Showing papers in "Journal of Vibration and Acoustics in 2008"

A Distributed Parameter Electromechanical Model for Cantilevered Piezoelectric Energy Harvesters

Abstract: Cantilevered beams with piezoceramic layers have been frequently used as piezoelectric vibration energy harvesters in the past five years. The literature includes several single degree-of-freedom models, a few approximate distributed parameter models and even some incorrect approaches for predicting the electromechanical behavior of these harvesters. In this paper, we present the exact analytical solution of a cantilevered piezoelectric energy harvester with Euler–Bernoulli beam assumptions. The excitation of the harvester is assumed to be due to its base motion in the form of translation in the transverse direction with small rotation, and it is not restricted to be harmonic in time. The resulting expressions for the coupled mechanical response and the electrical outputs are then reduced for the particular case of harmonic behavior in time and closed-form exact expressions are obtained. Simple expressions for the coupled mechanical response, voltage, current, and power outputs are also presented for excitations around the modal frequencies. Finally, the model proposed is used in a parametric case study for a unimorph harvester, and important characteristics of the coupled distributed parameter system, such as short circuit and open circuit behaviors, are investigated in detail. Modal electromechanical coupling and dependence of the electrical outputs on the locations of the electrodes are also discussed with examples.

Rotary Machine Health Diagnosis Based on Empirical Mode Decomposition

Abstract: This paper presents a signal decomposition and feature extraction technique for the health diagnosis of rotary machines, based on the empirical mode decomposition. Vibration signal measured from a defective rolling bearing is decomposed into a number of intrinsic mode functions (IMFs), with each IMF corresponding to a specific range of frequency components contained within the vibration signal. Two criteria, the energy measure and correlation measure, are investigated to determine the most representative IMF for extracting defect-induced characteristic features out of vibration signals. The envelope spectrum of the selected IMF is investigated as an indicator for both the existence and the specific location of structural defects within the bearing. Theoretical foundation of the technique is introduced, and its performance is experimentally verified.

Vibration and Acoustic Response of an Isotropic Plate in a Thermal Environment

Abstract: This paper presents numerical simulation studies on the vibration and acoustic response characteristics of an isotropic rectangular plate in a thermal environment using commercial finite element softwares ANSYS and SYSNOISE. First the critical buckling temperature is obtained, followed by modal and harmonic analyses considering prestress due to the thermal field in the plate, with the critical buckling temperature as a parameter. The vibration response predicted is then used to compute the sound radiation. It is found that the displacement response of the structure increases with an increase in temperature for all boundary conditions. The overall sound radiation of the plate marginally increases with an increase in temperature for all boundary conditions when the temperature approaches the critical buckling temperature although there is a sharp increase in sound power levels.

Vibration Suppression Using Electromagnetic Resonant Shunt Damper

Abstract: An electromagnetic actuator has the property to convert mechanical energy to electrical energy and vice versa. In this study, an electromagnetic resonant shunt damper, consisting of a voice coil motor with an electric resonant shunt circuit, is proposed. The optimal design of the shunt circuit is obtained theoretically for this electromagnetic resonant shunt damper. Furthermore, the effects of parameter errors of the elements of the electromagnetic resonant shunt damper are also investigated. The applicability of the theoretical findings for the proposed damper is justified by the experimental analysis.

Mechanical Domain Parametric Amplification

Abstract: Though utilized for more than 50 years in a variety of power and communication systems, parametric amplification, the process of amplifying a harmonic signal with a parametric pump, has received very little attention in the mechanical engineering community. In fact, only within the past 15-20 years has the technique been implemented in micromechanical systems as a means of amplifying the output of resonant microtransducers. While the vast potential of parametric amplification has been demonstrated, to date, in a number of micro- and nanomechanical systems (as well as a number electrical systems), few, if any, macroscale mechanical amplifiers have been reported. Given that these amplifiers are easily realizable using larger-scale mechanical systems, the present work seeks to address this void by examining a simple' representative example: a cantilevered beam with longitudinal and transverse base excitations. The work begins with the systematic formulation of a representative system model, which is used to derive a number of pertinent metrics. A series of experimental results, which validate the work's analytical findings, are subsequently examined, and the work concludes with a brief look at some plausible applications of parametric amplification in macroscale mechanical systems.

