updating method in which the discrepancies in both the eigenfrequencies and unscaled mode shape data obtained from ambient tests are minimized. Furthermore, the paper proposes the use of damage functions to approximate the stiffness distribution, as an efficient approach to reduce the number of unknowns. Additionally the optimization process is made more robust by using the trust region strategy in the implementation of the Gauss–Newton method, which is another original contribution of this work. The combination of the damage function approach with the trust region strategy is a practical alternative to the pure mathematical regularization techniques such as Tikhonov approach. Afterwards the updating procedure is validated with a real application to a prestressed concrete bridge. The damage in the highway bridge is identified by updating the Young's and the shear modulus, whose distribution over the FE model are approximated by piecewise linear functions.

Modelling and experiment of railway ballast vibrations

Abstract: The vibration of railway ballast is a key factor to cause track geometry change and increase of track maintenance costs. So far the methods for analyzing and testing the vibration of the granular ballast have not been well formed. In this paper, a five-parameter model for analysis of the ballast vibration is established based upon the hypothesis that the load-transmission from a sleeper to the ballast approximately coincides with the cone distribution. The concepts of shear stiffness and shear damping of the ballast are introduced in the model in order to consider the continuity of the interlocking ballast granules. A full-scale field experiment is carried out to measure the ballast acceleration excited by moving trains. Theoretical simulation results agree well with the measured results. Hence the proposed ballast vibration model has been validated.

A theoretical model for ground vibration from trains generated by vertical track irregularities

Abstract: A model is developed for predicting ground vibrations due to vertical track irregularities. This model incorporates vehicles, a track and a layered ground, and uses the moving axle loads and the vertical rail irregularities as its inputs. Outputs include the dynamic wheel–rail forces and the displacement power spectra of the track and the ground surface. Results from this model are presented for a single-axle vehicle model and a British Mark 3 passenger coach running on different tracks (a ‘lighter ballasted track’, a ‘heavier ballasted track’ and a slab track) at different speeds (25, 60 and 83 m/s). Based on these results, the effects of track structure, vehicle speed and frequency range on the observed vibration levels are identified. The different roles of the moving axle loads and the roughness-induced dynamic loads are indicated, at different frequencies and for train speeds below and above the lowest ground wave speed.

Machine fault diagnosis through an effective exact wavelet analysis

Abstract: Continuous wavelet transforms (CWTs) are widely recognized as effective tools for vibration-based machine fault diagnosis, as CWTs can detect both stationary and transitory signals. However, due to the problem of overlapping, a large amount of redundant information exists in the results that are generated by CWTs. The appearance of overlapping can smear the spectral features and make the results very difficult to interpret for machine operators. Misinterpretation of results may lead to false alarms or failures to detect anomalous signals. Moreover, as conventional CWTs only use a single mother wavelet to generate daughter wavelets, the distortion of the original signal in the resultant coefficients is inevitable. Obviously, this will significantly affect the accuracy in anomalous signal detection. To minimize the effect of overlapping and to enhance the accuracy of fault detection, a novel wavelet transform, which is named as exact wavelet analysis, has been designed for use in vibration-based machine fault diagnosis. The design of exact wavelet analysis is based on genetic algorithms. At each selected time frame, the algorithms will generate an adaptive daughter wavelet to match the inspected signal as exactly as possible. The optimization process of exact wavelet analysis is different from other adaptive wavelets as it considers both the optimization of wavelet coefficients and the satisfaction of the admissibility conditions of wavelets. The results obtained from simulated and practical experiments prove that exact wavelet analysis not only minimizes the undesirable effect of overlapping, but also helps operators to detect faults and distinguish the causes of faults. With the help from exact wavelet analysis, sudden shutdowns of production and services due to the fatal breakdown of machines could be avoided.

