Showing papers in "Journal of Vibration and Acoustics in 2009"

Effect of Strain Nodes and Electrode Configuration on Piezoelectric Energy Harvesting From Cantilevered Beams

Abstract: For the past five years, cantilevered beams with piezoceramic layer(s) have been frequently used as piezoelectric energy harvesters for vibration-to-electric energy conversion. Typically, the energy harvester beam is located on a vibrating host structure and the dynamic strain induced in the piezoceramic layer(s) results in an alternating voltage output across the electrodes. Vibration modes of a cantilevered piezoelectric energy harvester other than the fundamental mode have certain strain nodes where the dynamic strain distribution changes sign in the direction of beam length. It is theoretically explained and experimentally demonstrated in this paper that covering the strain nodes of vibration modes with continuous electrodes results in strong cancellations of the electrical outputs. A detailed dimensionless analysis is given for predicting the locations of the strain nodes of a cantilevered beam in the absence and presence of a tip mass. Since the cancellation issue is not peculiar to clamped-free boundary conditions, dimensionless data of modal strain nodes are tabulated for some other practical boundary condition pairs and these data can be useful in modal actuation problems as well. How to avoid the cancellation problem in energy harvesting by using segmented electrode pairs is described for single-mode and multimode vibrations of a cantilevered piezoelectric energy harvester. An electrode configuration-based side effect of using a large tip mass on the electrical response at higher vibration modes is discussed theoretically and demonstrated experimentally.

Effective and Robust Vibration Control Using Series Multiple Tuned-Mass Dampers

Abstract: Various types of tuned-mass dampers (TMDs), or dynamic vibration absorbers, have been proposed in literature, including the classic TMD, (parallel) multiple TMDs, multidegree-of-freedom (DOF) TMD, and three-element TMD. In this paper we sturdy the characteristics and optimization of a new type of TMD system, in which multiple absorbers are connected to the primary system in series. Decentralized H 2 and H ∞ control methods are adopted to optimize the parameters of spring stiffness and damping coefficients for random and harmonic vibration. It is found that series multiple TMDs are more effective and robust than all the other types of TMDs of the same mass ratio. The series two TMDs of total mass ratio of 5% can appear to have 31―66% more mass than the classical TMD, and it can perform better than the optimal parallel ten TMDs of the same total mass ratio. The series TMDs are also less sensitive to the parameter variance of the primary system than other TMD(s). Unlike in the parallel multiple TMDs where at the optimum the absorber mass is almost equally distributed, in the optimal series TMDs the mass of the first absorber is generally much larger than the second one. Similar to the 2DOF TMD, the optimal series two TMDs also have zero damping in one of its two connections, and further increased effectiveness can be obtained if a negative dashpot is allowed. The optimal performance and parameters of series two TMDs are obtained and presented in a form of ready-to-use design charts.

Self-Powered Magnetorheological Dampers

Abstract: This study addresses the feasibility and effectiveness of a self-powered magnetorheological (MR) damper using in-situ energy harvested from the vibration and shock environment in which it is deployed. To achieve this, an energy-harvesting device is designed and added to a MR damper. This energy-harvesting device consists of a stator, a permanent magnet, and a spring and operates as an energy-harvesting dynamic vibration absorber (DVA). The dynamic equation for the self-powered MR damper is derived. To evaluate the vibration isolation capability of the self-powered MR damper, a single-degree-of-freedom engine mount system using the MR damper is simulated. The governing equation of motion for the engine mount system is derived. A parametric study is conducted to find the optimal stiffness of the energy-harvesting DVA for the engine mount system. The isolation performance of the engine mount system employing the self-powered MR damper is theoretically evaluated in the frequency domain.

Structural Health Monitoring With Autoregressive Support Vector Machines

Abstract: The use of statistical methods for anomaly detection has become of interest to researchers in many subject areas. Structural health monitoring in particular has benefited from the versatility of statistical damage-detection techniques. We propose modeling structural vibration sensor output data using nonlinear time-series models. We demonstrate the improved performance of these models over currently used linear models. Whereas existing methods typically use a single sensor's output for damage detection, we create a combined sensor analysis to maximize the efficiency of damage detection. From this combined analysis we may also identify the individual sensors that are most influenced by structural damage.