Modeling of electrodynamic bearings

Abstract: A new model of electrodynamic bearings is presented in this paper. The model takes into account the R-L dynamics of the eddy currents on which this type of bearing is based, making it valid for both quasistatic and dynamic analyses. In the quasistatic case, the model is used to obtain the force generated by an off-centered shaft rotating at a fixed speed in a constant magnetic field. The model is then used to analyze the dynamic stability of a Jeffcott rotor supported by electrodynamic bearings. The essential role played by nonrotating damping in ensuring a stable operating range to the rotor is studied by means of root loci. Comparison with literature results is finally used to validate the model

Application of the Laplace-Wavelet Combined With ANN for Rolling Bearing Fault Diagnosis

Abstract: A new technique for an automated detection and diagnosis of rolling bearing faults is presented. The time-domain vibration signals of rolling bearings with different fault conditions are preprocessed using Laplace-wavelet transform for features' extraction. The extracted features for wavelet transform coefficients in time and frequency domains are applied as input vectors to artificial neural networks (ANNs) for rolling hearing fault classification. The Laplace-Wavelet shape and the ANN classifier parameters are optimized using a genetic algorithm. To reduce the computation cost, decrease the size, and enhance the reliability of the ANN, only the predominant wavelet transform scales are selected for features' extraction. The results for both real and simulated bearing vibration data show the effectiveness of the proposed technique for bearing condition identification with very high success rates using minimum input features.

Monitoring the Onset and Propagation of Natural Degradation Process in a Slow Speed Rolling Element Bearing With Acoustic Emission

Abstract: The monitoring and diagnosis of rolling element bearings with the high frequency acoustic emission (AE) technology has been ongoing since the late 1960s. This paper demonstrates the use of AE measurements to detect, locate, and monitor natural defect initiation and propagation in a conventional rolling element bearing. To facilitate the investigation a special purpose test rig was built to allow for accelerated natural degradation of a bearing race. It is concluded that subsurface initiation and subsequent crack propagation can be detected with the AE technology. The paper also presents comparative results between AE and vibration diagnosis.

Application of a Novel Hybrid Intelligent Method to Compound Fault Diagnosis of Locomotive Roller Bearings

Abstract: To diagnose compound faults of locomotive roller bearings accurately, a novel hybrid intelligent diagnosis method is proposed in this paper. First of all, vibration signals are preprocessed to mine valid fault characteristic information. They are filtered and at the same time, they are decomposed by the empirical mode decomposition method and eight intrinsic mode functions (IMFs) are acquired. The filtered signals and IMFs are further demodulated to obtain their Hilbert envelope spectrums. Second, six feature sets are extracted, and they are time- and frequency-domain statistical features of the raw and preprocessed signals. Then, each feature set is evaluated and a few salient features are selected from it by applying the improved distance evaluation technique. Correspondingly, six salient feature sets are obtained. Finally, the six salient feature sets are, respectively, input into six classifiers based on adaptive neurofuzzy inference system (ANFIS), and genetic algorithm is employed to combine the outputs of the six ANFISs and to attain the final diagnosis result. The diagnosis results of the compound faults of the locomotive roller bearings verify that the proposed hybrid intelligent method may accurately recognize not only a single fault and fault severities but also compound faults.

Balancing of Flexible Rotors Using Convex Optimization Techniques : Optimum Min-Max LMI Influence Coefficient Balancing

Abstract: In some industrial applications, influence coefficient balancing methods fail to find the optimum vibration reduction due to the limitations of the least-squares optimization methods. Previous min-max balancing methods have not included practical constraints often encountered in industrial balancing. In this paper, the influence coefficient balancing equations, with suitable constraints on the level of the residual vibrations and the magnitude of correction weights, are cast in linear matrix inequality (LMf) forms and solved with the numerical algorithms developed in convex optimization theory. The effectiveness and flexibility of the proposed method have been illustrated by solving two numerical balancing examples with complicated requirements. It is believed that the new methods developed in this work will help in reducing the time and cost of the original equipment manufacturer or field balancing procedures by finding an optimum solution of difficult balancing problems. The resulting method is called the optimum min-max LMI balancing method.