Vibration analysis of rectangular plates with general elastic boundary supports

Abstract: In this investigation, the Rayleigh–Ritz method is used to determine the modal characteristics of a rectangular plate with general elastic supports alone its edges. Each of the admissible functions here is composed of a trigonometric function and an arbitrary continuous function that is introduced to ensure the sufficient smoothness of the so-called residual displacement function at the edges. As a result, a drastic improvement of the convergence can be expected of the solution expressed as a series expansion in terms of the admissible functions. Perhaps more importantly, this study has developed a general approach for deriving a complete set of admissible functions that can be universally applied to various boundary conditions. Several numerical examples are given to demonstrate the accuracy and convergence of the current solution.

Coupled bending, longitudinal and torsional vibrations of a cracked rotor

Abstract: The coupling between longitudinal, lateral and torsional vibrations is studied together for a rotating cracked shaft These coupling mechanisms have been studied here with a response-dependent non-linear breathing crack model Most of the earlier work on coupled vibrations due to crack has been either on stationary shaft or on rotating shaft with open crack model The stiffness matrix of a Timoshenko beam element is modified to account for the effect of a crack and all the six degrees of freedom per node are considered Coupled torsional–longitudinal vibrations for a cracked rotor that has not been reported earlier and coupled torsional–bending vibrations with a breathing crack model have been studied An attempt has been made to reveal crack specific signatures by using additional external excitations Since all the couplings are accounted, the excitation in one mode leads to an interaction between all the modes This, coupled with the rotational effect of a cracked rotor and the non-linearities due to a breathing crack model introduces sum and difference frequencies in the response of cracked rotor The co-existence of frequencies of other modes in the frequency spectra of a particular mode and the presence of sum and difference frequencies around the excitation frequencies and its harmonics could be useful indicators for crack diagnosis

Simulation of dynamics of beam structures with bolted joints using adjusted Iwan beam elements

Abstract: Mechanical joints often affect structural response, causing localized non-linear stiffness and damping changes. As many structures are assemblies, incorporating the effects of joints is necessary to produce predictive finite element models. In this paper, we present an adjusted Iwan beam element (AIBE) for dynamic response analysis of beam structures containing joints. The adjusted Iwan model consists of a combination of springs and frictional sliders that exhibits non-linear behavior due to the stick–slip characteristic of the latter. The beam element developed is two-dimensional and consists of two adjusted Iwan models and maintains the usual complement of degrees of freedom: transverse displacement and rotation at each of the two nodes. The resulting element includes six parameters, which must be determined. To circumvent the difficulty arising from the non-linear nature of the inverse problem, a multi-layer feed-forward neural network (MLFF) is employed to extract joint parameters from measured structural acceleration responses. A parameter identification procedure is implemented on a beam structure with a bolted joint. In this procedure, acceleration responses at one location on the beam structure due to one known impulsive forcing function are simulated for sets of combinations of varying joint parameters. A MLFF is developed and trained using the patterns of envelope data corresponding to these acceleration histories. The joint parameters are identified through the trained MLFF applied to the measured acceleration response. Then, using the identified joint parameters, acceleration responses of the jointed beam due to a different impulsive forcing function are predicted. The validity of the identified joint parameters is assessed by comparing simulated acceleration responses with experimental measurements. The capability of the AIBE to capture the effects of bolted joints on the dynamic responses of beam structures, and the efficacy of the MLFF parameter identification procedure, are demonstrated.

Operational modal analysis in the presence of harmonic excitation

Abstract: Modal operational analysis methods are procedures to identify modal parameters of structures from the response to unknown random excitations existing on buildings and in machines during operation. In many practical cases, in addition to the random loads, harmonic excitations are also present due for instance to rotating components. If the frequency of the harmonic component of the input is close to an eigenfrequency of the system, operational modal analysis procedures fail to identify the modal parameters accurately. Therefore, we propose a modification of the least-square complex exponential identification procedure to include explicitly the harmonic component. In that way, the modal parameters can be identified properly. We illustrate the efficiency of the proposed approach on the example of a beam structure excited by multi-harmonic loads superposed on random excitation.

