bluuebunny/crossref_metadata_2025 huggingface dataset:
The Damping of Structural Vibration by Controlled Interfacial Slip in Joints
Authors: Beards C. F.
Published: December 2011

The most significant source of damping inherent in a structure is that damping which occurs in the structural joints due to interfacial slip. Thus, particular emphasis should be put on controlling and increasing the damping which occurs in these joints if the dynamic response, stress, and noise of a structure are to be reduced. It is shown that an optimum joint clamping force exists for maximum energy dissipation due to slip, and that the resonance frequencies of structures can be controlled to some extent by adjusting the clamping and, hence, the slip, in joints. The application of joint damping to beam-like structures, plates, and frameworks is considered, and its effect on the vibration of these structures discussed.
An Investigation of Dual Mode Phenomena in a Mistuned Bladed Disk
Authors: Stange W. A. , MacBain J. C.
Published: December 2011

This paper presents the results of an investigation addressing the effects of mistuning on the lower modes of vibration of a simple bladed-disk model. The phenomena of dual modes, also known as mode splitting, is studied using holographic interferometry and strain gage measurements under nonrotating and rotating conditions. Resonant amplitudes, mode shapes, and natural frequencies of the disk model were determined, without deliberately mistuning the disk. The tests were then repeated with the disk deliberately mistuned to varying degrees, paying particular attention to the second diameter (2N) dual modes. Additionally, tests were conducted on the disk at a rotational speed of 2000 rpm, in an effort to gain insight as to the vibratory characteristics of the disk under rotating conditions.
Aeroelastic Characteristics of a Cascade of Mistuned Blades in Subsonic and Supersonic Flows
Authors: Kielb R. E. , Kaza K. R. V.
Published: December 2011

An investigation of the effects of mistuning on flutter and forced response of a cascade in subsonic and supersonic flows is presented. The aerodynamic and structural coupling between the bending and torsional motions and the aerodynamic coupling between the blades are included. It is shown that frequency mistuning always has a beneficial effect on flutter. Additionally, the results indicate that frequency mistuning may have either a beneficial or an adverse effect on forced response, depending on the engine order of the excitation and Mach number.
A Parametric Study of Dynamic Response of a Discrete Model of Turbomachinery Bladed Disk
Authors: Muszyn´ska A. , Jones D. I. G.
Published: December 2011

A model consisting of n five-degree-of-freedom subsystems has been developed to characterize some of the mechanical response features of a bladed disk system, including four modes of each blade, n bending modes of the disk, blade-to-blade and blade-to-ground Coulomb friction, structural damping, blade-to-blade mistuning, and various types of excitation. The equations of motion and method of solution are described, and numerical results illustrate some of the interesting effects of various levels of frictional damping on tuned and mistuned systems, which may shed light on some aspects of damped system design and performance.
Seismic Analysis of a Gyroscopic Mechanical System
Authors: Soni A. H. , Srinivasan V.
Published: December 2011

The dynamic analysis of a gyroscopic mechanical system subjected to seismic excitation is presented. The gyroscopic system consists of a rigid rotor mounted on fluid film bearings. The seismic excitation subjects the base to translational as well as rotational motion. The analysis includes gyroscopic effects, Coriolis effects due to base rotation, and the stiffness and damping provided by the fluid film bearings. A numerical example is solved to show the importance of including the base rotation in the analysis.
Eigenanalysis of the Rigid Body Motion Effect on Elastic Systems
Authors: Maher A. , Schlack A. L.
Published: December 2011

In this paper, the influence of rigid body motion on the behavior of a vibrating elastic system is treated by the development of a difference eigenvalue problem. The maximum possible changes in eigenfrequencies due to removal of constraints are obtained by the employment of the bound approach [1, 2]. As an application to a structural system the Rayleigh-Ritz procedure is employed for constructing the difference eigenvalue problem. Discussion of the use of the method for various types of engineering problems is outlined. An example of a free vibration analysis of a simply supported beam in plane motion with a nonuniform mass and elasticity distribution is solved. A comparison between computer calculations and previously published results is presented.
Dynamic Analysis and Optimal Selection of Parameters of a Finite Element Modeled Lathe Spindle Under Random Cutting Forces
Authors: Sharan A. M. , Sankar S. , Sankar T. S.
Published: December 2011

The dynamic analysis of an elastically supported lathe spindle-workpiece system subjected to random cutting forces is presented. The stochastic partial differential equation characterizing the behavior of the system was formulated from the Euler-Bernouli equation. Based on free vibration analysis and experimental verification of the natural frequencies, the hinged boundary condition was considered for the running center. A finite element technique in conjunction with the modal analysis method were used to calculate the mean square displacement of the workpiece. The experimentally calculated power spectral density of the cutting forces was used as the input excitation to the mathematical model. The effect of bearing stiffness and damping, and bearing spacing on the mean square displacement were studied. A direct search optimization technique was carried out to select optimal bearing stiffness and the bearing spacing. Results are presented in the form of plots and tables.
Prediction of Aircraft Interior Noise Using the Statistical Energy Analysis Method
Authors: Miller V. R. , Faulkner L. L.
Published: December 2011

