bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Control of Chaos in Extended Structures
Authors: Barratt Carl
Published: March 2021

A mechanism is proposed for synchronizing the vibrations of an externally forced array of Duffing oscillators with nearest-neighbor viscoelastic coupling. The parameters of the individual oscillators and the couplings are chosen such that, in the absence of control, the oscillators vibrate chaotically and incoherently. The proposed control scheme brings the elements into synchrony with each other in a few tens of cycles of the external forcing function. It is robust, maintaining the desired state in the presence of noise. It is general in that it works with any form of external forcing. A modification of the mechanism is used to control the forced chaotic vibrations of a single Duffing oscillator allowed to vibrate out of the vertical plane.
Stability of Random Difference Systems
Authors: Lee W. C. , Ma F.
Published: March 2021

A random difference system may arise as a result of spatial discretization of a continuous structure with uncertain material parameters. The purpose of this paper is to present some criteria for the stability of linear and nonlinear random difference systems.
Optimal Paths, Caustics, and Boundary Layer Approximations in Stochastically Perturbed Dynamical Systems
Authors: Maier Robert S. , Stein Daniel L.
Published: March 2021

We study the asymptotic properties of overdamped dynamical systems with one or more point attractors, when they are perturbed by weak noise. In the weak-noise limit, fluctuations to the vicinity of any specified non-attractor point will increasingly tend to follow a well-defined optimal path. We compute precise asymptotics for the frequency of such fluctuations, by integrating a matrix Riccati equation along the optimal path. We also consider noise-induced transitions between domains of attraction, in two-dimensional double well systems. The optimal paths in such systems may focus, creating a caustic. We examine ‘critical’ systems in which a caustic is beginning to form, and show that due to criticality, the mean escape time from one well to the other grows in the weak-noise limit in a non-exponential way. The analysis relies on a Maslov-WKB approximation to the solution of the Smoluchowski equation.
Response of Linear Time-Periodic Systems Subjected to Stochastic Excitations: A Chebyshev Polynomial Approach
Authors: Spires J. M. , Sinha S. C.
Published: March 2021

In many situations engineering systems modeled by a system of linear second order differential equations with periodic damping and stiffness matrices are subjected to stochastic excitations. It has been shown that the fundamental solution matrix for such systems can be efficiently computed using a Chebyshev polynomial series solution technique. Further, it has been shown that the Liapunov-Floquet transformation matrix can be computed, and the original time-periodic system can be put into a time invariant form. In this paper, these techniques are applied in finding the transient mean square response and transient autocorrelation response of periodic systems subjected to stochastic forcing vectors. Two formulations are presented. In the first formulation, the mean square response of the original system is computed directly. In the second formulation, the original system is transformed to a time-invariant form. The autocorrelation response is found by determining the response of the time-invariant system. Both formulations utilize the convolution integral to form an expression for the response. This expression can be evaluated numerically, symbolically, or through Chebyshev polynomial expansion. Results for some time-invariant and periodic systems are included, as illustrative examples.
Nonlinear Friction-Induced Vibration in Water-Lubricated Bearings
Authors: Simpson T. A. , Ibrahim R. A.
Published: March 2021

The problem of friction-induced vibration and squeal in water-lubricated shipboard bearings has received extensive studies during the seventies. These studies were dominated by experimental tests of section models that emulated the actual bearing dynamics. Linear analytical models were analyzed to predict stability boundaries of the equilibrium position. The role of nonlinearity due to the friction-speed curve as well as the time variation of the friction coefficient were not considered. The purpose of the present study is to develop and analyze a nonlinear two-degree-of-freedom model which emulates the dynamics of water-lubricated bearings. Different dynamic characteristics are predicted from the numerical simulation of the equations of motion. A bifurcation diagram is constructed and exhibits different regimes. These regimes include modulated response signals characterized by two frequency responses, on-off intermittent motion representing the incipient of squeal behavior, and limit cycles accompanied with high frequency components. The squeal is revealed by the presence of a high frequency vibration superimposed on the fundamental system frequency. The occurrence of each regime mainly depends on the value of the slope of the friction-speed curve. Other parameters such as natural frequencies, damping ratios, mass ratio and the initial conditions have less influence on the incipient of squeal.
Self-Excited Oscillations in Sliding With a Constant Friction Coefficient
Authors: Adams George G.
Published: March 2021

The sliding of two surfaces with respect to each other involves many interacting phenomena. In this paper a simple model is presented for the dynamic interaction of two dry sliding surfaces. This model consists of a beam on elastic foundation acted upon by a series of moving linear springs, where the springs represent the asperities on one of the surfaces. The coefficient of friction is constant. Although a nominally steady-state solution exists, an analysis of the dynamic problem indicates that the steady solution is dynamically unstable for any finite speed. Eigenvalues with positive real parts give rise to self-excited motion which continues to increase with time. The mechanism responsible for the instability is a result of the interaction of certain complex modes of vibration (which result from the moving springs) with the friction force of the moving springs. It is expected that these vibrations play a role in the behavior of sliding members with dry friction.
Computational and Experimental Prediction of Multi-Disk Brakes Performance at the Design Stage
Authors: Chichinadze A. V. , Kokonin S. S. , Braun E. D. , Chebotarev L. V.
Published: March 2021