Design optimization with an uncertain vibroacoustic model

Abstract: This paper deals with the design optimization problem of a structural-acoustic system in the presence of uncertainties. The uncertain vibroacoustic numerical model is constructed by using a recent nonparametric probabilistic model, which takes into account model uncertainties and data uncertainties. The formulation of the design optimization problem includes the effect of uncertainties and consists in minimizing a cost function with respect to an admissible set of design parameters. The numerical application consists in designing an uncertain master structure in order to minimize the acoustic pressure in a coupled internal cavity, which is assumed to be deterministic and excited by an acoustic source. The results of the design optimization problem, solved with and without the uncertain numerical model, show significant differences.

Identification of Cracks in Beams With Auxiliary Mass Spatial Probing by Stationary Wavelet Transform

Abstract: This paper proposes a new approach based on auxiliary mass spatial probing by stationary wavelet transform (SWT) to provide a method for crack detection in beamlike structure. SWT can provide accurate estimation of the variances at each scale and facilitate the identification of salient features in a signal. The natural frequencies of a damaged beam with a traversing auxiliary mass change due to the change in flexibility and inertia of the beam as the auxiliary mass is traversed along the beam. Therefore, the auxiliary mass can enhance the effects of the crack on the dynamics of the beam and, therefore, facilitate the identification and location of damage in the beam. That is, the auxiliary mass can be used to probe the dynamic characteristic of the beam by traversing the mass from one end of the beam to the other. However, it is difficult to locate the crack directly from the graphical plot of the natural frequency versus axial location of auxiliary mass. This curve of the natural frequencies can be decomposed by SWT into a smooth, low order curve, called approximation coefficient, and a wavy, high order curve called the detail coefficient, which includes crack information that is useful for damage detection. The modal responses of the damaged simply supported beams with auxiliary mass used are computed using the finite element method (FEM). Sixty-four cases are studied using FEM and SWT. The efficiency and practicability of the proposed method is illustrated via experimental testing. The effects of crack depth, crack location, auxiliary mass, and spatial probing interval are investigated. From the simulated and experimental results, the efficiency of the proposed method is demonstrated.

Modeling Guided Waves for Damage Identification in Isotropic and Orthotropic Plates Using a Local Interaction Simulation Approach

Abstract: In this paper, a numerical simulation technique based on the local interaction simulation approach (LISA)/sharp interface model (SIM) is used to study the propagation of Lamb waves in aluminum and orthotropic plates and wave interactions with damage. The LISA/SIM model allows for accurate and fast simulations of sharp changes in material properties across interfaces associated with damage or specimen boundaries. Damage in the form of holes and changes in density and/or stiffnesses are studied for three different plates. These local changes in density and stiffness have dimensions not exceeding the wave length of the interrogating wave form. Wave scatter from these damage sites is shown at different time instants and at specific spatial locations. Multiple site damage cases are studied for all the plate structures. The different scatter patterns associated with intersecting and nonintersecting surface cracks are also studied. Results obtained from a combination of single site damage cases are compared with the composite multiple site damage case to study the usability of commonly applied algorithms for identifying damage. The benefits of observing multiple directions of the displacement field are demonstrated. It is shown that the out-of-plane measurements give a clearer indication of damage sites than the in-plane measurements.