An analytical model is developed to predict the transmission of noise into an airplane interior through the fuselage sidewall by the statistical energy analysis (SEA) method. The fuselage structure is represented as a series of curved, isotropic plates, the isotropic representation resulting from the effects of smearing out the stiffeners. Other complicating effects such as pressurization, acoustic transmission through windows or seal leaks, and aerodynamic excitation are excluded in this effort but could be modeled by these same methods. Evaluation of the model was made using measured full-scale acoustic data from both an adhesively bonded and a mechanically fastened airplane fuselage structure. Reasonable good agreement was obtained between predicted and measured levels in the higher frequencies. Predicted levels were shown to be sensitive to the value chosen for structural loss factor. Comparisons were also made with the measured data with an estimation procedure reported in the literature.
Analysis of the Response of a Multi-Rotor-Bearing System Containing a Transverse Crack in a Rotor
Authors: Mayes I. W. , Davies W. G. R.
Published: December 2011

The paper describes work that has been carried out into the flexural vibrational behavior of a rotor mounted on several bearings and containing a transverse crack. A method of solving the equations of motion of a general system is presented. This method utilizes standard rotor dynamics computer programs and enables calculations on large systems to be made on a routine basis. An approximate method of estimating the reduction of a section diameter required to model a crack for use in beam theory based on finite elements is given which is simple to use and gives acceptable results in practice. The application of the methods to some large turbogenerators is described.
The Vibrational Behavior of a Multi-Shaft, Multi-Bearing System in the Presence of a Propagating Transverse Crack
Authors: Davies W. G. R. , Mayes I. W.
Published: December 2011

The effects of a transverse crack on the dynamics of a multi-rotor, multi-bearing system have been studied experimentally using a spin rig. It is concluded that except for very large cracks, the vibrational behavior is similar to that of a slotted shaft with additional excitation due to the crack opening and closing. It confirms the theory, described elsewhere, that it is possible to calculate the behavior of a cracked and/or slotted rotor for a realistic turbogenerator model for crack depths sufficient to give a measurable vibration vector change. The dynamic stresses in the cracked shaft were also measured. The results show how the dynamic bending moment at the crack tip depends on the speed of rotation of the shaft and the crack depth. The results are compared with a theoretical treatment previously reported and good agreement obtained. It is concluded that for crack depths in excess of one third the way through, the shaft the dynamic bending moment must be used for fracture mechanics calculations.
State-of-the-Art Review: MSA—Mechanical Signature Analysis
Authors: Braun S.
Published: December 2011

Various aspects of MSA are presented, including a classification and application scheme. Described are general principles, common to applications of different character. These include data reduction, processing techniques, as well as the identification of some major existing problems. The MSA papers of this special issue of the Journal are briefly discussed in view of this presentation.
A Comparison of Fourier and Parametric Methods for Structural System Identification
Authors: Davies P. , Hammond J. K.
Published: December 2011

The aim of the paper is to compare Fourier methods and three parametric methods as techniques for the analysis of data acquired from a vibrating structure. The parametric methods include the Prony series, Recursive Least Squares, and Instrumental Variable Analysis. The methods are used to analyze simulated data as well as acceleration and force measurements obtained from a simple vibrating structure. The paper highlights the advantages and disadvantages of each method and shows that in certain circumstances the parametric methods provide useful alternatives to standard Fourier methods. The effect of noise on signal measurements for each method is also addressed, along with the problem of model order selection for the parametric approaches.
Whirl Speeds and Unbalance Response of Multibearing Rotors Using Finite Elements
Authors: O¨zgu¨ven H. Nevzat , O¨zkan Z. Levent
Published: December 2011

This paper presents dynamic modeling of rotor bearing systems with rigid disks, distributed parameter finite rotor elements and flexible, discrete multibearings. The previous works have included the effects of rotary inertia, gyroscopic moment, axial load, internal viscous and hysteretic damping and transverse shear deformations, but have not considered them all in the same model. A computer program is developed in this work to calculate the forward and backward whirl speeds, the corresponding mode shapes, the dynamic unbalance response of multibearing rotor systems and to evaluate rotor stability. It utilizes the banded property of the system matrices to reduce the computational effort for the complex eigensolution. A combined bisection and inverse iteration technique is used for the complex eigen-value problem. The combined effect of shear deformations and internal damping on the stability, forward and backward whirl speeds, as well as on the response to unbalance excitation, are investigated with the numerical examples given. This study confirms that any inherent material damping in the shaft itself does not affect the unbalance response if the bearings are isotropic, which is, however, not the case when the bearings are orthotropic causing elliptical synchronous whirl orbits.
Spectral Correlation Techniques Applied to Evaluate Noise and Safety Tradeoffs in Tire/Pavement Interaction
Authors: Clapp T. G. , Eberhardt A. C.
Published: December 2011