Friction and wear coefficients can vary a lot in multi-disk aircraft brakes under the condition of loaded friction regimes. That is why heat loading, friction duration and distance and also service life calculation procedures, based on constant friction and wear coefficients, are not always applicable to such devices. Such a calculation can provide sufficiently valid results only if experimental data are available, obtained by testing friction couples in a full-scale brake on a test bench. The results will be reliable if a full-scale brake structure is similar to a new one, which is under design, the same friction couple is used and brakes operation modes do not differ too much. It is also possible to use the results of friction couples specimens braking tests, in case the test procedure is based on friction and wear modelling theory recommendations.
Vibration Testing at High Loads and Frequencies
Authors: Occhiuto Scott F. , Jaquish David A. , Duleba George S.
Published: March 2021

This paper describes the design and conduct of high load, high frequency vibration tests of axially loaded brake rods used on typical aircraft landing gear. The main test objective was to evaluate damping characteristics of brake rods incorporating internal Coulomb damping. Tests were conducted with static and vibration loads combined at frequencies up to 350 Hz. Loads of 30,000 lb. static and ± 20,000 lb. dynamic were achieved. This combination of high static and dynamic loads at frequencies greater than 200 Hz is believed to never have been achieved before. This paper presents engineers and vibration test laboratories with a proven concept for analyzing and testing the damping and stiffness characteristics of brake rods and other load carrying members at high loads and frequencies.
Low and High-Frequency Vibrations of the Acoustic Range in Break Gears and Chassis of Highway and Flying Vehicles
Authors: Lukanin Valentin N. , Lujnov Yury M. , Derbaremdiker Anatoly D.
Published: March 2021

The report will focus on the interaction of friction-induced vibrations in break gears and oscillations in chassis of highway vehicles (HV) and in break and landing gears of flying vehicles (FV) when landing.

Mathematical modelling of the observed dependencies of low and high-frequency vibration in break gear and chassis units, as well as on vehicle body, and in cargo and passenger compartments is associated with solving incorrect tasks of the mentioned vehicles dynamics under non-stationary excitation.
Progress in the Application of Wavelet Theory to Vibration Analysis
Authors: Newland David E.
Published: March 2021

For vibration signal analysis, the objective is usually to extract frequency data from a signal and study how the signal’s frequency content changes with time. Because wavelets are local functions of time, each with a predetermined frequency content, wavelet analysis provides a good means of doing this. As a result, practical wavelet analysis is growing rapidly. There are many different wavelets to use but no accepted procedure for choosing between them. This paper discusses various alternative wavelets for practical calculations and describes two of the key numerical algorithms. Examples of recent applications using these algorithms are reviewed, including vibration monitoring and detection, transient signal analysis and denoising.
A Harmonic Tracking Technique for Recovery of Gear Motion From Non-Stationary Vibration Signals
Authors: Lerch Christopher A. , Lyon Richard H.
Published: March 2021

A method termed harmonic tracking is developed to recover time dependent gear motion from machine casing vibration. The harmonic tracking method uses short-time spectral generation and a subsequent set of algorithms to locate and track gear meshing frequencies as functions of time. The meshing frequencies are then integrated with respect to time to obtain the rotation of individual gears. More specifically, spectral generation is performed using the discrete Fourier transform, and the locating and tracking algorithms involve locating tones in each short-time spectrum and tracking them through successive spectra to recover gear meshing harmonics. The harmonic tracking method is found to be more robust than demodulation-based methods in the presence of measurement noise and signal distortion from the structural transfer function between gears and the casing.

The harmonic tracking method is tested, both through simulation and experiments involving motor-operated valves (MOV’s) as part of the development of a diagnostic system for MOV’s. In all cases, the harmonic tracking method is found to recover gear motion with sufficient accuracy to perform diagnostics.

The harmonic tracking method should be generally applicable to situations in which a non-invasive technique is required for determining the time-dependent angular speeds and displacements of gearbox input, intermediary, and output shafts.
Wavelet Analysis for Assessment of Localized Spectral Variations in Surface Topographic Data
Authors: Badami Vivek G. , Hefner Susan S. , Smith Stuart T.
Published: March 2021

