Showing papers on "Vibration published in 2007"

Vibration of nonlocal Timoshenko beams

Abstract: This paper is concerned with the free vibration problem for micro/nanobeams modelled after Eringen's nonlocal elasticity theory and Timoshenko beam theory. The small scale effect is taken into consideration in the former theory while the effects of transverse shear deformation and rotary inertia are accounted for in the latter theory. The governing equations and the boundary conditions are derived using Hamilton's principle. These equations are solved analytically for the vibration frequencies of beams with various end conditions. The vibration solutions obtained provide a better representation of the vibration behaviour of short, stubby, micro/nanobeams where the effects of small scale, transverse shear deformation and rotary inertia are significant. The exact vibration solutions should serve as benchmark results for verifying numerically obtained solutions based on other beam models and solution techniques.

Damage identification using inverse methods

Abstract: This paper gives an overview of the use of inverse methods in damage detection and location, using measured vibration data. Inverse problems require the use of a model and the identification of uncertain parameters of this model. Damage is often local in nature and although the effect of the loss of stiffness may require only a small number of parameters, the lack of knowledge of the location means that a large number of candidate parameters must be included. This paper discusses a number of problems that exist with this approach to health monitoring, including modelling error, environmental effects, damage localization and regularization.

Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics

Abstract: In this paper, the small scaling parameter e0 of the nonlocal Timoshenko beam theory is calibrated for the free vibration problem of single-walled carbon nanotubes (SWCNTs). The calibration exercise is performed by using vibration frequencies generated from molecular dynamics simulations at room temperature. It was found that the calibrated values of e0 are rather different from published values of e0. Instead of a constant value, the calibrated e0 values vary with respect to length-to-diameter ratios, mode shapes, and boundary conditions of the SWCNTs. In addition, the physical meaning of the scaling parameter is explored. The results show that scaling parameter assists in converting the kinetic energy to the strain energy, thus enabling the kinetic energy to be equal to the strain energy. The calibrated e0 presented herein should be useful for researchers who are using the nonlocal beam theories for analysis of micro and nano beams/rods/tubes.

A method to avoid negative damped low frequent tower vibrations for a floating, pitch controlled wind turbine

Abstract: Wind turbines mounted on floating platforms is subjected to completely different and soft foundation properties, than seen for onshore wind turbines. This leads to much lower natural frequencies, related to the rigid body motion of the structure which again leads to an unfavorable coupling between tower motion and the pitch control of the turbine. The tower motion in combination with the aerodynamics and the pitch control will be poor or even negative damped which causes large transient loads if not accounted for. The reason for this low damping is shown to be caused by a too fast pitch regulation compared to the motion of the tower or in other words the lowest control-structure natural frequency must be lower than the lowest critical tower frequency. A control algorithm is presented including the tuning method (pole-placement) to ensure the desired control frequency which provides stable tower vibration modes.

Aeroelastic instability problems for wind turbines

Abstract: This paper deals with the aeroelastic instabilities that have occurred and may still occur for modern commercial wind turbines: stall-induced vibrations for stall-turbines, and classical flutter for pitch-regulated turbines. A review of previous works is combined with derivations of analytical stability limits for typical blade sections that show the fundamental mechanisms of these instabilities. The risk of stall-induced vibrations is mainly related to blade airfoil characteristics, effective direction of blade vibrations and structural damping; whereas the blade tip speed, torsional blade stiffness and chordwise position of the center of gravity along the blades are the main parameters for flutter. These instability characteristics are exemplified by aeroelastic stability analyses of different wind turbines. The review of each aeroelastic instability ends with a list of current research issues that represent unsolved aeroelastic instability problems for wind turbines. Copyright © 2007 John Wiley & Sons, Ltd.