Defect Diagnosis for Rolling Element Bearings Using Acoustic Emission

Abstract: Rolling element bearings are very common components in rotating machinery. Hence, condition monitoring and the detection of defects are very important for the normal and safe running of these machines. Vibration based techniques are well established for the condition monitoring of rolling element bearings, although they are not so effective in detecting incipient defects in the bearing. Acoustic emission (AE) is receiving increasing attention as a complementary method for condition monitoring of bearings as AE is very sensitive to incipient defects. This paper presents an experimental study to investigate the AE characteristics of bearing defect and validates the relationship between various AE parameters and the operational condition of rolling element bearings. To analyze the characteristic vibration frequency of the bearing using the AE signal, short-time rms and autocorrelation functions are integrated to extract the actual characteristic frequency. The AE signal is then analyzed using standard parameters of the signals to explore the source characteristics and sensitivity of typical rolling element bearing faults. The results demonstrate that the proposed method is very effective to extract the actual characteristic frequency of the bearing by AE signal. Furthermore the AE parameters are always sensitive to the running and fault conditions, which have a strong influence on the strain and deformation within the bearing material.

Diffractions of Elastic Waves and Stress Concentration Near a Cylindrical Nano-Inclusion Incorporating Surface Effect

Abstract: The diffractions of plane compressional waves (P-wave) and shear waves (SV-wave) by a cylindrical nano-inclusion are investigated in this paper. To account for the surface/ interface effect at nanoscale, the surface/interface elasticity theory is adopted in the analysis. Using the displacement potential method, we obtain the solutions for the elastic fields induced by incident P- and SV-waves near a cylindrical nano-inclusion. The results show that surface/interface has a significant effect on the diffractions of elastic waves as the radius of the inclusion shrinks to nanoscale. For incident waves with different frequencies, the effects of interfacial properties on the dynamic stress concentration around the nano-inclusion are discussed in detail. DOI: 10.1115/1.4000479

On the Displacement Transmissibility of a Base Excited Viscously Damped Nonlinear Vibration Isolator

Abstract: In this article vibration isolators having linear and cubic nonlinearities in stiffness and damping terms are considered under base excitation. The influence of the system parameters on the relative and absolute displacement transmissibility is investigated. The performance characteristics of the nonlinear isolators are evaluated and compared with the performance characteristics of the linear isolators to highlight the beneficial effects in the nonlinear systems considered.

SEA Coupling Loss Factors of Complex Vibro-Acoustic Systems

Abstract: Reliability of statistical energy analysis (SEA) models depends on good estimates of coupling loss factors (CLFs), modal densities, and damping loss factors. Statistical modal energy distribution analysis (SmEdA), a finite element based method to compute CLFs from uncoupled finite elements models of subsystems, is used to generate SEA CLF for general subsystems. This method is based on the basic SEA relations for coupled oscillators and on a dual modal formulation to describe the vibration of coupled subsystems. Previous works have demonstrated the use of the SmEdA method for structureto- structure couplings. The current work extends the SmEdA process to structure-tocavity couplings. The estimation of CLF using the SmEdA approach is compared, for a simple test case, to analytical results and a classical expression obtained with a wave approach. Results show good comparison with analytical results even below critical frequency, where the wave approach underestimates CLF. Finally, an industrial application has been carried out to demonstrate that the SmEdA approach can be used in the case of complex structures.