In this paper, a two dimensional wavelet analysis using Daubechies D14 wavelets has been used to decompose an Atomic Force Microscope image of the surface of a two dimensional calibration grid. Operating the microscope in open loop mode results in image distortions due to nonlinearities of the scanning mechanism which are subsequently reduced under closed loop control. Such distortions in the image are not readily apparent even using Fourier transform techniques and may be overlooked in a routine calibration. Through an appropriate choice of sample length so that the periodicity of the grid is coincident with the bandpass cut-off of the wavelet transform, it is shown in this paper that distortions can be clearly identified in individual levels of the wavelet reconstruction.
A Statistical Index for Monitoring Tooth Cracks in a Gearbox
Authors: Ismail Fathy , Martin Hugh R. , Omar Farag
Published: March 2021

This paper is concerned with detecting and monitoring the growth of a tooth root crack in a gearbox. It uses the reciprocal of the Kurtosis of the beta distribution 1/k for each tooth period, as the damage indicator. A general equation to generate the statistical moments strictly in terms of the α and β parameters of the beta function is developed. To monitor the growth of the crack, a new index, called the “Kurtosis Index”, is formulated from 1/k’s of all the teeth. This index correlates well with the size of the crack, and it shows that small cracks can be detected.
Efficient Structural Acoustic Analysis Using Finite and Infinite Elements
Authors: Allik Henno , Dees Robert N. , Moore Stewart W.
Published: March 2021

The analysis of three-dimensional shell structures submerged in an infinite fluid and subjected to arbitrary loadings is a computationally demanding problem regardless of the analytical technique used. Over the past several years, we have developed a combined finite/infinite element method of solving this class of problems that is more efficient than other available techniques, and have implemented it in a comprehensive set of computer programs called SARA.

This paper presents an overview of our work. In the first part of the paper, we describe our method for solving the fluid-structure interaction equations including infinite element theory, and modeling practices that have evolved for solving cylindrical geometries.

The second part of the paper addresses another aspect of computational efficiency that is available for shells of basically axisymmetric geometry, but containing arbitrary, three-dimensional internal structures. The axisymmetric fluid-loaded shell can be solved as a series of uncoupled two-dimensional problems far more economically than as a full three-dimensional problem. Coupling this solution to three-dimensional parts of the problem can result in significant computational savings. The SARA implementation of the method is described along with sample problems, and a comparison to a SARA-3D solution is provided.
Static Design and Dynamic Analysis of Light Weight Machinery Support Structures
Authors: Remington Paul J. , Allik Henno , Martin Nathan
Published: March 2021

Light weight truss-like structures to support shipboard machinery are currently under consideration for a variety of marine applications by the US Navy. The objective of this study was to develop the structural acoustic design principles for minimizing the transmission of vibration through the truss to the hull of a vessel and thereby reduce radiated sound. A design procedure was developed to select truss member sizes to satisfy specified design criteria, e.g., minimum weight, minimum radius of gyration, etc., while ensuring that the structure will support the design loads. The procedure interacts with the ANSYS finite element computer code to perform structural analysis. The resulting truss configurations were then analyzed to determine their dynamic performance using the SARA family of finite element programs that incorporate a continuum beam element to increase computational efficiency. A number of two dimensional and three dimensional truss configurations have been analyzed. Results will be presented illustrating the influence of a variety of design parameters on the force transmissibility between excitation point and truss support points. In addition the strong influence of local drive point admittance on the force transmissibility will be illustrated.
Stochastic Behavior of Complex Submerged Systems
Authors: Ettouney Mohammed M. , Daddazio Raymond P. , Abboud Najib N.
Published: March 2021

Acoustic performance is an important issue in naval applications. The structural dynamics of internal systems strongly effects the acoustic performance of the entire structure. Due to the complexity of the internal structures, it is difficult to construct numerical models of sufficient fidelity to represent the essential physics of the system. Hence the complexity of internal systems essentially introduces uncertainty into the total structure. This paper develops a stochastic computational technique which can account for the uncertainties of the problem using physically based definitions of the governing statistical properties of the uncertain systems.
External Acoustic Mode Analysis
Authors: O’Regan Stephen D.
Published: March 2021

This paper presents first an acoustic mode theory for continuous surfaces. The necessary step of basis function normalization is made and is then introduced into the discrete theory to make the two theories consistent. Significant reductions in degrees-of-freedom are illustrated using an example of a cylinder with endcaps as the source surface. The analysis shows that the acoustic modes and radiation efficiencies vary with frequency and, notably, field geometry. A procedure is then described for developing acoustic modal filters to construct a cost function for active sound control.
Wave Component Analysis of Fluid-Loaded, Finite Cylindrical Shell Response
Authors: Grosh Karl , Pinsky Peter M.
Published: March 2021

In this paper, the surface displacement response of a finite fluid-loaded shell and the resulting far field acoustic pressure are studied. A high resolution signal processing algorithm is applied to the surface displacement to estimate the constituent wave numbers and corresponding amplitudes for these wave components. This parameter estimation technique identifies the fluid-loaded cylinder’s complex dispersion relations from finite shell data; the dispersion relations consist of subsonic, leaky, evanescent and oscillatory-decaying wave-number loci. The identified results are compared to the analytic dispersion relations. The far field pressure radiated due to each wave-number component is computed allowing for the determination of important contributors to the far field response. For the frequencies studied, the subsonic wave dominates the far field response due to the finite length of the shell and large amplitude of this component. The supersonic components have the next largest contribution to the far field pressure.
Identifying Critical Elastic Scales in Structural-Acoustic Models
Authors: Shepard W. Steve , Cunefare Kenneth A. , Ginsberg Jerry H.
Published: March 2021

