bluuebunny/crossref_metadata_2025 huggingface dataset:
Nonlinear Modes in Systems With Strong Nonlinearities
Authors: King Melvin E.
Published: February 2021

In this paper, a symbolic/numeric method is developed to compute nonlinear normal modes (NNMs) in conservative, two-degree-of-freedom (2-DoF) systems. Based upon the notion of NNMs, periodic motions are sought during which the two coordinates ‘vibrate-in-unison’. By parameterizing the response of one coordinate with respect to the response of the other (reference) coordinate and by imposing conservation of energy, we obtain a nonlinear, singular ordinary differential equation. Approximate solutions for these modal functions are obtained, for a given energy level, via truncated power-series expansions. The coefficients of the expansion, along with the maximum and minimum reference displacements, are then computed by (i) symbolically evaluating the singular differential equation at various (distinct) reference displacements, and then (ii) numerically solving the resulting set of nonlinear algebraic equations. Since the approximate solution inherently depends upon the order of the expansion, convergence studies must be performed in order to ensure sufficient accuracy. Note that even though the formulation presented herein is based on 2-DoF systems, the methodology is quite general and can readily be extended to higher-order discrete systems. Moreover, since it does not rely upon any ‘small-quantity’ assumptions, it can be used to investigate the dynamics of coupled, strongly nonlinear systems.
On Residual Vibration Control of Time-Varying Redundant Open-Chain Linkage With Joint and Link Flexibility
Authors: Shigang Yue
Published: February 2021

Residual vibration control of time-varying redundant open-chain linkage with link and joint flexibility is studied in this paper. The control equations of the flexible open-chain linkage is time-varying. Computer simulation of a planar flexible open-chain linkage with only one degree of redundancy shows that the residual vibration is decreased effectively, thus the endpoint is almost stabel at the fixed point though compensation is not considered.
Dynamics of Two Coupled Van der Pol Oscillators With Delay Coupling
Authors: Wirkus Stephen , Rand Richard
Published: February 2021

We investigate the dynamics of a system of two van der Pol oscillators with delayed velocity coupling. We use the method of averaging to reduce the problem to the study of a slow-flow in three dimensions. In particular we study the stability of the in-phase and out-of-phase modes, and the bifurcations associated with changes in their stability. Our interest in this system is due to its relevance to coupled laser oscillators.
A Comparison of Analytical Methods for Studying a Single-DOF Nonlinear System
Authors: Guttalu Ramesh S. , Flashner Henryk
Published: February 2021

Qualitative analysis of periodic nonlinear dynamical systems is often carried out using perturbation and averaging methods. Important topics of study for this class of systems are determination of periodic solutions, their stability analysis and their bifurcation characteristics. Since perturbation and averaging methods rely on expanding the solution in terms of a small parameter, important questions such as convergence and accuracy of the solution arise which are often difficult to answer. This paper presents a preliminary study of the comparison of the method of averaging, Liapunov-Floquet transformation, and point mapping. The methods are applied for the analysis of a damped pendulum subjected to periodic support motion. To evaluate the accuracy of various methods, the results of stability analysis are compared with direct numerical solution for different parameter values of the system.
Dynamic Response of a Spinning Timoshenko Shaft With Coupled Bending and Torsion
Authors: Zu Jean W. , Wong Edward
Published: February 2021

The dynamic behavior of a simply-supported spinning Timoshenko shaft with coupled bending and torsion is analyzed. This is accomplished by transforming the set of nonlinear partial differential equations of motion into a set of linear ordinary differential equations. This set of ordinary differential equations is a time-varying system and the solution is obtained analytically in terms of Chebyshev series. The analytical method is a viable alternative to numerical methods and can provide the full range of the required solutions. A beating phenomenon is observed from the numerical simulations. This phenomenon occurs when the system has two natural frequencies close to each other. It is also shown that the period of torsional vibrations is much shorter than the period of oscillations in transverse deflections and in bending angles.
Prevention of Low-Frequency Vibration of High-Capacity Steam Turbine Units
Authors: Kanki H. , Kaneko Y. , Kurosawa M. , Yamamoto T. , Yamamoto Y. , Ninomiya F.
Published: February 2021

The causes of low-frequency vibration (subsynchronous vibration) of a high pressure turbine were investigated analytically and also via vibration excitation tests on actual machines under operation. From the results, it was concluded that low-frequency vibrations may be caused by either the decrease of the rotor system damping or by external forces, such as flow disturbance in the control stage and the rubbing between the rotor and casing. After identifying the cause of the low-frequency vibration, appropriate countermeasures such as installation of a squeeze-film damper and modification of valve opening sequence were taken. Vibration measurements and vibration excitation tests for the high pressure turbine under actual operating conditions were carried out in order to verify the validity of the countermeasures. These field tests confirmed that the problems of low-frequency vibration can be solved completely by taking the appropriate countermeasure depending on the cause of the vibration.