Effects of a Cracked Blade on Mistuned Turbine Engine Rotor Vibration

Abstract: An efficient methodology for predicting the nonlinear forced vibration response of a turbine engine rotor with a cracked blade is presented and used to investigate the effects of the damage on the forced response. The influence of small random blade-to-blade differences (mistuning) and rotation on the forced response are also considered. Starting with a finite element model, a hybrid-interface method of component mode synthesis (CMS) is employed to generate a reduced-order model (ROM). The crack surfaces are retained as physical degrees of freedom in the ROM so that the forces due to contact in three-dimensional space can be properly calculated. The resulting nonlinear equations of steady-state motion are solved by applying an alternating frequency/time-domain method, which is much more computationally efficient than traditional time integration. Using this reduced-order modeling and analysis framework, the effects of the cracked blade on the system response of an example rotor are investigated for various mistuning levels and rotation speeds. First, the advantages of the selected hybrid-interface CMS method are discussed and demonstrated. Then, the resonant frequency shift associated with the stiffness loss due to the crack and the vibration localization about the cracked blade are thoroughly investigated. In addition, the results of the nonlinear ROMs are compared with those obtained with linear ROMs, as well as blade-alone ROMs. It is shown that several key system vibration characteristics are not captured by the simpler models, but that some insight into the system response can be gained from the blade-alone response predictions. Furthermore, it is demonstrated that while the effects of the crack often appear similar to those of mistuning, the effects of mistuning and damage can be distinguished by observing and comparing the response across multiple families of system modes.

Gas Void Fraction Measurement in Two-Phase Gas/Liquid Slug Flow Using Acoustic Emission Technology

Abstract: The gas-liquid two-phase slug flow regime phenomenon is commonly encountered in the chemical engineering industry, particularly in oil and gas production transportation pipelines. Slug flow regime normally occurs for a range of pipe inclinations, and gas and liquid flowrates. A pipeline operating in the slug flow regime creates high fluctuations in gas and liquid flowrates at the outlet. Therefore, the monitoring of slugs and the measurement of their characteristics, such as the gas void fraction, are necessary to minimize the disruption of downstream process facilities. In this paper, a correlation between gas void fraction, absolute acoustic emission energy and slug velocities in a two-phase air/water flow regime was developed using an acoustic emission technique. It is demonstrated that the gas void fraction can be determined by measurement of acoustic emission.

A New Rotor-Ball Bearing-Stator Coupling Dynamics Model for Whole Aero-Engine Vibration

Abstract: In this paper, a new rotor-ball bearing-stator coupling system dynamics model is established for simulating the practical whole aero-engine vibration. The main characteristics of the new model are as follows: (I) the coupling effect between rotor, ball bearing, and stator is fully considered; (2) the elastic support and the squeeze film damper are considered ; (3) the rotor is considered as an Euler free beam of equal-section model, and its vibration is analyzed through truncating limited modes; (4) nonlinear factors of ball bearing such as the clearance of bearing, nonlinear Hertzian contact force, and the varying compliance vibration are modeled; and (5) rubbing fault between rotor and stator is considered. The Zhai method, which is a new explicit fast numerical integration method, is employed to obtain system's responses, and the whole aero-engine vibration characteristics are studied. Finally, aero-engine tester including casing is established to carry out rubbing fault experiment, the simulation results from rotor-ball bearing-stator coupling model are compared with the experiment results, and the correctness of the new model is verified to some extent.

Study on Nonlinear Dynamic Response of an Unbalanced Rotor Supported on Ball Bearing

Abstract: An unbalanced rotor dynamic model supported on ball bearings is established. In the model, three nonlinear factors of ball bearing are considered, namely, the clearance of bearing, nonlinear Hertzian contact force between balls and races, and the varying compliance vibrations because of periodical change in contact position between balls and races. The numerical integration method is used to obtain the nonlinear dynamic responses; the effects of the rotating speed and the bearing clearance on dynamic responses are analyzed; and the bifurcation plots, the phase plane plots, the frequency spectra, and the Poincare maps are used to carry out the analyses of bifurcation and chaotic motion. Period doubling, quasiperiod loop breaking, and mechanism of intermittency are observed as the routes to chaos.