The level of detail required for accurate structural acoustic modeling of fluid loaded structures remains an issue of significant debate. Analytical solutions are rarely available, and discrete numerical solutions are typically too complex for ready extraction of physical understanding. In addition, numerical techniques introduce their own explicit scales, through the minimum mesh dimension. However, the wavenumber based formulation of the surface variational principle describes the surface pressure and displacement as a comparatively small set of interacting waves. Coupling the SVP with distributed methods of representing structural attachment features provides a means to introduce, control and investigate features of differing scales. We present here a technique for assessing the critical resolution scales for a fluid loaded two-dimensional plate. For feature attachments, we consider a line-mass elastically suspended by a line-spring from the wetted plate. We then use a spatial expansion for the elastic attachment to the wetted plate. The excitation applied to the plate is taken as a concentrated harmonic force. With the excitation held fixed, the influence of the scale of the feature spatial representation on the radiated power is assessed.
Wideband Spatial Filters for the Active Control of the Radiation of Elastic Shells in an Acoustic Fluid
Authors: Borgiotti Giorgio V. , Jones Kenneth E.
Published: March 2021

It is known that by linearly filtering the outputs of a dense set of accelerometers, sensing the motion of the boundary of an acoustically radiating object, a relatively small set of quantities is obtained, from which the far field (FF) can be identified. Key properties of the spatial filters are: a) the filters are purely combinatorial (i.e. non-dispersive) and, b) the filtering functions are algorithmically identified from the geometry of the radiator boundary and the highest frequency of the disturbance exciting the system. Abating the acoustic radiation does not require to stop the boundary vibration motion, being sufficient instead to actively modify the boundary normal velocity with the objective of nulling, or practically, substantially reducing the outputs of the radiation filters. The shell here considered has rotational symmetry and the disturbance, modeled as a ring force excited by either a single tone or by a broadband process, is also assumed to be axisymmetric. The radiation filter outputs constitute the signals fed back to the multivariate controller that drives a set of uniform ring force actuators. The number of actuators is the minimum possible (or close to it) for the given boundary geometry and the highest frequency of the disturbance. The controller includes a compensating network subtracting electronically the effect of the actuators from the outputs of the sensors. With this scheme the system becomes essentially feedforward, and therefore is inherently stable. The controller and the compensating network are causally implemented via finite impulse response (FIR) matrix filters. The identification of the FIR matrix coefficients of the controller is obtained by minimizing the average residual power which is radiated when the controller is acting. A highly efficient optimization algorithm is established. Several numerical examples for different disturbance configurations show the effectiveness of the approach here presented for radiating noise cancellation. The simulation was performed by using the well known NASHUA computer model for a shell in water.
Acoustics of Layered Poroelastic Obstacles in Poroelastic Hosts
Authors: Lim Raymond
Published: March 2021

A transition matrix for the field scattered by a 3-dimensional, multilayered, poroelastic obstacle embedded in an unbounded poroelastic host is derived. The result is analogous to Peterson and Ström’s (1975) solution for fluid obstacles and Boström’s (1980) extension for elastic obstacles. An exact solution of the vector Biot equations is obtained, obeying all boundary conditions prescribed on all boundaries of the layered obstacle. By numerically implementing the solution for general poroelastic media, scattering with hosts and obstacles made of nonporous materials is also included in this formulation by choosing material parameters in a limiting sense. By incorporating this solution into a recently reported transition-matrix formulation of scattering in a plane-stratified, poroelastic environment, it becomes possible to study the acoustics of obstacles such as shells buried in ocean sediments. Examples are presented to study the acoustics of spheres with porous outer layers and buried spherical shells.
Relation of the Sound Insulating and Reflecting Properties With Noise Dampening Effect of the Construction With Coatings
Authors: Kouzmitchev Michail N.
Published: March 2021

Calculated evaluation of the relation of the sound insulating and reflecting properties taking into account noise damping effect of an external coating put on construction elements in water is presented by the example of a measurement made using “Underwater Measuring Tubes” installation. The expressions permitting to determine first frequency range and the frequency of largest negative effect in dependence on the parameters of a construction and coating and their materials are obtained.
Numerical Investigation of the Problem of a Plane Acoustic Wave Scattering by a Triaxial Ellipsoid
Authors: Abramov Aleksander A. , Konyukhova Nadezhda B. , Levitina Tatyana V.
Published: March 2021