Experimental Verification of Models for Microfabricated Piezoelectric Vibration Energy Harvesters

Abstract: Experiments have been performed to verify power-optimized modal models of piezoelectric vibration harvesters for microelectromechanical systems. Such harvesters can power a variety of sensors, and there have been recent national workshops dedicated to harvesting. Detailed experimental results, including displacement histories and electrical output, are provided over a range of frequencies and electrical loadings to compare with (optimized) modal models. The harvester geometry considered is that of a symmetric bimorph macroscale cantilever. Although some experimental work for cantilevered bimorph harvesters has been published, key testing and/or device parameters needed for model verification are missing and/or data at and near power optima (the most interesting operating points) are not provided. Therefore, a detailed set of experiments was performed using power-optimized modeling results to guide the test matrix. Over the broad range of parameters tested, the models accurately predicted all trends and device performance away from device resonances (resonance and antiresonance frequencies). Near the resonance frequencies, the model consistently underpredicts electrical performance, which is satisfactorily attributed (and experimentally supported) to the well-known piezoelectric coupling nonlinearity in the large-strain region. The data presented herein can serve as benchmark data to verify other modeling efforts. The verified models have been used to optimally design microelectromechanical system harvesters for commercial aircraft and microfabrication is ongoing.

An adaptive extended Kalman filter for structural damage identifications II: unknown inputs

Abstract: After a major event, such as a strong earthquake, a rapid assessment of the state (or damage) of the structure, including buildings, bridges and others, is important for post-event emergency responses, rescues and management. Time domain analysis methodologies based on measured vibration data, such as the least squares estimation and the extended Kalman filter (EKF), have been studied and shown to be useful for the on-line tracking of structural damages. The traditional EKF method requires that all the external excitation data (input data) be measured or available, which may not be the case for many structures. In this paper, an EKF approach with unknown inputs (excitations), referred to as EKF-UI, is proposed to identify the structural parameters, such as the stiffness, damping and other nonlinear parameters, as well as the unmeasured excitations. Analytical solution for the proposed EKF-UI approach is derived and presented. Such an analytical solution for EKF-UI is not available in the previous literature. An adaptive tracking technique recently developed is also implemented in the proposed EKF-UI approach to track the variations of structural parameters due to damages. Simulation results for linear and nonlinear structures demonstrate that the proposed approach is capable of identifying the structural parameters, their variations due to damages, and unknown excitations. Copyright © 2006 John Wiley & Sons, Ltd.