Effects of the wind profile at night on wind turbine sound

Abstract: Since the start of the operation of a 30 MW, 17 turbine wind park, residents living 500 m and more from the park have reacted strongly to the noise; residents up to 1900 m distance expressed annoyance. To assess actual sound immission, long term measurements (a total of over 400 night hours in 4 months) have been performed at 400 and 1500 m from the park. In the original sound assessment a fixed relation between wind speed at reference height (10 m) and hub height (98 m) had been used. However, measurements show that the wind speed at hub height at night is up to 2.6 times higher than expected, causing a higher rotational speed of the wind turbines and consequentially up to 15 dB higher sound levels, relative to the same reference wind speed in daytime. Moreover, especially at high rotational speeds the turbines produce a ‘thumping’, impulsive sound, increasing annoyance further. It is concluded that prediction of noise immission at night from (tall) wind turbines is underestimated when measurement data are used (implicitly) assuming a wind profile valid in daytime.

Minimax optimization of multi-degree-of-freedom tuned-mass dampers

Abstract: Many methods have been developed for the design of a single-degree-of-freedom (SDOF) absorber to damp SDOF vibration. Yet there are few studies for the case where both the absorber and the main system have multiple degrees of freedom. In this paper, an efficient numerical approach based on the descent-subgradient method is proposed to maximize the minimal damping of modes in a prescribed frequency range for general viscous or hysteretic multi-degree-of-freedom (MDOF) tuned-mass systems. Examples are given to illustrate the efficiency of the minimax method and the damping potential of MDOF tuned-mass dampers (TMDs). The performance of minimax, H2, and H∞ optimal TMDs are compared. Finally, the results of an experiment in which a 2-DOF TMD is optimized to damp the first two flexural modes of a free–free beam are presented.

Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes

Abstract: The definition of a non-linear normal mode (NNM) as an invariant manifold in phase space is used. In conservative cases, it is shown that normal form theory allows one to compute all NNMs, as well as the attendant dynamics onto the manifolds, in a single operation. Then, a single-mode motion is studied. The aim of the present work is to show that too severe truncature using a single linear mode can lead to erroneous results. Using single-non-linear mode motion predicts the correct behaviour. Hence, the nonlinear change of co-ordinates allowing one to pass from the linear modal variables to the normal ones, linked to the NNMs, defines a framework to properly truncate non-linear vibration PDEs. Two examples are studied: a discrete system (a mass connected to two springs) and a continuous one (a linear Euler-Bernoulli beam resting on a non-linear elastic foundation). For the latter, a comparison is given between the developed method and previously published results.

A model of the correlation function of leak noise in buried plastic pipes

Abstract: A common technique for locating leaks in buried water distribution pipes is the use of the cross-correlation on two measured acoustic signals, on either side of a leak. This technique can be problematic for locating leaks in plastic pipes as the acoustic signals in these pipes are generally narrow-band and low frequency. The effectiveness of the cross-correlation technique for detecting leaks in plastic pipes has been investigated experimentally in an earlier study. This paper develops an analytical model to predict the cross-correlation function of leak signals in plastic pipes. The model is based on a theoretical formulation of wave propagation in a fluid-filled pipe in vacuo and the assumption that the leak sound, at source, has a flat spectrum over the bandwidth of interest. The analytical model is used to explain some of the features of correlation measurements made in actual water pipes. Leak noise signals are generally passed through a band-pass filter before calculating the cross-correlation function. The model is used to demonstrate the importance of the cut-off frequency of the high-pass filter and the insensitivity of the correlation to the cut-off frequency of the low-pass filter.