The problem of scalar scattering by a triaxial ellipsoid is considered. A triaxial ellipsoid is the unique essentially three-dimensional object for which the scattering problem may be solved ‘exactly’ via separation of variables. The solution is expressed in terms of ellipsoidal coordinates associated with a given ellipsoid. The expansions in ellipsoidal wave functions are given for a point source field, a plane wave, and diffraction characteristics of a scattering ellipsoid. These expansions were first obtained by Fedoryuk. The resultant formulas have permitted, in particular, numerical investigation of plane acoustic wave scattering by both ideally soft and ideally rigid triaxial ellipsoids. Far field amplitudes have been calculated and plotted for various parameter values. Separation of the variables allows effective parallel implementation.
Materials Issues in Underwater Transducer Systems
Authors: Cross L. Eric
Published: March 2021

In poled piezoelectric ceramic lead zirconate:lead titanate (PZT) compositions, the non zero components of the piezoelectric tensor are d33, d31 = d32, d15 = d24 (Bornstein, 1981). When the positive directions of the three axis in the ceramic is taken as the poling direction and a tensile stress is considered positive, d33 is a positive coefficient and d31 is negative (Jaffe, Cook, Jaffe, 1971). For the very high coupling compositions with zirconia titania ratio close to that of the morphotropic phase boundary between tetragonal an rhombohedral ferroelectric phases (Zr/Ti = 53/48) in the PZT phase diagram there is an unfortunate effect that d33 ∼ 2d31 (Setter and Cola, 1993). Thus in attempting to use monolithic PZT as a hydrostatic pressure wave sensor dh = h33 + 2d31 is unusually small. For all PZTs, the dielectric permittivity ε33 is large (Herbert, 1982) so that the hydrostatic voltage coefficient gh = dh/ε33 is now very small. For many hydrophone applications the product dhgh is often taken as a figure of merit and so monolithic PZT in spite of its very high individual coefficients is useless as a hydrostatic sensor.
Piezoelectric Composite Panels for Underwater Acoustic Control
Authors: Gentilman Richard L. , Bowen Leslie J. , Corsaro Robert D. , Houston Brian H.
Published: March 2021

Large area 1–3 composite piezoelectric transducer panels have been produced by Materials Systems Inc. (MSI). These SonoPanels™ measure 250 × 250 mm and have excellent response as underwater actuators as well as sensors. Piezocomposite panel manufacturing has been facilitated by an injection molding technology for fabricating net-shape lead zirconate titanate (PZT) ceramic preforms.

An array of fifteen 250 × 250 mm 1–3 composite actuator panels, integrated with surface mounted pressure and velocity sensors, has been attached to a steel backing structure. The array has been evaluated for underwater active surface control applications at the Naval Research Laboratory. Sensor-actuator coupling was investigated, with good agreement between calculated and measured performance.
Simultaneous Harmonic and Transient Suppression for Nonlinear Transducers
Authors: Piquette Jean C. , Forsythe S. E.
Published: March 2021

The Navy is constantly developing new materials for use as the active element(s) in high-performance underwater projectors. One such class of materials is the electrostrictive ceramics such as lead magnesium niobate/lead titanate (PMN/PT). These materials are characterized by high strain per unit electric field, high permittivity (ε = 12000), and a low Curie temperature. These ceramics must be used in their unpoled state in contrast to other classes of ceramic, such as lead zirconate titanate (PZT) ceramics that are usually poled before use.

For PMN/PT, the strain as a function of electric field is an almost perfect square-law, s = kE2, over a large range of voltages, neglecting higher-order effects such as hysteresis and saturation. This response suggests that a transducer made of PMN/PT should be driven by superimposing an ac signal upon a large bias voltage. The bias voltage is needed to achieve a large effective strain/volt (d33) in response to the ac signal. If the ac signal amplitude is greater than a few percent of the bias voltage, significant distortion appears in the output due to the material’s nonlinear response (Fig. 1). Further, when this material is incorporated into an electromechanical transducer the transducer’s transient response is a complex combination of the material’s nonlinearity and the poles and zeros of the mechanical system. If the output displacement of the transducer is to be a large fraction of the maximum possible displacement, a method must be found to overcome the effects of nonlinearity and transient response.

The goal of this work is to generate an output signal that is a near-perfect replica of a desired signal (e.g., a sinusoid that is turned on at t = 0) by driving the transducer with an “inverse” signal derived from a nonlinear model of the transducer. The nonlinear model used for a PMN/PT transducer is the Hunt electrostatic model, modified to include both polarization in the PMN material and the effects of radiation loading on the transducer. The model is presented in the form of coupled ordinary (but nonlinear) differential equations. Parameters for the model are estimated by fitting the model to actual data obtained by driving a PMN stack. Results for the parameters and for the goodness-of-fit of the model are presented. The model and its associated parameters for the stack are then effectively inverted by calculating the drive voltage required to produce a given sinusoidal displacement at the face of the transducer. Finally, the transducer is driven by the calculated drive and the resulting waveform is compared with the desired sinusoidal output. Measures of harmonic distortion reduction for a given output amplitude are presented.
A Magnetostrictive Sonar Projector Utilizing a Terfenol Driver
Authors: Dunlap R. A. , Purcell C. J.
Published: March 2021