Experimental Identification of Generalized Proportional Viscous Damping Matrix

Abstract: A simple and easy-to-implement algorithm to identify a generalized proportional viscous damping matrix is developed in this work. The chief advantage of the proposed technique is that only a single drive-point frequency response function (FRF) measurement is needed. Such FRFs are routinely measured using the standard techniques of an experimental modal analysis, such as impulse test. The practical utility of the proposed identification scheme is illustrated on three representative structures: (1) a free-free beam in flexural vibration, (2) a quasiperiodic three-cantilever structure made by inserting slots in a plate in out-of-plane flexural vibration, and (3) a point-coupled-beam system. The finite element method is used to obtain the mass and stiffness matrices for each system, and the damping matrix is fitted to a measured variation of the damping (modal damping factors) with the natural frequency of vibration. The fitted viscous damping matrix does accommodate for any smooth variation of damping with frequency, as opposed to the conventional proportional damping matrix. It is concluded that a more generalized viscous damping matrix, allowing for a smooth variation of damping as a function of frequency, can be accommodated within the framework of standard finite element modeling and vibration analysis of linear systems.

A Mathematical Model for Vibration-Induced Loosening of Preloaded Threaded Fasteners

Abstract: A mathematical model is proposed for studying the vibration induced loosening of threaded fasteners that are subjected to harmonic transverse excitation, which often causes slippage between the contact surfaces between engaged threads and under the bolt head. Integral equations are derived for the cyclic shear forces as well as the bearing and thread friction torque components. They depend on the ratio of the relative rotational to translational velocities. The relationship between the dynamic thread shear force and bending moment is developed. When the external transverse excitation is large enough, it causes the threaded fasteners to loosen. Numerical results show that the dynamic transverse shear forces on the underhead contact surface, and between the engaged threads, decrease the bearing, and thread friction torque components. The effect of bolt preload, bearing and thread friction coefficients, the amplitude of the harmonic transverse excitation, and the bolt underhead bending on the bolt loosening are investigated. Experimental verification of the analytical model results of the bolt twisting torque is provided.

A Combination of WKNN to Fault Diagnosis of Rolling Element Bearings

Abstract: This paper presents a new method for fault diagnosis of rolling element bearings, which is developed based on a combination of weighted K nearest neighbor WKNN classifiers. This method uses wavelet packet transform based on the lifting scheme to preprocess the vibration signals before feature extraction. Time- and frequency-domain features are all extracted to represent the operation conditions of the bearings totally. Sensitive features are selected after feature extraction. And then, multiple classifiers based on WKNN are combined to overcome the two disadvantages of KNN and therefore it may enhance the classification accuracy. The experimental results of the proposed method to fault diagnosis of the rolling element bearings show that this method enables the detection of abnormalities in bearings and at the same time identification of fault categories and levels. DOI: 10.1115/1.4000478

An Efficient Method for Crack Identification in Simply Supported Euler–Bernoulli Beams

Abstract: An effective crack identification procedure has been developed based on the dynamic behavior of a Euler-Bernoulli cracked beam. It is very well known that the presence of a crack in a structure produces a change in its frequency response that can be used to determine the crack properties (position and size) solving what is called an inverse problem. In this work, such an inverse problem has been solved by the use of the classical optimization technique of minimizing the least square criterion applied to the closed-form expression for the frequencies obtained through the perturbation method. The advantage of this method with respect to the ones derived previously is that the knowledge of the material and its properties (Young's modulus and mass density) is not necessary, not even the behavior of the uncracked element. The methodology has been successfully applied to I a simply supported Euler-Bernoulli beam.

Theoretical Modeling of TLD With Different Tank Geometries Using Linear Long Wave Theory

Abstract: This study focuses on the modeling of tuned liquid dampers (TLDs) with triangular-bottom, sloped-bottom, parabolic-bottom, and flat-bottom tanks using the linear long wave theory. The energy dissipated by damping screens is modeled theoretically utilizing the method of virtual work. In this proposed model, only the fundamental sloshing mode is considered, and the assumption of small free surface fluid response amplitude is made. Subsequently, the equivalent mechanical properties including effective mass, natural frequency, and damping ratio of the TLDs, having different tank geometries, are compared. It is found that the normalized effective mass ratio values for a parabolic-bottom tank and a sloped-bottom tank with a sloping angle of 20 deg are larger than the normalized effective mass ratio values for triangular-bottom and flat-bottom tanks. An increase in the normalized effective mass ratio indicates that a greater portion of the water inside the tank participates in the sloshing motion. The derived equivalent mechanical models for the TLD tank geometries considered in this study can be used for the preliminary design of structural-TLD systems.