Wave Analysis of In-Plane Vibrations of H- and T-shaped Planar Frame Structures

Abstract: This paper concerns in-plane vibration analysis of coupled bending and longitudinal vibrations in H- and T-shaped planar frame structures. An exact analytical solution is obtained using wave vibration approach. Timoshenko beam theory, which takes into account the effects of both rotary inertia and shear distortion, is applied in modeling the flexural vibrations in the planar frame. Reflection and transmission matrices corresponding to incident waves arriving at the "T" joint from various directions are obtained. Bending and longitudinal waves generated by a combination of point longitudinal forces, point bending forces, and bending moments are also obtained. Assembling these wave relations provides a concise and systematic approach to both free and forced vibration analyses of coupled bending and longitudinal vibrations in H- and T-shaped planar frame structures. Natural frequencies, modeshapes, and forced responses are obtained from wave vibration standpoint. The results are compared to results available in literature. Good agreement has been reached.

Vibration Control and Trajectory Tracking for General In-Plane Motion of an Euler–Bernoulli Beam Via Two-Time Scale and Boundary Control Methods

Abstract: In this paper, general in-plane trajectory tracking problem of a flexible beam is studied. To obtain the dynamic equations of motion of the beam, Hamiltonian dynamics is used and then Lagrange’s equations of beam dynamics and corresponding expressions for boundary conditions are derived. Resulting equations show that the coupled beam dynamics including beam vibration and its rigid in-plane motion take place in two different time domains. By using two-time scale (TTS) control theory, a control scheme is elaborated that makes the orientation and position of the mass center of the beam track a desired trajectory while suppressing its vibration. TTS composite controller has two parts: one is a tracking controller designed for the slow (rigid) subsystem, and the other one is a stabilizing controller for the fast (flexible) subsystem. For the fast subsystem, the proposed boundary control (BC) method does not require any information about vibration along the beam except at the end points, nor requires discretizing the partial differential equation of beam vibration to a set of ordinary differential equations. So, the method avoids the need for instruments to measure data from vibration of any point along the beam or designing an observer for estimating this information. Also, the proposed method prevents control spillover due to discretization. Simulation results show that fast BC is able to remove undesirable vibration of the flexible beam and the slow controller provides very good trajectory tracking with acceptable actuating forces/moments.

Coupled Flexural-Torsional Nonlinear Vibrations of Piezoelectrically Actuated Microcantilevers With Application to Friction Force Microscopy

Abstract: The problem of vibrations of microcantilevers has recently received considerable attention due to its application in several nanotechnological instruments, such as atomic force microscopy, nanomechanical cantilever sensors, and friction force microscopy. Along this line, this paper undertakes the problem of coupled flexural-torsional nonlinear vibrations of a piezoelectrically actuated microcantilever beam as a typical configuration utilized in these applications. The actuation and sensing are both facilitated through bonding a piezoelectric layer (here, ZnO) on the microcantilever surface. The beam is considered to have simultaneous flexural, torsional, and longitudinal vibrations. The piezoelectric properties combined with nonlinear geometry of the beam introduce both linear and nonlinear couplings between flexural vibration as well as longitudinal and torsional vibrations. Of particular interest is the inextensibility configuration, for which the governing equations reduce to coupled flexural-torsional nonlinear equations with piezoelectric nonlinearity appearing in quadratic form while inertia and stiffness nonlinearities as cubic. An experimental setup consisting of a commercial piezoelectric microcantilever installed on the stand of an ultramodern laser-based microsystem analyzer is designed and utilized to verify the theoretical developments. Both linear and nonlinear simulation results are compared to the experimental results and it is observed that nonlinear modeling response matches the experimental findings very closely. More specifically, the softening phenomenon in fundamental flexural frequency, which is due to nonlinearity of the system, is analytically and experimentally verified. It is also disclosed that the initial twisting in the microcantilever can influence the value ofthe flexural vibration resonance. The experimental results from a macroscale beam are utilized to demonstrate such twist-flexure coupling. This unique coupling effect may lead to the possibility of indirect measurement of small torsional vibration without the need for any angular displacement sensor. This observation could significantly extend the application of friction force microscopy to measure the friction of a surface indirectly.