Defence Research Establishment Atlantic (DREA) is developing a flextensional barrel-stave projector which utilizes a magnetostrictive Terfenol-D driver. Our attention has focussed on three critical aspects of the design of the projector: (1) reduction of eddy currents, (2) incorporation of permanent magnets to bias the Terfenol and (3) a low reluctance magnetic flux return path. Here we describe a projector design which deals with these three aspects. The Terfenol rod is sectioned radially in order to reduce eddy current losses. Co-Sm permanent magnets are used to provide the magnetic bias field to the Terfenol. The magnetic flux return path is comprised of ferrite disks at the ends of the drive rod and a high permeability cylinder constructed of Metglas 2605TCA. The total projector mass is 3.85 kg. In water the resonance occurs at approximately 1.0 kHz and the bandwidth is 310 Hz. At resonance the distortion limited source level was measured to be 197.7 dB re 1μPa@ 1m and the efficiency was 32.3%.
Alternative Concepts for Vibration Test Fixtures Used in Quiet Product Manufacture
Authors: Bowen David L.
Published: March 2021

Test fixtures are widely used in industry for quality control to determine the potential of a product to make excessive noise. Since acceptable parts may be rejected unnecessarily, or noisy parts may be passed if the test is inaccurate, it is desirable to have a reliable test setup, including the test fixture. When the part being tested is a motor and gearbox, and the test measurement is vibration, the vibratory response may vary significantly, depending on exactly how the motor and gear tones line up with the test fixture resonances. This potential for variability has led to vibration test fixtures being designed to be as precise as possible, so that the construction of the test fixture can be repeated from one application to the next. However, such an approach has led to rather stiff and massive designs, with few resonant modes, with the result that the repeatability of the measurements can be affected by rather small variations in motor speed and mounting conditions. A similar situation in acoustics leads to the use of reverberation chambers with rotating diffusers. This paper describes an investigation into the possibility of employing a vibration analog to the reverberant room as a test fixture, in order to make vibration measurements on a production line more reliable. The fixture is a plate, sized to achieve a higher modal density than exists in a typical test fixture. The geometry, edge restraints and interior loads are varied, either through analysis or experiments, to produce a variability of response to be averaged over during the data analysis period. Our conclusion is that the reverberant plate test fixture is able to reduce the variability of vibrational response in comparison to a more standard test fixture.
Structural-Acoustic Design at High Frequency Using the Energy Finite Element Method
Authors: Bernhard Robert J. , Huff John E.
Published: March 2021

Energy flow analysis methods, particularly as implemented using the finite element method, are useful as design techniques for high frequency structural-acoustic applications. In this paper, the derivation of energy flow analysis techniques are summarized. Particular attention is given to the specification of joint models for situations where there is a discontinuity in either geometric properties or material properties. The finite element formulation of this approach is also summarized. A case study is included to illustrate the utility of the method as a design technique.
Reducing the Noise of Pressure Pulp Screen: Theory and Application
Authors: Berry Alain , Oddo Rémy , Panneton Raymond , Nicolas Jean
Published: March 2021

A pressure pulp screen is a machine used in the pulp and paper industry to remove and class cellulose fibres in paper pulp. It involves an inner perforated cylindrical basket which receives the pulp under pressure, an inner rotor with profiled blades used to clear the holes or slits of the basket, and an outer cylindrical shell. The noise radiated by the outer shell is characterized by discrete frequencies in mid- and high frequency (1–4 kHz). A preliminary study has shown that the radiated noise is due to the vibration of the perforated basket under the moving load of the rotor. This vibration is transmitted to the outer shell through various paths which were analyzed and classified. An analytical model of the vibroacoustic behavior of a cylindrical shell under a circumferentially moving load was used to establish various rotating speed regimes with respect to the vibration and sound radiation of the shell. It was shown that a circumferential modulation of the load (corresponding to the effect of holes or slits on the inner basket) leads to theoretical noise spectra similar to measured data. On the practical front, the model was used to identify significant design parameters with respect to the noise of the machine. The paths of energy transmission from the basket to the outer shell were studied and various noise reduction approaches have been investigated.
The Vibroacoustic Behavior of a Rotating Annular Complex Plate With Application to the Design of Circular Saws
Authors: Atalla Noureddine , Côté André , Cournoyer Benoît , Nicolas Jean
Published: March 2021