A New 3D Finite Element for Sandwich Beams With a Viscoelastic Core

Abstract: A sandwich finite element for laminated steels is presented. It is based on a discrete displacement approach and allows for both symmetrical and unsymmetrical configurations. The three-layer sandwich model is built assuming a Timoshenko hypothesis for the viscoelastic core and Euler–Bernoulli hypotheses for the elastic faces, but the latter is modified to account for the rotational influence of the transversal shearing in the core. The validity and accuracy of the presented element are assessed through comparisons with numerical results of sandwich beams and sandwich rings with a variety of geometrical and mechanical properties and various boundary conditions. The present results are also compared with analytical, finite element, and experimental solutions for various boundary conditions.

Vibration Suppression of Mistuned Coupled-Blade-Disk Systems Using Piezoelectric Circuitry Network

Abstract: For bladed-disk assemblies in turbomachinery, the elements are often exposed to aerodynamic loadings, the so-called engine order excitations. It has been reported that such excitations could cause significant structural vibration. The vibration level could become even more excessive when the bladed disk is mistuned, and may cause fatigue damage to the engine components. To effectively suppress vibration in bladed disks, a piezoelectric transducer networking concept has been explored previously by the authors. While promising, the idea was developed based on a simplified bladed-disk model without considering the disk dynamics. To advance the state of the art, this research further extends the investigation with focus on new circuitry designs for a more sophisticated and realistic system model with the consideration of coupled-blade-disk dynamics. A novel multicircuit piezoelectric transducer network is synthesized and analyzed for multiple-harmonic vibration suppression of bladed disks. An optimal network is derived analytically. The performance of the network for bladed disks with random mistuning is examined through Monte Carlo simulation. The effects of variations (mistuning and detuning) in circuit parameters are also studied. A method to improve the system performance and robustness utilizing negative capacitance is discussed. Finally, experiments are carried out to demonstrate the vibration suppression capability of the proposed piezoelectric circuitry network.

Mathematical modeling, analysis, and design of magnetorheological (MR) dampers

Abstract: Most magnetorheological (MR) fluid dampers are designed as fixed-pole valve mode devices, where the MR fluid is forced to flow through a magnetically active annular gap. This forced flow generates the damping force, which can be continuously regulated by controlling the strength of the applied magnetic field. Because the size of the annular gap is usually very small relative to the radii of the annulus, the flow of the MR fluid through this annulus is usually approximated by the flow of fluid through two infinitely wide parallel plates. This approximation, which is widely used in designing and modeling of MR dampers, is satisfactory for many engineering purposes. However, the model does not represent accurately the physical processes and, therefore, expressions that correctly describe the physical behavior are highly desirable. In this paper, a mathematical model based on the flow of MR fluids through an annular gap is developed. Central to the model is the solution for the flow of any fluid model with a yield stress (of which MR fluid is an example) through the annular gap inside the damper. The physical parameters of a MR damper designed and fabricated at the University of Manchester are used to evaluate the performance of the damper and to compare with the corresponding predictions of the parallel plate model. Simulation results incorporating the effects of fluid compressibility are presented, and it is shown that this model can describe the major characteristics of such a device-nonlinear, asymmetric, and hysteretic behaviors-successfully.