Relationships between pavement surface geometry, truck tire sound, and skid number are investigated to provide an understanding of the tire/pavement interaction mechanism. Correlation techniques are used to determine the relationship between each pair of the three parameters. Results show 1) the relationship between pavement profile and truck tire sound as a function of frequency, 2) a positive relationship between pavement profile spectral amplitudes, and pavement skid number, and 3) no significant relationship existing between truck tire sound and skid number.
TRAXION: A Model for Predicting Dynamic Track Loads in Military Vehicles
Authors: Galaitsis A. G.
Published: December 2011

This paper outlines a method that can be used to predict the dynamic track loads and suspension loads that occur in high-speed track vehicles. The presentation includes a description of the mechanical model that was synthesized and a comparison of the predicted and measured dynamic track loads on an M113 armored personnel carrier. It concludes with a discussion of other possible applications.
Improved Off-Road Tractor Ride via Passive Cab and Seat Suspensions
Authors: Rakheja S. , Sankar S.
Published: December 2011

Low frequency terrain-induced vibrations transmitted to off-road vehicle operators are quite severe and exceed ISO specified “fatigue-decreased-proficiency” (FDP) limits. Ride improvement of an agricultural tractor is investigated via passive suspensions at the seat and/or cab for their relatively simpler adaptability to an existing tractor construction. The investigation has been carried out in three phases, namely: seat suspension incorporating bounce, longitudinal, lateral, roll, and pitch modes on a rigidly mounted cab; cab suspension with a rigidly mounted seat; seat suspension in bounce, bounce-lateral, and bounce-roll, mounted on a suspended cab. Optimum suspension parameters in each phase of study are selected to maintain all translational acceleration PSDs at the operator’s location within 4 hours’ exposure-FDP limits, and to minimize roll and pitch acceleration PSD response. The relative displacement in each case is constrained to a selected minimum. Ride improvement achieved during each phase of investigation is compared to ISO-FDP acceleration PSD limits, and conclusions are drawn. Contribution of factors such as seat-location and cab-geometry to ride improvement is also presented.
Estimation of the Wavevector-Frequency Spectrum of Turbulent Boundary Layer Wall Pressure by Multiple Linear Regression
Authors: Hwang Y. F. , Geib F. E.
Published: December 2011

This paper examines the wavevector-frequency spectrum of the turbulent boundary layer wall pressure in the incompressive, inviscid domain in the intermediate and high frequencies range, i.e, ωδ*/U∞ >> 0.5. It is shown that the wavevector-frequency spectrum can be normalized by a factor so that it becomes simply a function of nondimensional Strouhal wavenumber Uck1/ω and Uck3/ω, where Uc is the convective flow velocity, and k1 and k3 are the wavenumbers in the plane of the wall along the streamwise and the crossflow directions, respectively. The normalization factor is the point pressure frequency spectrum times (Uc/ω)2. It follows that the normalized wavevector-frequency spectrum can be scaled with respect to the Strouhal wavenumbers Uck1/ω and Uck3/ω. The rationale of using a linear regression model for estimating the normalized wavevector-frequency spectrum with a set of measured response data from a wavevector filter is presented. The contention is that the actual spectrum can be obtained by the multiplication of a trial spectrum with a correction spectrum. The correction spectrum is approximated by a polynomial in Uck1/ω with a set of coefficients to be determined. The multiple linear regression model relates the response of a measuring system to these coefficients which are determined by least square minimization of a set of measured response data. The advantages of the regression approach are that it relaxes the requirements of the wavevector filter’s ability to discriminate against the spectral elements outside the wavenumber bandwidth of the filter, and this approach is capable of better estimating the entire wavevector spectrum as compared to the existing methods which are limited to measurements of the low-wavenumber spectra. Some preliminary numerical results are presented.
Excitation of Plates and Hydrofoils by Trailing Edge Flows
Authors: Blake W. K.
Published: December 2011

The flow-induced vibration of lifting surfaces is discussed from the perspective of the properties of the various flow regimes that exist on the surfaces. Depending on the Reynolds number and the geometry of the foil, the flow excitation may be tonal (generated by periodic vortex shedding) or random (generated by turbulent flow on the surface). Conditions will be cited for the existence of vortex shedding excitation, and relationships will be given for estimating the levels of flow-induced vibration to be expected from each flow source. The governing parameters for feedback between vibration and vortex shedding, which are necessary to produce singing, are quantified through measurements of surface pressures generated by wakes which are forced with oscillating trailing edges. Criteria will be given for estimating the upper bound of singing vibration amplitudes of hydrofoils and merchant marine propellers as a function of structural parameters.
Wave Models of Turbulent Flow Over Compliant Surfaces
Authors: Ffowcs-Williams J. E.
Published: December 2011