This paper discusses the vibroacoustic behavior of an annular rotating complex plate with application to the design of circular saws. The effects of rotation and constrained viscoelastic damping are investigated both theoretically and experimentally. On the theoretical front, a model based on the variational approach has been developed. Special attention has been devoted to 1) the effects of rotation on both the vibration and the noise radiated by the annular plate and 2) the optimization of viscoelastic constrained damping. On the experimental front, several set ups have been devised to validate the theoretical models and to test some noise reduction avenues. Examples showing predictions from the theoretical models will be presented together with comparisons to experimental data. Finally, application of the above results to the design of a quieter circular saw will be discussed.
Quieting Plate Modes With Optimally Sized Point Masses: A Volume Velocity Approach
Authors: Wodtke Hans-Walter , Koopmann Gary H.
Published: March 2021

The radiated sound power of the second symmetric mode of a clamped square plate is minimized by attaching optimally sized point masses to the plate. The plate is driven by a point force at its center and the positions of the masses are prescribed. The structural vibration problem is solved using a simple Rayleigh-Ritz approach. Solving the acoustic radiation problem is simplified by making a low-ka-assumption, i.e., the point masses are determined so as to minimize the surface volume velocity of the plate. The predicted results are verified experimentally by means of sound intensity measurements. It is shown that a structural resonance can be deleted from the acoustic response by exploiting volume velocity cancellation. The effects involved are illustrated in detail.
Reducing Noise Emissions of Impact Dot Matrix Printers
Authors: Rückert Carsten
Published: March 2021

To reduce noise emissions of existing impact dot matrix printers, design changes were made and additional devices developed. Their design is described in the paper.
Optimum Design of Vibration Absorbers Using Genetic Algorithm
Authors: Chen Ting-Yu , Lan Jun-Jei
Published: March 2021

The genetic algorithm (GA) is used to design vibration absorbers. The problem is formulated as mixed continuous and discrete variable problem. The continuous design variables include the mass, the spring constant and the damping coefficient of the vibration absorbers. The discrete variables are the installing locations of the absorbers. GA fits in this problem very well. Two examples are given. The near optimum solutions show that when the number of constrained frequency responses is less than or equal to the number of vibration absorbers, the optimum locations of the absorbers are exactly the nodes where the frequency response constraints are imposed. On the other hand, if the number of constrained frequency responses is greater than the number of absorbers, the optimum locations for the absorbers tend to be at the nodes that keep near equal distances to those constrained nodes.
Dynamic Behavior of the Band/Wheel Mechanical System of Industrial Band Saws
Authors: Chung Y. Y. , Sung C. K.
Published: March 2021

This paper presents an analytical and experimental investigation on the dynamic behavior of the band/wheel mechanical system of an industrial metal-cutting band saws. In practice, as a result of the existence of the wheel tilt angle, a pair of roller bearings in which one of them is movable must be employed to twist the saw band perpendicular to the workpiece. Therefore, the saw band is modelled as a finite moving beam span that composes of three consecutive segments, in which the middle segment, that is, the cutting span, and the neighboring two segments may be assumed to be a straight and a twisted beams, respectively. The deformation of the band must satisfy the continuity condition at the connections between segments.

The equations of motion governing the dynamic behavior of the beam span in axial, torsional and transverse directions are derived using mixed variational principle. The axial motion of the beam span couples linearly with its torsional motion. The dynamic responses and the natural frequencies of the beam are computed when parameters vary, such as the transport velocity of the saw band, band tension, wheel tilt angle, and the length of the cutting span. Finally, an experimental study is performed on an industrial band saw for the verification of the mathematical model and the predictive capability proposed in this investigation. Favorable comparisons between the analytical and experimental results are obtained.
Broadband Dynamic Modification Using Feedforward Control
Authors: Alberts Thomas E. , Pota Hemanshu R.
Published: March 2021

This paper presents a general proof of a result due to Fuller and Burdisso, that asserts that system eigenvalues can be modified using feedforward control. The original result applies to the case of steady-state harmonic excitation. This paper extends that work to allow for broadband excitation. The results apply to any flexible structure representable using modal expansion, and are applicable to systems with non-minimum phase zeros. A design procedure is presented to allow arbitrary assignment of the controlled system’s poles, using a fixed feedforward compensator.
Application of Method of Moments to Acoustic Scattering From Fluid Filled Cylinders Using Three Different Formulations
Authors: Sun S. P. , Raju P. K. , Rao S. M.
Published: March 2021

In this work, we present three different formulations Viz. The pressure field integral equation formulation (PFIE), the velocity field integral equation formulation (VFIE), and the combined field integral equation formulation (CEDE) for solving acoustic scattering problems associated with two dimensional fluid-filled bodies of arbitrary cross section. In particular using the boundary conditions on the surface of the body, two equivalent problems, each valid for the outside and inside regions of the scatterer, are derived. By properly selecting the associated equations for these equivalent problems, the three different formulations are derived. The PFIE, VFIE, and CFIE are then solved by approximating the cylindrical cross section by linear segments and employing the method of moments. Further, it is shown that the moment matrices generated by the PFIE and VFIE are ill-conditioned at resonant frequencies of the cylinder, whereas the CFIE generates a well-conditioned matrix at all frequencies. The solution techniques presented in this work are simple, efficient and applicable to truly arbitrary geometries. Numerical results are presented for certain canonical shapes and compared with other available data.
Space-Time hp-Version Finite Elements Applied to Wave Propagation With Moving Loads
Authors: Zhao Bo , Peters David A.
Published: March 2021