Optimal design of passive linear suspension using genetic algorithm

Abstract: In this paper the genetic algorithm (GA) method is applied to the optimization problem of a linear one-degree-of-freedom (1-DOF) vibration isolator mount and the method is extended to the optimization of a linear quarter car suspension model. A novel criterion for selecting optimal suspension parameters is presented. An optimal relationship between the root mean square (RMS) of the absolute acceleration and the RMS of the relative displacement is found. Although the systems are linear, it is difficult to find such optimal relation analytically. The optimum solution is obtained numerically by utilizing GA and employing a cost function that seeks minimizing absolute acceleration RMS sensitivity to changes in relative displacement RMS. The combination of RMS and absolute acceleration sensitivity minimization produces optimal suspension that is robust to broadband frequency excitation. The GA method increases the probability of finding the global optimum solution and avoids convergence to a local minimum which is a drawback of gradient-based methods. Given allowable mount relative displacement (working space), designers can use the results to specify the optimal mount and suspension. The cost function employed can be extended to optimize multi-DOF (MDOF) and non-linear vibrating mechanical systems in frequency domain. Applying the method to a linear quarter car model illustrates the applicability of the method to MDOF systems. An example is given to demonstrate the optimality of the solution obtained by the GA technique.

On the simulation of trailing edge noise with a hybrid LES/APE method

Abstract: A hybrid method is applied to predict trailing edge noise based on a large eddy simulation (LES) of the compressible flow problem and acoustic perturbation equations (APE) for the time-dependent simulation of the acoustic field. The acoustic simulation in general considers the mean flow convection and refraction effects such that the computational domain of the flow simulation has to comprise only the significant acoustic source region. Using a modified rescaling method for the prediction of the unsteady turbulent inflow boundary layer, the LES just resolves the flow field in the immediate vicinity of the trailing edge. The linearized APE completely prevent the unbounded growth of hydrodynamic instabilities in critical mean flows.

Free vibration analysis of a cracked beam by finite element method

Abstract: In this paper, the natural frequencies and mode shapes of a cracked beam are obtained using the finite element method. An ‘overall additional flexibility matrix’, instead of the ‘local additional flexibility matrix’, is added to the flexibility matrix of the corresponding intact beam element to obtain the total flexibility matrix, and therefore the stiffness matrix. Compared with analytical results, the new stiffness matrix obtained using the overall additional flexibility matrix can give more accurate natural frequencies than those resulted from using the local additional flexibility matrix. All the elements in the overall additional flexibility matrix are computed by 128-point (1D) or (128×128)-point (2D) Gauss quadrature, and then further best fitted using the least-squares method. The explicit form best-fitted formulas agree very well with the numerical integration results, and are very convenient for use and valuable for further reference. In addition, the authors constructed a shape function that can perfectly satisfy the local flexibility conditions at the crack locations, which can give more accurate vibration modes.

Continuous wavelet transform for modal identification using free decay response

Abstract: This paper deals with the use of the continuous wavelet transform for system identification purposes. The wavelet analysis of the free responses of a linear mechanical system allows the estimation of its natural frequencies, viscous damping ratios and mode shapes, using either the modulus or the phase of the wavelet transform. A complete procedure for modal identification from free responses based on the continuous wavelet transform is presented. Two difficulties during the implementation of this technique are highlighted: the edge effect and the choice of the time–frequency localization of the wavelet transform. Some upper and lower bounds for the mother wavelet's parameters are given in order to improve the numerical computation. Three complex-valued mother wavelets are studied and the full procedure is applied to a damped discrete system. The correct choice of the mother wavelet's parameters leads to an accurate identification of the modal parameters.