The mechanics by which sound evolves from unsteady boundaries and flow can be represented in acoustic analogies which provide a formal structure for analyzing the process of sound creation. The acoustic analogy of Lighthill has been the firmest foundation for modeling the jet noise problem. Studies of that problem have gradually increased in sophistication and scope to a point where the analogy itself has been developed to display characteristics that are novel and a little startling. The early models regarded turbulence as prescribed and concentrated purely on the acoustical consequences of that turbulence. But the more advanced analogies recognize definite constraints on acoustically important elements of turbulence and point to the susceptibility of the noise generating elements of turbulence to external stimulus. Other long waves induced by turbulence can be similarly analyzed and correspondingly interesting deductions made on vibrational fields induced by turbulent flow. This paper will describe some of the developments leading to notions that turbulence can be influenced by well-chosen external stimuli and speculate a little on areas where these effects might have significant practical applications.
Finite Element-Integral Acoustic Simulation of JT15D Turbofan Engine
Authors: Baumeister K. J. , Horowitz S. J.
Published: December 2011

An iterative finite element-integral technique is used to predict the sound field radiated from the JT15D turbofan inlet. The sound field is divided into two regions: the sound field within and near the inlet which is computed using the finite element method, and the radiation field beyond the inlet which is calculated using an integral solution technique. The velocity potential formulation of the acoustic wave equation was employed in the program. For some single mode JT15D data, the theory and experiment are in good agreement for the far field radiation pattern as well as suppressor attenuation. Also, the computer program is used to simulate flight effects that cannot be performed on a ground static test stand.
Aerodynamic Far Field Noise in Idling Circular Sawblades
Authors: Mote C. D. , Zhu Wen Hua
Published: December 2011

The acoustic pressure radiated to the far field from dipole sources at the rim of a rotating circular sawblade is investigated theoretically and experimentally. Scattering from the sawblade surfaces and the presence of dipole source components in both the normal and radial coordinate directions explain the observed directivity and the dependence of the sound pressure upon sawblade rim velocity.
The Condition Monitoring of Rolling Element Bearings Using Vibration Analysis
Authors: Mathew J. , Alfredson R. J.
Published: December 2011

A brief review on techniques of machine condition monitoring is presented followed by a description and results of a study involving the monitoring of vibration signatures of several rolling element bearings with a view to detecting incipient failure. The vibration data were analyzed and several parameters were assessed with regard to their effectiveness in the detection of bearing condition. It was found that all the parameters were of some value depending on the type of bearing failure encountered. Generally, frequency domain parameters were more consistent in the detection of damage than time domain parameters. However, sufficient evidence is produced to show that it would be unreliable to depend exclusively on any one technique to detect bearing damage.
Reliability Estimates Through Statistics of Random Response Excursions
Authors: Sankar T. S. , Xistris G. D.
Published: December 2011

In the direct methods for evaluating reliability of industrial machinery, performance indicators are ascertained from statistical analyses of the randomly fluctuating response variable using pre-established threshold levels of acceptable performance. The accuracy of the results depends directly on the rigor of the probabilistic procedure employed. In this paper, a new approach for calculating the probability measures of the randomly enveloped areas of the response excursions about any given threshold level is presented. The area excursions contain important information on both the time durations of the excursions as well as their intensity levels above the critical value and thus give a direct reliability estimate of the system performance. The mathematical development of the method, derivation of reliability indices, sample calculations, and life estimates are included.
Lateral Vibration Analysis of Large Vertical Motor Installations
Authors: Raghavan K. S.
Published: December 2011

The paper deals with analysis of lateral vibration behavior of vertical motor installations. The studies are based on the finite element method. Based on the results obtained with three-dimensional idealization of the stator frame, a simpler two-dimensional model is developed. The latter predicts accurately the first lateral mode. In order to study the nature of rotor-stator interactions, coupled models are also analyzed. The studies reveal that, depending on the relative dynamic characteristics of the rotor and the stator, there can be strong interactions that influence the frequencies considerably.
Random Vibrations of Elastic Beams and Circular Plates Resting on Viscoelastic Foundations
Authors: Lin Y. J.
Published: December 2011

Analytical and numerical results are reported for the dynamic responses of elastic beams and circular plates resting on viscoelastic foundations and excited by stationary, wide-band random forces. Each viscoelastic foundation is treated as a series of an infinite number of many spring-dashpot systems. Three different types of linear viscoelastic models, namely, the Kelvin-Voigt, Maxwell, and Linear Standard Solid, are considered. Numerical results are presented for free-edged elastic beams and circular plates.
Vibratory Feeding by Nonsinusoidal Vibration—Optimum Wave Form
Authors: Okabe S. , Kamiya Y. , Tsujikado K. , Yokoyama Y.
Published: December 2011