Generalized eigenvalue decomposition in time domain modal parameter identification

Abstract: This paper is intended to point out the relationship among current time domain modal analysis methods by employing generalized eigenvalue decomposition. Ibrahim time domain (ITD), least-squares complex exponential (LSCE) and eigensystem realization algorithm (ERA) methods are reviewed and chosen to do the comparison. Reformulation to their original forms shows these three methods can all be attributed to a generalized eigenvalue problem with different matrix pairs. With this general format, we can see that single-input multioutput (SIMO) methods can easily be extended to multi-input multioutput (MIMO) cases by taking advantage of a generalized Hankel matrix or a generalized Toeplitz matrix.

Stochastic Averaging of Strongly Nonlinear Oscillators Under Combined Harmonic and Wide-Band Noise Excitations

Abstract: Physical and engineering systems are often subjected to combined harmonic and random excitations. The random excitation is often modeled as Gaussian white noise for mathematical tractability. However, in practice, the random excitation is nonwhite. This paper investigates the stationary response probability density of strongly nonlinear oscillators under combined harmonic and wide-band noise excitations. By using generalized harmonic functions, a new stochastic averaging procedure for estimating stationary response probability density of strongly nonlinear oscillators under combined harmonic and wide-band noise excitations is developed. The damping can be linear and (or) nonlinear and the excitations can be external and (or) parametric. After stochastic averaging, the system state is represented by two-dimensional time-homogeneous diffusive Markov processes. The method of reduced Fokker–Planck–Kolmogorov equation is used to investigate the stationary response of the vibration system. A nonlinearly damped Duffing oscillator is taken as an example to show the application and validity of the method. In the case of primary external resonance, based on the stationary joint probability density of amplitude and phase difference, the stochastic jump of the Duffing oscillator and P-bifurcation as the system parameters change are examined for the first time. The agreement between the analytical results and those from Monte Carlo simulation of original system shows that the proposed procedure works quite well.

Steady-State Dynamic Response of a Bernoulli–Euler Beam on a Viscoelastic Foundation Subject to a Platoon of Moving Dynamic Loads

Abstract: A Bernoulli-Euler beam resting on a viscoelastic foundation subject to a platoon of moving dynamic loads can be used as a physical model to describe railways and highways under traffic loading. Vertical displacement, vertical velocity, and vertical acceleration responses of the beam are initially obtained in the frequency domain and then represented as integrations of complex function in the space-time domain. A bifurcation is found in critical speed against resonance frequency. When the dimensionless frequency is high, there is a single critical speed that increases as the dimensionless frequency increases. When the dimensionless frequency is low, there are two critical speeds. One speed increases as the dimensionless frequency increases, while the other speed decreases as the dimensionless frequency decreases. Based on the fast Fourier transform, numerical methods are developed for efficient computation of dynamic response of the beam.

Shock Isolation Systems Using Magnetorheological Dampers

Abstract: This study addresses the feasibility and applicability of a semiactive magnetorheological (MR) shock isolation system to replace a conventional passive shock isolation system for commercial-off-the-shelf (COTS) equipment. To this end, an analysis of a shock isolation system with an MR damper was theoretically developed. To improve shock mitigation performance, semiactive control strategies such as skyhook and sliding mode control were incorporated into our analysis. Controlled responses of the semiactive MR shock isolation system were simulated and compared with those of a conventional passive shock isolation system for two different representative shock loads for COTS equipment.

Experimental and Computational Models for Simulating Sound Propagation Within the Lungs.

Abstract: An acoustic boundary element model is used to simulate sound propagation in the lung parenchyma and surrounding chest wall. It is validated theoretically and numerically and then compared with experimental studies on lung-chest phantom models that simulate the lung pathology of pneumothorax. Studies quantify the effect of the simulated lung pathology on the resulting acoustic field measured at the phantom chest surface. This work is relevant to the development of advanced auscultatory techniques for lung, vascular, and cardiac sounds within the torso that utilize multiple noninvasive sensors to create acoustic images of the sound generation and transmission to identify certain pathologies.