Vibration damping, control, and design

Abstract: VIBRATION DAMPING Vibration Damping Clarence W. de Silva Introduction Types of Damping Representation of Damping in Vibration Analysis Measurement of Damping Interface Damping DAMPING THEORY Randall D. Peters Preface Introduction Background Hysteresis - More Details Damping Models Measurements of Damping Hysteretic Damping Failure of the Common Theory Air Influence Noise and Damping Transform Methods Hysteretic Damping Internal Friction Mathematical Tricks - Linear Damping Approximations Internal Friction Physics Zener Model Toward a Universal Model of Damping Nonlinearity Concluding Remark EXPERIMENTAL TECHNIQUES IN DAMPING Randall D. Peters Electronic Considerations Data Processing Sensor Choices Damping Examples Driven Oscillators with Damping Oscillator with Multiple Nonlinearities Multiple Modes of Vibration Internal Friction as Source of Mechanical Noise Viscous Damping - Need for Caution Air Influence STRUCTURE AND EQUIPMENT ISOLATION Y.B. Yang, L.Y. Lu, and J.D. Yau Introduction Mechanisms of Base-Isolated Systems Structure-Equipment Systems with Elastomeric Bearings Sliding Isolation Systems Sliding Isolation Systems with Resilient Mechanism Issues Related to Seismic Isolation Design VIBRATION CONTROL Nader Jalili and Ebrahim Esmailzadeh Introduction Vibration-Control Systems Concept Vibration-Control Systems Design and Implementation Practical Considerations and Related Topics HELICOPTER ROTOR TUNING Kourosh Danai Introduction Neural Network-Based Tuning Probability-Based Tuning Adaptive Tuning Case Study Conclusion VIBRATION DESIGN AND CONTROL Clarence W. de Silva Introduction Specification of Vibration Limits Vibration Isolation Balancing of Rotating Machinery Balancing of Reciprocating Machines Whirling of Shafts Design through Modal Testing Passive Control of Vibration Active Control of Vibration Control of Beam Vibrations Appendix 7A: MATLAB Control Systems Toolbox STRUCTURAL DYNAMIC MODIFICATION AND SENSITIVITY ANALYSIS Su Huan Chen Introduction Structural Dynamic Modification of Finite Element Model Perturbation Method of Vibration Modes Design Sensitivity Analysis of Structural Vibration Modes High-Accuracy Modal Superposition for Sensitivity Analysis of Modes Sensitivity of Eigenvectors for Free-Free Structures Matrix Perturbation Theory for Repeated Modes Matrix Perturbation Method for Closely Spaced Eigenvalues Matrix Perturbation Theory for Complex Modes VIBRATION IN ROTATING MACHINERY H. Sam Samarasekera Introduction Vibration Basics Rotordynamic Analysis Vibration Measurement and Techniques Vibration Control and Diagnostics REGENERATIVE CHATTER IN MACHINE TOOLS Robert G. Landers Introduction Chatter in Turning Operations Chatter in Face-Milling Operations Time-Domain Simulation Chatter Detection Chatter Suppression Case Study FLUID-INDUCED VIBRATION Seon M. Han Description of the Ocean Environment Fluid Forces Examples SOUND LEVELS AND DECIBELS S. Akishita Introduction Sound Wave Characteristics Levels and Decibels HEARING AND PSYCHOLOGICAL EFFECTS S. Akishita Introduction Structure and Function of the Ear Frequency and Loudness Response Hearing Loss Psychological Effects of Noise NOISE CONTROL CRITERIA AND REGULATIONS S. Akishita Introduction Basic Ideas behind Noise Policy Legislation Regulation Measures of Noise Evaluation INSTRUMENTATION Kiyoshi Nagakura Sound Intensity Measurement Mirror-Microphone System Microphone Array SOURCE OF NOISE S. Akishita Introduction Radiation of Sound DESIGN OF ABSORPTION Teruo Obata Introduction Fundamentals of Sound Absorption Sound-Absorbing Materials Acoustic Characteristic Computation Compound Wall Attenuation of Lined Ducts Attenuation of Dissipative Mufflers General Considerations Practical Example of Dissipative Muffler DESIGN OF REACTIVE MUFFLERS Teruo Obata Introduction Fundamental Equations Effects of Reactive Mufflers Calculation Procedure Application Range of Model Practical Example DESIGN OF SOUND INSULATION Kiyoshi Okura Theory of Sound Insulation Application of Sound Insulation STATISTICAL ENERGY ANALYSIS Takayuki Koizumi Introduction Power Flow Equations Estimation of SEA Parameters Application in Structures INDEX

Mode coupling instability in friction-induced vibrations and its dependency on system parameters including damping

Abstract: Friction-induced vibrations due to coupling modes can cause severe damage and are recognized as one of the most serious problems in industry. In order to avoid these problems, engineers must find a design to reduce or to eliminate mode coupling instabilities in braking systems. Though many researchers have studied the problem of friction-induced vibrations with experimental, analytical and numerical approaches, the effects of system parameters, and more particularly damping, on changes in stable-unstable regions and limit cycle amplitudes are not yet fully understood. The goal of this study is to propose a simple non-linear two-degree-of-freedom system with friction in order to examine the effects of damping on mode coupling instability. By determining eigenvalues of the linearized system and by obtaining the analytical expressions of the Routh-Hurwitz criterion, we will study the stability of the mechanical system's static solution and the evolution of the Hopf bifurcation point as functions of the structural damping and system parameters. It will be demonstrated that the effects of damping on mode coupling instability must be taken into account to avoid design errors. The results indicate that there exists, in some cases, an optimal structural damping ratio between the stable and unstable modes which decreases the unstable region. We also compare the evolution of the limit cycle amplitudes with structural damping and demonstrate that the stable or unstable dynamic behaviour of the coupled modes are completely dependent on structural damping.