This paper presents the conveying velocity on a vibratory conveyor whose track is vibrated by nonsinusoidal vibration. The velocity wave form of the vibrating track is approximated by six straight lines, and five distortion factors of the wave form are defined. Considering the modes of motion of the particle, the mean conveying velocity is calculated for various conditions. Referring to these results, the optimum wave form is clarified analytically. The theoretical results show that the mean conveying velocity is considerably larger than that of ordinary feeders if the proper conveying conditions are chosen. The theoretical results are confirmed by experimental results.
Computation of Far-Field Sound Generation in a Fluid-Structure Interaction Problem
Authors: Conlisk A. T.
Published: December 2011

The problem of generation of sound in moving media has become an important problem in recent years. Accordingly, in this paper we examine the inviscid flow past a bump on a plane wall in which vorticity disturbances initially placed upstream convect downstream and interact with the bump. The physical situation of interest is that of a flow in which vortices are formed far upstream and then impinge on a surface protrusion. The bump in the wall is assumed to be cylindrical in shape and mounted on a mechanical spring. It may undergo nonlinear transverse oscillations as a result of the unsteady loading caused by the vortices. The flow field and the structure are then fully coupled and solutions for the vortex paths and consequent structure position must be obtained interactively and numerically at each time step. The relevant acoustic variables such as pressure, and potential may then be obtained in the limit as the Mach number M → 0 by asymptotic methods for any number of vortices. An acoustic point dipole is generated by impingement of an isolated vortex on the structure but a much more complicated behavior of the acoustic pressure is generated for more complex vortex arrays. Results for a single vortex and two vortices are presented.
A New Look at Sound Generation by Blade/Vortex Interaction
Authors: Hardin J. C. , Mason J. P.
Published: December 2011

As a preliminary attempt to understand the dynamics of blade/vortex interaction, the two-dimensional problem of a rectilinear vortex filament interacting with a Joukowski airfoil is analyzed in both the lifting and nonlifting cases. The vortex velocity components could be obtained analytically and integrated to determine the vortex trajectory. With this information, the aeroacoustic low-frequency Green’s function approach could then be employed to calculate the sound produced during the encounter. The results indicate that the vortex path deviates considerably from simple convection due to the presence of the airfoil and that a reasonably sharp sound pulse is radiated during the interaction whose fundamental frequency is critically dependent upon whether the vortex passes above or below the airfoil. Determination of this gross parameter of the interaction is shown to be highly nonlinearly dependent upon airfoil circulation, vortex circulation, and initial position.
Design of Belt-Tensioner Systems for Dynamic Stability
Authors: Ulsoy A. G. , Whitesell J. E. , Hooven M. D.
Published: December 2011

Belt drive systems are an effective means for power transmission which offer the advantages of light weight, low cost, quietness, and efficiency. Recently in automotive applications there has been a trend to power several accessories with a single drive belt in order to reduce overall vehicle size and weight. Since these belts are typically longer than conventional belts, a tensioner component is added to maintain acceptable belt tension levels. In this paper we describe several potential instability mechanisms for belt-tensioner systems, and present a design methodology to ensure good dynamic performance of such systems. A mathematical model of the belt-tensioner system, and numerical solution methods, are utilized to develop a computer-aided design procedure. Numerical results, and confirming experimental data, are presented for a particular automotive belt-tensioner system.
Free Vibration of Polar-Orthotropic Sector Plates Resting on Point Supports
Authors: Narita Y.
Published: December 2011

An accurate Ritz solution for the free vibration of point-supported annular sector plates of polar orthotropy is presented. A double power series function is used to represent deflection of the plate, with Lagrange multipliers to impose the constraint conditions. To establish accuracy of the approach, the frequency parameters of a sector plate with some supporting points distributed along the boundary are compared to those of a uniformly simply supported plate. The natural frequencies and mode shapes are presented for wide ranges of the opening angle, radius ratio, and orthotropic parameters.
Exact Analysis of an Oscillator Hitting a Stop
Authors: Bapat C. N. , Sankar S.
Published: December 2011

An exact analysis of a harmonically excited oscillator contacting a springy stop is performed on a digital computer. The agreement between the present theoretical and simulation results and the previous results using the iterative approach is very good. The effects of amplitude and frequency of excitation, damping, stiffness, and gap on the duration of contact, extreme values of displacement and the ratio of velocity of an oscillator as it leaves the stop and enters it are studied.
Minimizing Residual Vibration for Point-to-Point Motion
Authors: Meckl P. H. , Seering W. P.
Published: December 2011

This paper describes an appropriately shaped forcing function for moving a dynamic system over an incremental distance with minimum residual vibration. The function is constructed by combining harmonics of a “ramped sinusoid” function so that minimum energy is introduced to the system at its resonant frequencies. A test fixture to evaluate this approach is described and experimental results are given. Residual vibration amplitudes for the ramped sinusoid function are compared with those for a square wave input and a bang-bang function. In practice, the ramped sinusoid achieves nearly an order-of-magnitude reduction in residual vibration amplitude as compared to the square wave forcing function.
Time Domain Parameter Identification Methods for Linear Modal Analysis: A Unifying Approach
Authors: Leuridan J. M. , Brown D. L. , Allemang R. J.
Published: December 2011