A New Dynamic Model of High-Speed Railway Vehicle Moving on Curved Tracks

Abstract: A new dynamic model of railway vehicle moving on curved tracks is proposed. In the new model, the motion of the car body is considered and the motion of the truck frame is not restricted by a virtual boundary. Based on the heuristic nonlinear creep model, the nonlinear coupled differential equations of the motion of an eight degrees of freedom car system-considering the lateral displacement and the yaw angle of each wheelset, the truck frame, and the half car body-moving on curved tracks are derived completely. To illustrate the accuracy of the analysis, the limiting cases are examined. It is shown that the influence of the gyroscopic moment of the wheelsets on the critical hunting speed is negligible. In addition, the influences of the suspension parameters, including those losing in the six degrees of freedom system, on the critical hunting speeds evaluated via the linear and the nonlinear creep models are studied and compared.

Effect of Boundary Conditions on Nonlinear Vibration and Flutter of Laminated Cylindrical Shells

Abstract: A nonlinear vibration analysis of laminated cylindrical shells is presented in which the effect of the specified boundary conditions at the shell edges, including nonlinear fundamental state deformations, can be accurately taken into account. The method is based on a perturbation expansion for both the frequency parameter and the dependent variables. The present theory includes the effects of finite vibration amplitudes, initial geometric imperfections, and a nonlinear static deformation. Nonlinear Donnell-type equations formulated in terms of the radial displacement W and an Airy stress function F are used, and classical lamination theory is employed. Furthermore, an extension of the theory is presented to analyze linearized flutter in supersonic flow, based on piston theory. The effect of different types of boundary conditions on the nonlinear vibration and linearized flutter behavior of cylindrical shells is illustrated for several characteristic cases.

Robust Optimal Balancing of High-Speed Machinery Using Convex Optimization

Abstract: For high-speed rotating machinery, such as turbomachinery, the vibration caused by the rotor mass imbalance is a major source of maintenance problems. Vibration reduction by balancing under practical constraints and data uncertainty is often a challenging problem. In this paper, we formulate the problem of high-speed flexible rotor balancing as a convex optimization problem. This formulation not only solves the minmax balancing problem efficiently, but also allows the inclusion of various practical constraints. This formulation can be extended in a generalized unified balancing approach, which combines the advantages of both the influence coefficient approach and the modal balancing. Furthermore, a robust balancing approach is also developed to handle uncertainties in the influence coefficient and in the vibration response. This robust balancing approach provides the safeguard for the worse case scenario under the unknown but bounded uncertainty. All the resulting optimization problems are solved by second order cone programming. A large turbine generator balancing case is used to demonstrate that the proposed balancing technique provides the flexibility and efficiency beyond those of the existing balancing methods.

Dynamic Substructuring Based on a Double Modal Analysis

Abstract: Modal synthesis methods have long been studied because the use of generalized coordinates makes it possible to reduce calculation costs. Our approach uses modes to describe each part of the assembly of several substructures. This method, called "Double Modal Synthesis," is presented through primal and dual formulations. As modal truncation usually introduces a lack of precision, we will use an omega2 development if necessary. These formulations will first be explained using a continuous formulation. A finite element method will then be proposed. Another aim of the paper is to introduce formulations needed to understand the multimodal analysis methods that will be presented in a forthcoming paper.

Modal Analysis of Rubbing Acoustic Emission for Rotor-Bearing System Based on Reassigned Wavelet Scalogram

Abstract: Rubbing between the rotor and the stator is the frequent and harmful malfunction in the rotating machinery, which will cause a very serious accident, even catastrophe, to the machine. Thus, such fault needs timely detection to avoid severe consequences. Vibration based methods are the traditional ones for the detection and diagnosis of the rubbing fault, which are effective when the rubbing has been severe, but always do not work in early detection of such fault. Rubbing between the rotor and the stator will cause elastic strain in the rubbing location and thus can produce acoustic emission (AE). Apparently, such AE contains direct and abundant information about the rubbing and thus can be used to detect and diagnose such fault effectively. In this paper, the AE based method is proposed for detecting and identifying the rubbing of the rotor-bearing system. Using the modal acoustic emission (MAE) theory and reassigned wavelet scalogram, the present study emphasizes on modal analysis and time-frequency characteristics analysis for further understanding the characteristics, phenomenon, and features of the rubbing AE. The results show that the rubbing AE is the elastic wave with multiple modals, which has an impact characteristic and mainly consists of the flexural wave and extensional wave. The transmission of the rubbing AE has some directivity. Moreover, different modals have different transmission characteristics: The flexural wave has lower frequency and its attenuation is influenced mainly by the sectional area of the transmission passage. The extensional wave has higher frequency and its attenuation is mainly sensitive to the interface transmission between the two surfaces. The results also reveal that the reassigned wavelet scalogram is more effective than its original scalogram for the characteristic analysis of the rubbing AE. DOI: 10.1115/1.2981091