Optimum parameters of tuned mass damper for damped main system

Abstract: A tuned mass damper (TMD) is a device consisting of small damped spring–mass system attached to a vibrating main system in order to attenuate any undesirable vibrations In this paper, optimum parameters of TMD system attached to a viscously damped single degree-of-freedom main system are derived for various combinations of excitation and response parameters The excitation applied to the main system consists of external force and base acceleration modelled as Gaussian white-noise random process Using numerical searching technique, the optimum damping and tuning frequency ratio of the TMD are obtained for minimization of various mean square responses such as relative displacement, velocity of main mass and force transmitted to the support The optimum parameters of the TMD system and the corresponding response quantities are obtained for different damping ratios of the main system and the mass ratios of the TMD system Explicit formulae for damper damping, tuning frequency and the corresponding minimized response are then derived using curve-fitting technique that can be conveniently used for applications in dynamical systems The error in these expressions is found to be negligible and hence these expressions are convenient for use in damped single degree-of-freedom main system The optimum damping ratio of the TMD is not much influenced by the damping of the main system However, the optimum tuning frequency of TMD is significantly affected by the damping of main system Lastly, a comparison of the optimum damping and tuning frequency of the TMD under filtered white-noise and white-noise excitation is also made Copyright © 2006 John Wiley & Sons, Ltd

Linearization Methods for Stochastic Dynamic Systems

Abstract: Mathematical Preliminaries.- Moment Equations for Linear Stochastic Dynamic Systems (LSDS).- Moment Equations for Nonlinear Stochastic Dynamic Systems (NSDS).- Statistical Linearization of Stochastic Dynamic Systems Under External Excitations.- Equivalent Linearization of Stochastic Dynamic Systems Under External Excitation.- Nonlinearization Methods.- Linearization of Dynamic Systems with Stochastic Parametric Excitations.- Applications of Linearization Methods in Vibration Analysis of Stochastic Mechanical Structures.- Accuracy of Linearization Methods.

Vibration-induced climbing of drops

Abstract: We report an experimental study of liquid drops moving against gravity, when placed on a vertically vibrating inclined plate, which is partially wetted by the drop. The frequency of vibrations ranges from 30 to 200 Hz, and, above a threshold in vibration acceleration, drops experience an upward motion. We attribute this surprising motion to the deformations of the drop, as a consequence of an up or down symmetry breaking induced by the presence of the substrate. We relate the direction of motion to contact angle measurements. This phenomenon can be used to move a drop along an arbitrary path in a plane, without special surface treatments or localized forcing.

Analysis of free and forced vibration of a cracked cantilever beam

Abstract: Structures are weakened by cracks. When the crack size increases in course of time, the structure becomes weaker than its previous condition. Finally, the structure may breakdown due to a minute crack. Therefore, crack detection and classification is a very important issue. In this study, free and forced vibration analysis of a cracked beam were performed in order to identify the crack in a cantilever beam. Single- and two-edge cracks were evaluated. The study results suggest that free vibration analysis provides suitable information for the detection of single and two cracks, whereas forced vibration can detect only the single crack condition. However, dynamic response of the forced vibration better describes changes in crack depth and location than the free vibration in which the difference between natural frequencies corresponding to a change in crack depth and location only is a minor effect.

Minimization of sound radiation from vibrating bi-material structures using topology optimization

Abstract: Up to now, work on topological design optimization of vibrating structures against noise radiation has mainly addressed the maximization of eigenfrequencies and gaps between consecutive eigenfrequencies of free vibration, and minimization of the dynamic compliance subject to harmonic loading on the structure. In this paper, we deal with topology optimization problems formulated directly with the design objective of minimizing the sound power radiated from the structural surface(s) into a surrounding acoustic medium. Bi-material elastic continuum structures without material damping are considered. The structural vibrations are excited by time-harmonic external mechanical loading with prescribed frequency and amplitude. It is assumed that air is the acoustic medium and that a feedback coupling to the structure can be neglected. Certain conditions are assumed that imply that the sound power emission from the structural surface can be obtained in a simpler way than by solving Helmholz’ integral equation. Hereby, the computational cost of the structural-acoustical analysis is substantially reduced. Several numerical results are presented and discussed for plate- and pipe-like structures with different sets of boundary and loading conditions.