Development of elastic force model for wheel/rail contact problems

Abstract: In this investigation, a new formulation for the wheel/rail contact problem based on the elastic force approach is presented. Crucial to the success of any elastic force formulation for the wheel/rail contact problem is the accurate prediction of the location of the contact points. To this end, features of multibody formulations that allow introducing additional differential equations are exploited in this investigation in order to obtain a good estimate of the rail arc length travelled by the wheel set. In the formulation presented in this paper, four parameters are used to describe the wheel and the rail surfaces. In order to determine the location of the points of contact between the wheel and the rail, a first order differential equation for the rail arc length is introduced and is integrated simultaneously with the multibody equations of motion of the wheel/rail system. The method presented in this paper allows for multiple points of contact between the wheel and the rail by using an optimized search for all possible contact points. The normal contact forces are calculated and used with non-linear expressions for the creepages to determine the creep forces. The paper also discusses two different procedures for the analysis of the two-point contact in the wheel/rail interaction. Numerical results obtained using the elastic force model are presented and compared with the results obtained using the constraint approach.

A Study of Random Vibration Characteristics of the Quarter-Car Model

Abstract: In this paper, the quarter-car model is used to study the response of the vehicle to profile imposed excitation with randomly varying traverse velocity and variable vehicle forward velocity. Root-mean-square response of the vehicle to white and colored noise velocity road inputs is analyzed. In the latter case, a recently developed subspace-based identification algorithm is used to design a linear shape filter with output spectrum matching the measured road spectrum. The linear shape filter is used in constructing charts that illustrate the trade-offs among the passenger comfort, the road-holding, and the suspension travel as functions of the vehicle forward velocity.

Statistical model-based damage detection and localization: subspace-based residuals and damage-to-noise sensitivity ratios

Abstract: The vibration-based structural health monitoring problem is addressed as the double task of detecting damages modeled as changes in the eigenstructure of a linear dynamic system, and localizing the detected damages within (a FEM of) the monitored structure. The proposed damage detection algorithm is based on a residual generated from a stochastic subspace-based covariance driven identification method and on the statistical local approach to the design of detection algorithms. This algorithm basically computes a global test, which performs a sensitivity analysis of the residuals to the damages, relative to uncertainties and noises. How this residual relates to some residuals for damage localization and model updating is discussed. Damage localization is stated as a detection problem. This problem is addressed by plugging aggregated sensitivities of the modes and mode-shapes w.r.t. FEM structural parameters in the above setting. This results in directional tests, which perform the same type of damage-to-noise sensitivity analysis of the residual as for damage detection. How the sensitivity aggregation mechanism relates to sub-structuring is outlined. Numerical results obtained on one example are reported.

Vibration and sound radiation of sandwich beams with honeycomb truss core

Abstract: The vibrations of and the sound radiation from sandwich beams with truss core are analyzed. The structure of the core is composed of a sequence of identical unit cells repeating along the beam length and across the core thickness. Each cell is composed of beam elements assembled to form a frame structure. Layouts with the typical honeycomb pattern arranged through the thickness of the core are here considered. This design represents an alternative with respect to the traditional application of honeycombs in sandwich construction. The proposed configuration provides sandwich beams with interesting structural as well as acoustic characteristics. A finite element model is developed to evaluate the structural and the acoustic behavior of the considered class of sandwich beams. The model is formulated by employing dynamic shape functions, derived directly from the distributed parameter model of beam elements. This formulation, often denoted as “spectral”, allows an accurate evaluation of the dynamic behavior of the considered structures at high frequencies and with a limited number of elements. In addition, the spectral model can be easily coupled with a Fourier transform based analysis of the sound radiated by the fluid-loaded structure. The model is used to analyze the performance of beams with various core configurations. The comparison is carried out in terms of structural response and sound transmission reduction index. In addition the sound pressure levels and distributions resulting from the beam vibration in an unbounded acoustic half-plane are evaluated and compared. Hexagonal and re-entrant configurations are considered in an effort to study the effects of core geometry on structural response and acoustic radiation.