The space-time finite element method has emerged as a promising alternative numerical analysis technique for structural dynamics. This paper concentrates on hp-version triangular elements based on a variational statement of elasto-dynamics formed on Hamilton’s law of varying action. As such, forces and momenta are weak; and element boundaries may cut across space and time. This forms a natural framework for problems with both moving load and wave propagation. This paper presents applications of the method to such problems with numerical results and conclusions regarding proper mesh geometry.
Possible Scenarios of Nonlinear Vibrations at High Energies
Authors: Berdichevsky Victor L.
Published: March 2021

The results of numerical simulations of nonlinear string dynamics are considered. Possible extrapolations of these results to nonlinear elastic continua leads to qualitatively different ways of dynamical behavior. They are described and discussed.
Nonlinear Transient Response and its Sensitivity Using Finite Elements in Time
Authors: Kapania Rakesh K. , Park Sungho
Published: March 2021

The bilinear formulation proposed earlier by Peters and Izadpanah to develop finite elements in time to solve undamped linear systems, is extended (and found to be readily amenable) to develop time finite elements to obtain transient responses of both linear and nonlinear, and damped and undamped systems. The formulation is used in the h-, p- and hp-versions. The resulting linear and nonlinear algebraic equations are differentiated to obtain the sensitivity of the transient response with respect to various design parameters. The present developments were tested on a series of linear and nonlinear examples and were found to yield, when compared with results obtained using other methods, excellent results for both the transient response and its sensitivity to system parameters. Mostly, the results were obtained using the Legendre polynomials as basis functions, though, in some cases other orthogonal polynomials namely, the Hermite, the Chebyshev, and integrated Legendre polynomials were also employed (but to no great advantage). A key advantage of the time finite element method, and the one often overlooked in its past applications, is the ease in which the sensitivity of the transient response with respect to various system parameters can be obtained.
Second-Order Systems With Singular Mass Matrix and an Extension of Guyan Reduction
Authors: Bhat Sanjay P. , Bernstein Dennis S.
Published: March 2021

The set of consistent initial conditions for a second-order system with singular mass matrix is obtained. In general, such a system can be decomposed (i.e., partitioned) into three coupled subsystems of which the first is algebraic, the second is a regular system of first-order differential equations, and the third is a regular system of second-order differential equations. Under specialized conditions, these subsystems are decoupled. This result provides an extension of Guyan reduction to include viscous damping.
Coupled Bending-Torsion Vibration of Geared Rotors
Authors: Rao J. S. , Chang J. R. , Shiau T. N.
Published: March 2021

A general finite element model is presented for determining the coupled bending-torsion natural frequencies and mode shapes of geared rotors. Uncoupled bending and torsion frequencies are obtained for examples available in literature and the present program is verified against these. The effect of the gear box is considered to determine the coupled frequencies. Parameters studied include the pressure angle, gear mesh stiffness, and bearing properties. The gear pressure angle is shown to have no effect on the natural frequencies of rotors supported on isotropic bearing supports. Several case studies with bending-torsion coupling are considered and the results obtained are compared with those available in literature. The results of a general rotor system with 8lodes are also presented.
Studies of the Rotor Dynamics of Gas Centrifuges for Fine Particulate Separation
Authors: Al-Ajlouni Musa , Syred Nick
Published: March 2021

A range of techniques have been used to evaluate the performance of an existing design of gas centrifuge for separating sub-micron particles from gas streams. The rotor dynamics of the system are complex, very dependant on the bearing type, design, and layout. The first harmonic typically occurs at low speeds of about 15,000 rpm and can be of sufficient a high amplitude to require special bearing systems.

This paper analyses the performance of an existing unit with a number of tools, including a computer aided package called ROMAX II that carries out a dynamic vibrational analysis of the self acting foil and annular air thrust bearing system. Results are compared with experiment. It is shown that the first harmonic vibrational mode is well predicted. Changes in performance occurring from detail design alterations made to the thrust bearings are also shown to be sensibly predicted.

Finally extrapolations are made to units of 1 metre in length and performance predictions made. It is clearly shown that by an appropriate choice of bearing system the first natural frequency can be raised to well above that required for sensible centrifuge operation.
Finite Element Analysis of an Automotive Turbocharger Turbine Wheel
Authors: Subramani D. A. , Ramamurti V. , Sridhara K.
Published: March 2021

This paper describes the finite element analysis carried out on a typical automotive turbocharger turbine wheel using the concept of cyclic symmetry. The results of this analysis are compared with those obtained using a relatively simple analysis carried out by treating the blade and the hub separately.