Imbalance Vibration Suppression of a Supercritical Shaft via an Automatic Balancing Device

Abstract: This research explores the use of automatic balancing (AB) devices or "autobalancers" for imbalance vibration suppression of flexible shafts operating at supercritical speeds. Essentially an autobalancer is a passive device consisting of several freely moving eccentric masses or balancer balls free to roll within a circular track mounted on a rotor that is to be balanced. At certain speeds, the stable equilibrium positions of the balls are such that they reduce or cancel the rotor imbalance. This "automatic balancing" phenomenon occurs as a result of the nonlinear dynamic interactions between the balancer balls and the rotor transverse vibration. Thus, autobalancer devices can passively compensate for unknown imbalance without the need for a control system and are able to naturally adjust for changing imbalance conditions. Autobalancers are currently utilized for imbalance correction in some single plane rotor applications such as computer hard-disk drives, CD-ROM drives, machine tools and energy storage flywheels. While autobalancers can effectively compensate for imbalance of planar, disk-type, rigid rotors, the use of autobalancing devices for nonplanar and flexible shafts with multiple modes of vibration has not been fully considered. This study explores the dynamics and stability of an imbalanced flexible shaft-disk system equipped with a dual-ball automatic balancing device. The system is analyzed by solving a coupled set of nonlinear equations to determine the fixed-point equilibrium conditions in rotating coordinates, and stability is assessed via eigenvalue analysis of the perturbed system about each equilibrium configuration. It is determined that regions of stable automatic balancing occur at supercritical shaft speeds between each flexible mode. Additionally the effects of bearing support stiffness, axial mounting offset between the imbalance and autobalancer planes, and ball/track viscous damping are explored. This investigation develops a new, efficient, analysis method for calculating the fixed-point equilibrium configurations of the flexible shaft-AB system. Finally, a new effective force ratio parameter is identified, which governs the equilibrium behavior of flexible shaft/AB systems with noncollocated autobalancer and imbalance planes. This analysis yields valuable insights for balancing of flexible rotor systems operating at supercritical speeds.

Periodic Motions With Impacting Chatter and Stick in a Gear Transmission System

Abstract: In this paper, an impact model with possible stick between the two gears is proposed for gear transmission systems, which includes the piecewise backlash model and the traditional impact model for the first time. The new model presented in this paper possesses a time-varying boundary for two dynamical systems either to switch or to impact. Such a model can catch impacting chatter and stick phenomena in gear transmission systems. Based on the new model, periodic impacting chatter and stick in a gear transmission system can be investigated. For doing so, switching sets on the time-varying boundaries are introduced to define basic mappings. Mapping structures based on basic mappings are developed for characterizing motions in gear transmission systems, and from such mapping structures, periodic motions with impacting chatter and stick in such a gear transmission system are predicted analytically. Numerical simulations are performed for illustration of periodic motions with impacting chatter and stick phenomena.

An Improvement of a Nonclassical Numerical Method for the Computation of Fractional Derivatives

Abstract: Standard methods for the numerical calculation of fractional derivatives can be slow and memory consuming due to the nonlocality of the differential operators. Yuan and Agrawal (2002, "A Numerical Scheme for Dynamic Systems Containing Fractional Derivatives, " ASME J. Vibr. Acoust., 124, pp. 321-324) have proposed a more efficient approach for operators whose order is between 0 and I that differs substantially from the traditional concepts. It seems, however, that the accuracy of the results can be poor. We modify the approach, adapting it better to the properties of the problem, and show that this leads to a significantly improved quality. Our idea also works for operators of order greater than 1.

Ground-Based Vibration Response of a Spinning, Cyclic, Symmetric Rotor With Gyroscopic and Centrifugal Softening Effects