Optimization of a Two Degree of Freedom System Acting as a Dynamic Vibration Absorber

Abstract: This paper deals with the problem of finding the optimal stiffnesses and damping coefficients of a two degree of freedom (2DOF) system acting as a dynamic vibration absorber (DVA) on a beam structure. In this sense, a heuristic criterion for the optimization problem will be developed to contemplate this particular type of DVA. Accordingly, it is planned to minimize the amplitude of vibration in predetermined points of the main structure. Two optimizations will be proposed for two DVAs of 1DOF to compare their performances with the optimized 2DOF system. A simulated annealing algorithm is used to obtain the DVA’s optimal parameters for minimum amplitude in a given point of the beam. The best configuration depends on the location of the absorbers on the beam and, for a fixed location, on the distribution of the stiffness constants.

Self-Similarity in Vibration Time Series: Application to Gear Fault Diagnostics

Abstract: The vibration time series of gear systems exhibit self-similarity. The time-series behavior is characterized by an exponent, known as the scaling exponent. An algorithm is proposed for the estimation of both global and local exponents, thus providing a means of examining the time-series fine structure. The proposed algorithm is applied to experimental data recorded from gear pairs with localized defects in the form of bending fatigue cracks. It is shown that an examination of the exponent empirical histogram allows detection of damage at an early stage and also provides an estimate of the defect magnitude.

Dynamic Modeling and Experimental Validation of Eddy Current Dampers and Couplers

Abstract: The interest in eddy current dampers is increasing especially in aeronautic and automotive industry. Such devices seem to be a valid alternative to conventional fluid film and viscoelastc dampers. Even if several papers have been published on this topic, an electromechanical model taking into account both the resistance and the inductance of the conductor is still lacking. The aim of the present paper is to model the electromagnetic interaction of an eddy current device operating as a damper or as a coupler and to validate it by means of experimental tests performed at steady state and vibrating about a fixed position. The study is based on the computation of the damping torque starting from the basic principles. The analytical models are developed using the bond graph formalism that allows to obtain purely mechanical analogs of the electromechanical system. The main results are the identification of eddy current damper dynamic model and the definition of a set of "conversion rules" allowing to readily obtain the mechanical impedance from the torque to slip speed characteristic and vice versa. The experimental results confirm the band limited effect of the damping, which cannot be neglected for practical applications. The effect can be exploited in eddy current couplers to filter higher order disturbances

Nonlinear Transverse Vibrations and 3:1 Internal Resonances of a Beam With Multiple Supports

Abstract: In this study, nonlinear transverse vibrations of an Euler-Bernoulli beam with multiple supports are considered. The beam is supported with immovable ends. The immovable end conditions cause stretching of neutral axis and introduce cubic nonlinear terms to the equations of motion. Forcing and damping effects are included in the problem. The general arbitrary number of support case is considered at first, and then 3-, 4-, and 5-support cases are investigated. The method of multiple scales is directly applied to the partial differential equations. Natural frequencies and mode shapes for the linear problem are found. The correction terms are obtained from the last order of expansion. Nonlinear frequencies are calculated and then amplitude and phase modulation figures are presented for different forcing and damping cases. The 3:1 internal resonances are investigated. External excitation frequency is applied to the first mode and responses are calculated for the first or second mode. Frequency-response and force-response curves are drawn.