Frequencies in the Vibration Induced by the Rotor Stator Interaction in a Centrifugal Pump Turbine

Abstract: The highest vibration levels in large pump turbines are, in general, originated in the rotor stator interaction (RSI). This vibration has specific characteristics that can be clearly observed in the frequency domain: harmonics of the moving blade passing frequency and a particular relationship among their amplitudes. It is valuable for the design and condition monitoring to count on these characteristics. A CFD model is an appropriate tool to determine the force and its characteristics. However, it is time consuming and needs highly qualified human resources while usually these results are needed immediately and in situ. Then, it is useful to determine these characteristics in a simple, quick, and accurate method. At present, the most suitable method indicates a large amount of possible harmonics to appear, without indicating the relative importance of them. This paper carries out a theoretical analysis to predict and explain in a qualitative way these frequencies and amplitudes. The theoretical analysis incorporates the number of blades, the number of guide vanes, the RSI nonuniform fluid force, and the sequence of interaction. This analysis is compared with the method currently in use, and both methods are applied to a practical case. The theoretical analysis gives a resulting force over the pump turbine, which corresponds well to the measured behavior of a pump turbine in terms of its frequencies and the relationship between their amplitudes. A corrective action is proposed as a result of the analysis and after it is carried out in one of the units, the vibration levels are reduced. The vibration induced by the RSI is predicted considering the sequence of interaction and different amplitudes in the interactions between the same moving blade and different stationary blades, giving a different and original interpretation about the source of the vibration characteristics. A successful corrective action is proposed as a consequence of this new interpretation.

Suppressing Aeroelastic Instability Using Broadband Passive Targeted Energy Transfers, Part 2: Experiments

Abstract: This paper presents experimental results corroborating the analysis developed in the companion paper, Part 1 (Lee, Y., Vakakis, A., Bergman, L., McFarland, M., and Kerschen G., "Suppression Aeroelastic Instability Using Broadband Passive Targeted Energy Transfers, Part 1: Theory," AIAA Journal, Vol. 45, No. 3,2007, pp. 693-711), and demonstrates that a nonlinear energy sink can improve the stability of an aeroelastic system. The nonlinear energy sink was, in this case, attached to the heave (plunge) degree of freedom of a rigid airfoil which was supported in a low-speed wind tunnel by nonlinear springs separately adjustable in heave and pitch. This airfoil was found to exhibit a limit cycle oscillation at flow speeds above the critical ("flutter") speed of 9.5 m/s, easily triggered by an initial heave displacement. After attachment of a single degree of freedom, essentially nonlinear energy sink to the wing, the combined system exhibited improved dynamic response as measured by the reduction or elimination of limit cycle oscillation at flow speeds significantly greater than the wing's critical speed. The design, application, and performance of the nonlinear energy sink are described herein, and the results obtained are compared to analytical predictions. The physics of the interaction of the sink with the wing is examined in detail.

Numerical and experimental validation of a hybrid finite element-statistical energy analysis method

Abstract: The finite element (FE) and statistical energy analysis (SEA) methods have, respectively, high and low frequency limitations and there is therefore a broad class of "mid-frequency" vibro-acoustic problems that are not suited to either FE or SEA. A hybrid method combining FE and SEA was recently presented for predicting the steady-state response of vibro-acoustic systems with uncertain properties. The subsystems with long wavelength behavior are modeled deterministically with FE, while the subsystems with short wavelength behavior are modeled statistically with SEA. The method yields the ensemble average response of the system where the uncertainty is confined in the SEA subsystems. This paper briefly summarizes the theory behind the method and presents a number of detailed numerical and experimental validation examples for structure-borne noise transmission.