The paper describes a method that uses a multivariate model in the form of a nonhomogeneous finite difference equation to identify modal parameters of a mechanical structure. The modal parameters of this equation are estimable using a model that involves multiple input, multiple output vibration data. Thus, improved global estimates of modal parameters can be obtained, including the identification of highly coupled and pseudo-repeated modes of vibration. When the data are in the form of impulse or free decay responses, then the parameters of the homogeneous part of the equation can be estimated separately, and the method is then related to the Least Squares Complex Exponential method, the Polyreference Time Domain method and the Ibrahim Time Domain method.
The Forced Response of Shrouded Fan Stages
Authors: Menq C.-H. , Griffin J. H. , Bielak J.
Published: December 2011

This paper presents a general approach for modeling shrouded blade vibration that takes into consideration the nonlinear friction constraint at the shroud interface. In this approach, linear structures are characterized by receptances and shroud constraints by nonlinear impedances. The proposed methodology is presented in detail for simplified models of the bladed disk and shroud interface. The corresponding governing equations for the dynamic response are derived for both tuned and mistuned stages. As an example the method is applied to an idealized tuned stage. Two cases are considered, a lubricated shroud for which the coefficient of friction is equal to zero, and a frictionally constrained shroud. The effect of varying the shroud-to-shroud preload is studied. In the lubricated case nonlinear behavior is seen when vibrations are strong enough to result in separation of the shroud interfaces. In the case of finite friction there is a profound change in resonant frequencies when the preload is increased sufficiently to prevent gross slip at the shrouds.
Control Effects of Damped Sandwich Beam on Random Vibration
Authors: Xi Dechang , Chen Qinghua , Cai Guoqiang
Published: December 2011

This paper investigates the control effects of sandwich beam to random excitation. The statistical properties of the transverse displacement and stress are analyzed. The control effects of the damping layer (including the viscoelastic layer and the constraining layer) on random transverse displacement and random stress are investigated. The results for a sandwich beam are compared with those for the original beam. Finally, examples are given to illustrate the method.
Characteristics of the Diametral Resonant Response of a Shrouded Fan Under a Prescribed Distortion
Authors: Jay R. L. , Burns D. W.
Published: December 2011

A comprehensive controlled study of the resonant vibratory structural response of a shrouded fan blade/disk due to known excitation was performed. A full circumferential definition of the inlet velocity field was obtained at five radial locations for three axial spacings and for four unique patterns of distortion and three mass flow rates. Harmonic analyses of the velocity patterns were used to establish a gust perturbation velocity normal to the blade chord. From these spanwise perturbation velocities, a normalized force parameter was established. In-vacuum, nonrotating testing of the fan assembly allowed identification of individual blade frequencies and system modes. This testing used strain gaging and holography to identify mistuning, damping and split factors for diametral patterns of the 3, 4, 5, and 6 diametral mode families. Dynamic strain signatures from rotating rig resonant responses were obtained for inlet flows having 3, 4, 5, and 6 distorted regions to simulate inlet struts. Groups of 1/4-in. rods were used to create these regions of distorted flow. System mode responses to these distortion patterns included occurrences of standing and traveling waves. Trends of gust perturbation force parameter and measured dynamic stress with varying axial gap, mass flow, and loading were established. The data collectively quantify the strong cause and effect relationship between force parameter and measured dynamic stress.
Vibration and Buckling of Rotating, Pretwisted, Preconed Beams Including Coriolis Effects
Authors: Subrahmanyam K. B. , Kaza K. R. V.
Published: December 2011

The effects of pretwist, precone, setting angle and Coriolis forces on the vibration and buckling behavior of rotating, torsionally rigid, cantilevered beams are studied in this investigation. The beam is considered to be clamped on the axis of rotation in one case, and off the axis of rotation in the other. Two methods are employed for the solution of the vibration problem: one based upon a finite-difference approach using second-order central differences for solution of the equations of motion, and the other based upon the minimum of the total potential energy functional with a Ritz type of solution procedure making use of complex forms of shape functions for the dependent variables. Numerical results obtained by using these methods are compared to those existing in the literature for specialized simple cases. Results indicating the individual and collective effects of pretwist, precone, setting angle, thickness ratio, and Coriolis forces on the natural frequencies and the buckling boundaries are presented and discussed. Furthermore, it is shown that the inclusion of Coriolis effects is necessary for blades of moderate-to-large thickness ratios while these effects are not so important for small thickness ratio blades. Finally, the results show the possibility of buckling due to centrifugal softening terms for large values of precone and rotation.
Linear Dynamic Coupling in Geared Rotor Systems
Authors: David J. W. , Mitchell L. D.
Published: December 2011