Abstract: This paper is to study ground-based vibration response of a spinning, cyclic, symmetric rotor through a theoretical analysis and an experimental study. The theoretical analysis consists of three steps. The first step is to analyze the vibration characteristics of a stationary, cyclic, symmetric rotor with N identical substructures. For each vibration mode, we identify a phase index n and derive a Fourier expansion of the mode shape in terms of the phase index n. The second step is to predict the rotor-based vibration response of the spinning, cyclic, symmetric rotor based on the Fourier expansion of the mode shapes and the phase indices. The rotor-based formulation includes gyroscopic and centrifugal softening terms. Moreover, rotor-based response of repeated modes and distinct modes is obtained analytically. The third step is to transform the rotor-based response to ground-based response using the Fourier expansion of the stationary mode shapes. The theoretical analysis leads to the following conclusions. First, gyroscopic effects have no significant effects on distinct modes. Second, the presence of gyroscopic and centrifugal softening effects causes the repeated modes to split into two modes with distinct frequencies ω 1 and ω 2 in the rotor-based coordinates. Third, the transformation to ground-based observers leads to primary and secondary frequency components. In general, the ground-based response presents frequency branches in the Campbell diagram at ω 1 ±kω 3 and ω 2 ±kω 3 , where k is phase index n plus an integer multiple of cyclic symmetry N. When the gyroscopic effect is significantly greater than the centrifugal softening effect, two of the four frequency branches vanish. The remaining frequency branches take the form of either ω 1 +kω 3 and ω 2 -kω 3 or ω 1 -kω 3 and ω 2 +kω 3 . To verify these predictions, we also conduct a modal testing on a spinning disk carrying four pairs of brackets evenly spaced in the circumferential direction with ground-based excitations and responses. The disk-bracket system is mounted on a high-speed, air-bearing spindle. An automatic hammer excites the spinning disk-bracket system and a laser Doppler vibrometer measures its vibration response. A spectrum analyzer processes the hammer excitation force and the vibrometer measurements to obtain waterfall plots at various spin speeds. The measured primary and secondary frequency branches from the waterfall plots agree well with those predicted analytically.

Fractional Optimal Control of Continuum Systems

Abstract: This paper presents a formulation and a numerical scheme for fractional optimal control (FOC) of a class of continuum systems. The fractional derivative is defined in the Caputo sense. The performance index of a fractional optimal control problem is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a partial fractional differential equation. The scheme presented relies on reducing the equations of a continuum system into a set of equations that have no space parameter. Several strategies are pointed out for this task, and one of them is discussed in detail. The numerical scheme involves discretizing the space domain into several segments, and expressing the spatial derivatives in terms of variables at spatial node points. The calculus of variations, the Lagrange multiplier, and the formula for fractional integration by parts are used to obtain the Euler-Lagrange equations for the problem. The numerical technique presented in the work ofAgrawal (2006, "A Formulation and a Numerical Scheme for Fractional Optimal Control Problems," Proceedings of the Second IFAC Conference on Fractional Differentiations and Its Applications, FDA '06, Porto, Portugal) for the scalar case is extended for the vector case. In this method, the FOC equations are reduced to the Volterra type integral equations. The time domain is also discretized into a number of subintervals. For the linear case, the numerical technique results in a set of algebraic equations that can be solved using a direct or an iterative scheme. An example problem is solved for various orders of fractional derivatives and different spatial and temporal discretizations. For the problem considered, only a few space grid points are sufficient to obtain good results, and the solutions converge as the size of the time step is reduced. The formulation presented is simple and can be extended to FOC of other continuum systems.

Experimental Evaluation of a Unified Time-Scale-Frequency Technique for Bearing Defect Feature Extraction

Abstract: A systematic experimental study is presented in this paper on evaluating the effectiveness of a unified, multidomain algorithm for defect feature extraction in bearing condition monitoring and health diagnosis The algorithm decomposes vibration signals measured on bearings by discrete wavelet transform and subsequently performs the Fourier transform on the wavelet coefficients The effectiveness of such a unified technique is demonstrated through experimental case studies, which confirmed its advantage over the wavelet or Fourier transform techniques employed alone Also, the unified technique has shown to be computationally more efficient than the enveloping technique based on continuous wavelet transform, thus providing a good signal processing tool for bearing defect diagnosis

Acoustic Radiation From an Infinite Laminated Composite Cylindrical Shell With Doubly Periodic Rings