Damage localization in plate structures from uniform load surface curvature

Abstract: Although a large number of methods exist for detecting damage in a structure using measured modal parameters, many of them require a correlated finite element model, or at least, modal data of the structure for the intact state as baseline. For one-dimensional beam-like structures, curvature techniques, e.g., mode shape curvature and flexibility curvature, have been applied to localize damage. In this paper a damage localization method based on changes in uniform load surface (ULS) curvature is developed for two-dimensional plate structures. A new approach to compute the ULS curvature is proposed based on the Chebyshev polynomial approximation, instead of the central difference method. The proposed method requires only the frequencies and mode shapes of the first few modes of the plate before and after damage, or only the eigenpairs for the damaged state if a gapped-smoothing technique is applied. Numerical simulations considering different supported conditions, measurement noise, mode truncation, and sensor sparsity are studied to evaluate the effectiveness of the proposed method. It is found that the ULS curvature is sensitive to the presence of local damages, even with truncated, incomplete, and noisy measurements.

Robust adaptive boundary control of an axially moving string under a spatiotemporally varying tension

Abstract: In this paper, a vibration suppression scheme for an axially moving string under a spatiotemporally varying tension and an unknown boundary disturbance is investigated. The lower bound of the tension variation is assumed to be sufficiently larger than the derivatives of the tension. The axially moving string system is divided into two spans, i.e., a controlled span and an uncontrolled span, by a hydraulic touch-roll actuator which is located in the middle section of the string. The transverse vibration of the controlled span part of the string is controlled by the hydraulic touch-roll actuator, and the position of the actuator is considered as the right boundary of the controlled span part. The mathematical model of the system, which consists of a hyperbolic partial differential equation describing the dynamics of the moving string and an ordinary differential equation describing the actuator dynamics, is derived by using the Hamilton's principle. The Lyapunov method is employed to design a robust boundary control law and adaptation laws for ensuring the vibration reduction of the controlled span part. The asymptotic stability of the closed loop system under the robust adaptive boundary control scheme is proved through the use of semigroup theory. Simulation results verify the effectiveness of the robust adaptive boundary controller proposed.

Crack identification in plates using wavelet analysis

Abstract: In this paper, a method for crack identification in plates based on wavelet analysis is presented. The case of an all-over part-through crack parallel to one edge of the plate is considered. The vibration modes of the plate are analyzed using the continuous wavelet transform and both the location and depth of the crack are estimated. The position of the crack is determined by the sudden change in the spatial variation of the transformed displacement response. To estimate the depth of the crack, an intensity factor is defined which relates the depth of the crack to the coefficients of the wavelet transform. An intensity factor law is established which allows accurate prediction of crack depth. The viability of the proposed approach is demonstrated using simulation examples. In view of the obtained results, the advantages and limitations of the proposed approach as well as suggestions for future work are presented and discussed.

Non-linear dynamic behaviors of rolling element bearings due to surface waviness

Abstract: An analytical model to predict non-linear dynamic responses in a rotor bearing system due to surface waviness has been developed. In the analytical formulation the contacts between the rolling elements and the races are considered as non-linear springs, whose stiffness are obtained by using Hertzian elastic contact deformation theory. The governing differential equations of motion are obtained by using Lagrange's equations. The implicit type numerical integration technique Newmark-β with Newton–Raphson method is used to solve the non-linear differential equations iteratively. A computer program is developed to simulate surface waviness of the components. Results presented in the form of fast Fourier transformation with agreement of various author's experimental researches.

Damage detection in structures using a few frequency response measurements

Abstract: This paper presents methods to identify the locations and severity of damage in structures using frequency response function (FRF) data. Basic methods detect the location and severity of structural damage by minimizing the difference between test and analytic FRFs, which is a type of model updating or optimization method; however, the preferred method proposed in this paper uses only a subset of vectors from the full set of FRFs for a few frequencies and calculates the stiffness matrix and reductions in explicit form. To verify the proposed method, examples for a simple cantilever and a helicopter rotor blade are numerically demonstrated. The proposed method identified the location of damage in these objects, and characterized the damage to a satisfactory level of precision.