The ability to analyze accurately the torsional-axial-lateral coupled response of geared systems is the key to the prediction of dynamic gear forces, shaft moments and torques, dynamic reaction forces, and moments at all bearing points. These predictions can, in turn, be used to estimate gear-tooth lives, shaft lives, housing vibrational response, and noise generation. Typical applications would be the design and analysis of gear drives in heavy-lift helicopters, industrial speed reducers, Naval propulsion systems, and heavy, off-road equipment. In this paper, the importance of certain linear dynamic coupling terms on the predicted response of geared rotor systems is addressed. The coupling terms investigated are associated with those components of a geared system that can be modeled as rigid disks. First, the coupled, nonlinear equations of motion for a disk attached to a rotating shaft are presented. The conventional argument for ignoring these dynamic coupling terms is presented and the error in this argument is revealed. It is shown that in a geared system containing gears with more than about 50 teeth, the magnitude of some of the dynamic-coupling terms is potentially as large as the magnitude of the linear terms that are included in most rotor analyses. In addition, it is shown that the dynamic coupling terms produce the multi-frequency responses seen in geared systems. To quantitatively determine the effects of the linear dynamic-coupling terms on the predicted response of geared rotor systems, a trial problem is formulated in which these effects are included. The results of this trial problem shows that the inclusion of the linear dynamic-coupling terms changed the predicted response up to eight orders of magnitude, depending on the response frequency. In addition, these terms are shown to produce sideband responses greater than the unbalanced response of the system.
Statistical Analysis of Fatigue Failure Due to Flow Noise Excitations
Authors: Fenech H. , Rao A. K.
Published: December 2011

The power spectrum of the stress induced by a narrow-band (vortex shedding) and broad-band (impingement, near field) flow noise on a simply supported square plate is used to determine the fatigue failure probability of that plate. A lognormal distribution of the material properties and a Rayleigh distribution of the stress peaks are implied in the statistical model. The Poisson failure rate and reliability are computed for several crack propagation factors and statistical distributions of the initial strength of materials. The plate fatigue lifetime obtained by statistical analysis is generally shorter than the one given by a deterministic Palmgren-Miner cumulative model for narrowband and broad-band excitations. The two models predict similar fatigue lifetime for cases corresponding to small initial material cracks or low rates of crack propagation.
A Design Guide Proposal for Avoidance of Acoustic Resonances in In-Line Heat Exchangers
Authors: Fitzpatrick J. A.
Published: December 2011

A variety of methods for the prediction of acoustic resonances in heat exchangers are recommended in the literature. There is currently no clear guideline available to designers for the avoidance of these resonances. This paper compares some of the latest developments in this field, proposes a new procedure for design and outlines a specific example of the procedure.
Dynamics of Coupled Fluid-Shells
Authors: Au-Yang M. K.
Published: December 2011

The hydrodynamic mass approach to the solution of dynamic problems in coupled fluid-cylindrical shells is reviewed; simplified equations for computing the hydrodynamic masses and for the subsequent solution of the eigenvalue problem are given in several commonly encountered special cases. Methods of incorporating the hydrodynamic mass concept into finite element structural analysis computer programs for the more general cases are discussed.
Stepping Motored System Dynamics
Authors: Kojima Masakazu , Niimura Yoshihisa
Published: December 2011

Stepping motors have several advantages over other motor systems, especially in the field of digital control system; however, they also have a disadvantage in that the vibrational exciting source exists within their driving principle. This study deals with this vibrational problem of stepping motored machine system in consideration of the interaction between mechanical and electrical parts of the system. In this report one basic mathematical modeling, i.e., Spanworm equation, is proposed for analysis and applied to some practical examples. The calculational results agree well with measured results. Consequently, to install the stepping motors in a machine system, the usefulness of Spanworm equation is endorsed.
Application of Viscoelastic Material for a Dynamic Damper
Authors: Kim K. J. , Yeo T. I.
Published: December 2011

An optimization procedure in the design of a viscoelastic dynamic damper is proposed for a single-degree-of-freedom primary system with the effects of prestrain taken into account. The performance is compared with that by a conventional spring-dashpot-mass damper. Applicability of the proposed procedure to a resonance-frequency-varying system is also shown.
Equivalent Linearization of a Squeeze Film Damper
Authors: Chen Songqi , Liu Shengpei
Published: December 2011

In this paper, the equivalent linearization of an intershaft squeeze film damper in a two shaft engine system is investigated. The two shaft centers at the damper position are assumed to move in different elliptical offset orbits and at synchronous frequency with the unbalanced rotor (e.g., the high pressure rotor). The nonlinear damper force is resolved into two orthogonal components along the absolute coordinate directions and, in turn, each of these force components is supposed to be equivalent to the sum of an average force, a linear spring force, and a linear damping force in the corresponding direction. By using the method of equivalent linearization by harmonic balance, the six parameters of the equivalent forces, including two average forces, two equivalent spring coefficients, and two equivalent damping coefficients, are expressed analytically by the squeeze film forces and the assumed orbital motion of the two shaft centers at the damper position. The analytical expressions of the squeeze film forces are derived from an approximate solution of the basic Reynolds equation. The results obtained are verified by the method of equivalent linearization by minimum mean square errors. It shows that the six obtained parameters make the mean square errors minimum over a cycle period of motion, the errors being the difference between the equivalent forces and the actual nonlinear forces.
Application of the Boundary Element Method to Acoustic Cavity Response and Muffler Analysis
Authors: Seybert A. F. , Cheng C. Y. R.
Published: December 2011