Abstract: Acoustic radiation from a point-driven, infinite fluid-loaded, laminated composite shell, which is reinforced by doubly periodic rings, is investigated theoretically. The theory is based on the classical laminated composite shell theory, the Helmholtz equation, and the boundary conditions at the shell-fluid interface as well as at the junctions between the shell and the rings. The rings interact with the shell only through normal forces. The solution for the radial displacement in wave number domain is developed by using Mace’s method (1980, “Sound Radiation Form a Plate Reinforced by Two Sets of Parallel Stiffeners,” J. Sound Vib., 71(3), pp. 435‐441) for an infinite flat plate. The stationary phase approximate is then employed to find the expression for the far-field pressure. Numerical results are presented for discussion of the effects of lamination schemes, Poisson’s ratios, ply angles, and damping on the far-field acoustic radiation, which may lend themselves to better understanding the characteristics of acoustic radiation from the laminated composite shells. In addition, the helical wave spectra of the stiffened cylinders are presented, in which the effects of wave number conversion due to the periodic rings are obviously identified as additional bright patterns. DOI: 10.1115/1.2980376

Prediction of Pressure Pulsation for the Reciprocating Compressor System Using Finite Disturbance Theory

Abstract: Pressure pulsations in the piping system of the reciprocating compressor produce excessive noise and even lead to damage in piping and machinery. Therefore, it is very important to predict precisely the pressure pulsation with large amplitude in the piping system. In this paper, the finite disturbance theory is used to solve the nonlinear partial differential equations that describe the unsteady one-dimensional compressible flow in the complex piping system. The solution is then compared with experimental results. The comparison shows that the finite theory fits the large pressure disturbance more precisely than the acoustic theory.

Parametric Analyses of Multispan Viscoelastic Shear Deformable Beams Under Excitation of a Moving Mass

Abstract: This paper presents a numerical parametric study on design parameters of multispan viscoelastic shear deformable beams subjected to a moving mass via generalized moving least squares method (GMLSM). For utilizing Lagrange’s equations, the unknown parameters of the problem are stated in terms of GMLSM shape functions and the generalized Newmark- scheme is applied for solving the discrete equations of motion in time domain. The effects of moving mass weight and velocity, material relaxation rate, slenderness, and span number of the beam on the design parameters and possibility of mass separation from the base beam are scrutinized in some detail. The results reveal that for low values of beam slenderness, the Euler–Bernoulli beam theory or even Timoshenko beam theory could not predict the real dynamic behavior of the multispan viscoelastic beam properly. Moreover, higher beam span number would result in higher inertial effects as well as design parameters values. Also, more distinction has been observed between the predicted values of design parameters regarding the shear deformable beams and those of Euler–Bernoulli beams, specifically for high levels of moving mass velocity and low values of material relaxation rate. Furthermore, the possibility of mass separation from the base beam moves to a greater extent as the beam span number increases and the relaxation rate of the beam material decreases, regardless of the assumed beam theory. DOI: 10.1115/1.3147165

Effect of Nonhomogeneity on Vibration of Orthotropic Rectangular Plates of Varying Thickness Resting on Pasternak Foundation

Abstract: Free transverse vibrations of nonhomogeneous orthotropic rectangular plates of varying thickness with two opposite simply supported edges (y = 0 and y =b) and resting on two-parameter foundation (Pasternak-type) have been studied on the basis of classical plate theory. The other two edges (x =0 and x=a) may be any combination of clamped and simply supported edge conditions. The nonhomogeneity of the plate material is assumed to arise due to the exponential variations in Young's moduli and density along one direction. By expressing the displacement mode as a sine function of the variable between simply supported edges, the fourth order partial differential equation governing the motion of such plates of exponentially varying thickness in another direction gets reduced to an ordinary differential equation with variable coefficients. The resulting equation is then solved numerically by using the Chebyshev collocation technique for two different combinations of clamped and simply supported conditions at the other two edges. The lowest three frequencies have been computed to study the behavior of foundation parameters together with other plate parameters such as nonhomogeneity, density, and thickness variation on the frequencies of the plate with different aspect ratios. Normalized displacements are presented for a specified plate. A comparison of results with those obtained by other methods shows the computational efficiency of the present approach.