This paper is concerned with the application of the Boundary Element Method (BEM) to interior acoustics problems governed by the reduced wave (Helmholtz) differential equation. The development of an integral equation valid at the boundary of the interior region follows a similar formulation for exterior problems, except for interior problems the Sommerfeld radiation condition is not invoked. The boundary integral equation for interior problems does not suffer from the nonuniqueness difficulty associated with the boundary integral equation formulation for exterior problems. The boundary integral equation, once obtained, is solved for a specific geometry using quadratic isoparametric surface elements. A simplification for axisymmetric cavities and boundary conditions permits the solution to be obtained using line elements on the generator of the cavity. The present formulation includes the case where a node may be placed at a position on the boundary where there is not a unique tangent plane (e.g., at an edge or a corner point). The BEM capability is demonstrated for two types of classical interior axisymmetric problems: the acoustic response of a cavity and the transmission loss of a muffler. For the cavity response comparison data are provided by an analytical solution. For the muffler problem the BEM solution is compared to data obtained by a finite element method analysis.
Critical Speeds of Turbomachinery: Computer Predictions vs. Experimental Measurements—Part I: The Rotor Mass—Elastic Model
Authors: Vance J. M. , Murphy B. T. , Tripp H. A.
Published: December 2011

This is the first part (Part I) of two papers describing results of a research program directed at verifying computer programs used to calculate critical speeds of turbomachinery. This research program was undertaken since questions existed about the accuracy of calculations for the second and higher critical speeds. Part I describes improvements in computer programs and data modeling that resulted from comparing measured and calculated “free-free” natural frequencies of several shafts and rotors. Program modifications to improve accuracy include consideration of the effect of disk/shaft attachment stiffness, revised treatment of the end masses, and an improved convergence. Modifications resulting from the study are applicable to many other damped and undamped critical speed computer programs.
Prediction of Acoustical Behavior in Cavities Using an Indirect Boundary Element Method
Authors: Kipp C. R. , Bernhard R. J.
Published: December 2011

An indirect boundary element method is developed to predict sound fields in acoustical cavities. An isoparametric quadratic boundary element is utilized. The formulations of pressure, velocity and/or impedance boundary conditions are developed and incorporated into the method. The capability to include acoustic point sources within the cavity is also implemented. The method is applied to the prediction of sound fields in spherical and rectangular cavities. All three boundary condition types are verified. Cases having a point source within the cavity domain are also studied. Numerically determined cavity pressure distributions and responses are presented. The numerical results correlate well with available analytical results.
The Effects of Modal Coupling on the Acoustic Power Radiation From Panels
Authors: Keltie R. F. , Peng H.
Published: December 2011

The effects of modal coupling on the acoustic power radiated from line forced panels of unit width with s-s (simply supported-simply supported) and c-c (clamped-clamped) end conditions have been studied. The expressions for the power radiated by the total square terms and by the coupling terms in these two one-dimensional problems were derived using Heckl’s power integral. A qualitative and quantitative discussion regarding the properties of Pmn (the power radiation coefficient of the m- and nth modes) and Dmn (the wavenumber cross-spectrum of modal velocities) for the s-s panel are presented. Numerical calculations (for both s-s and c-c cases) were carried out to investigate the relative importance of the modal coupling in the acoustic radiation. The results show that if the panel is under resonant excitation or if the driving force is at high frequency, then the effects due to modal coupling are negligible. At low frequency, however, or if the panel is under off-resonant excitation, then the contributions due to the modal coupling may be important.
Estimation of the Surface Roughness on the Race or Balls of Ball Bearings by Vibration Analysis
Authors: Kanai H. , Abe M. , Kido K.
Published: December 2011

This paper describes a vibration-based diagnostic method by estimating the surface roughness on the rotating ring or balls in ball bearings. The surface roughness has been measured by a stylus that directly traverses the surface of the ring or balls obtained by taking apart the ball bearing. We developed a new method to estimate accurately the surface roughness by analyzing the short-length vibration signal that is excited when balls encounter flaws on the rotating ring or when races encounter flaws on the balls in a ball bearing. Our experimental results confirm that the roughness estimated by the proposed method agrees with that measured directly by using a stylus even in the case of crack μm wide. We applied this new method to the diagnosis of surface roughness in small-sized ball bearings and inferior samples were detected with a 95.3 percent accuracy rate.