This paper presents some field experiences of low-frequency vibration and the effective solution approach.
Wave Propagation Analysis of an Axially Strained, Rotating Timoshenko Shaft: Part I
Authors: Kang Bongsu , Tan Chin An
Published: February 2021

In this paper, transverse waves propagating in an infinitely long, rotating Timoshenko shaft subjected to axial forces are studied. The model includes the contributions of axial deformation to the transverse vibration of the rotating shaft. Four different types of wave motions, two cutoff frequencies and frequency spectra are defined and discussed. The wave reflection and transmission characteristics of the shaft at arbitrary point supports are also examined by deriving the reflection and transmission matrices for an incident waves upon a general intermediate support. Numerical results showing the effects of axial force, shaft rotation speed, shear deformation, and rotary inertia on the wave reflection and transmission coefficients for classical supports are presented for both the Timoshenko and Euler-Bernoulli beams. It is found that the wave motions are generally independent of the rotation speed and the axial load affects significantly the wave motions at small real wavenumbers.
Unidirectional Excitation Technique for Complex Modal Testing of Asymmetric Rotor Systems: Application to DTG
Authors: Lee Seok-Ku , Lee Chong-Won
Published: February 2021

Unidirectional excitation technique is presented for the complex modal testing of asymmetric rotor systems. The theoretical development, which is made strictly in the stationary coordinate system, enables the unidirectional excitation to effectively estimate the directional frequency response functions. It far lessens the testing efforts a numerical example of the dynamically tuned gyroscope (DTG) is treated to demonstrate the practicality of the complex modal testing.
A Comprehensive Torsional Vibration Analysis Procedure: Part I
Authors: Corbo Mark A. , Malanoski Stanley B.
Published: February 2021

One of the foremost concerns facing turbomachinery users today is that of torsional vibration. In contrast to lateral vibration problems, torsional failures are especially heinous since the first symptom of a problem is often a broken shaft, gear tooth, or coupling. The difficulty of detecting incipient failures in the field makes the performance of a thorough torsional vibration analysis an essential component of the turbomachinery design process.

The aim of this paper1 is to provide users with a practical design procedure that can be used to ensure that their systems will not encounter major difficulties in the field. It has been the authors’ experience that most turbomachinery users encounter little difficulty in determining their machine’s natural frequencies due to the large number of resources available in that area. However, problems often arise when they must translate this information into an accurate prediction of whether or not their design will experience torsional vibration problems. Accordingly, this two-part paper concentrates on the steps that should be taken once the natural frequencies have been found.
Effect of Crack on the Natural Frequency of Rotating Twisted Blades
Authors: Neogy Sumanta , Ramamurti V.
Published: February 2021

Cracks appearing in turbo machine blades during manufacture or operation is not an impossibility. Such cracks may lead to failure of the blade. Previous work by the authors has considered the feasibility of natural frequency as a parameter for damage detection of blades by assuming them to be nonrotating. The present work more realistically models a blade by accounting for the effect of rotation. It not only brings out as to how rotation affects the fall of frequency in presence of crack but also hints at the unsuitability of natural frequency as a criterion for crack diagnosis.
Experimental Investigation of Dynamic Nonlinearities in Rotating Machinery
Authors: Horattas Georgios A. , Adams Maurice L. , Abdel Magied Mohammed F. , Loparo Kenneth A.
Published: February 2021

This paper presents laboratory experiments that confirm and further explore earlier computer simulations related to oil-whip and rub-impact. Both phenomena were explored using Spectrum Analysis, and Chaos tracking techniques (e.g. Poincare’ maps). The results show that oil-whip induces quasi-periodic rotor vibrations, while rub-impact generates complex dynamical behavior, such as chaotic vibrational motion. The nonlinear oil-whip hysteresis loop results presented confirm phenomena uncovered in previous computer simulations. A Sommerfeld number-consistent “instability threshold load” was experimentally observed, along with its corresponding hysteresis loop similar to the classic instability speed hysteresis loop, but probably the most important experimental discovery was a second Hopf bifurcation-Saddle node instability hysteresis loop (i.e., at higher speed than the classical hysteresis loop), separated by a region of stable-in-the-small operation. Another result of especially high practical importance, was the discovery that spectrum analysis of speed-up, or coast-down rotor-vibration data can be effectively used to locate the saddle node speed.
Large Amplitude Radial Oscillations of Viscoelastic Cylindrical Shells
Authors: Yu Jang-Horng
Published: February 2021

We study the large amplitude oscillation of a viscoelastic cylindrical shell where the energy is dissipated through the material relaxation property and the material memory function is of the farm of an exponentially decaying influence function. We construct a Lyapunov functional and show that the equilibrium is nonlineariy stable in free oscillations. Numerical simulations indicate that the equilibrium state is globally stable. For materials with fast relaxation, the motion is similar to that of Newtonian viscous solids. However, for sufficiently slow relaxation where the history effect becomes dominant, we exhibit that the solution trajectory traces a cyclone pattern in the phase plane. We finally examine a forced oscillation case with three equilibria.
Observations on the Performance of Vibration-Isolated Railway Track
Authors: Hunt Hugh E. M.
Published: February 2021

Vibration generated by underground railways is difficult to control because of the very limited space available in a tunnel. A popular approach is to use ‘floating slab track’ whereby the rails are fixed to a large concrete foundation separated from the tunnel wall by a resilient material. This paper investigates some of the vibration characteristics of floating slab track from measurements made in situ. These measurements are compared with the theoretical response of an infinite beam on an elastic foundation taking into account the torsional response of the beam. The transmission of vibration through the tunnel wall and into the surrounding medium is discussed with reference to the relative speed of travelling waves and the coincidence frequencies.
In-Plane Vibration Modes of Arbitrarily Thick Disks
Authors: Tzou Kevin I. , Wickert Jonathan A. , Akay Adnan
Published: February 2021

The three-dimensional vibration of an arbitrarily thick annular disk is investigated for two classes of boundary conditions: all surfaces traction-free, and all free except for the clamped inner radius. These two models represent limiting cases of such common engineering components as automotive and aircraft disk brakes, for which existing models focus on out-of-plane bending vibration. For a disk of significant thickness, vibration modes in which motion occurs within the disk’s equilibrium plane can play a substantial role in setting its dynamic response. Laboratory experiments demonstrate that in-plane modes exist at frequencies comparable to those of out-of-plane bending even for thickness-to-diameter ratios as small as 10−1. The equations for three-dimensional motion are discretized through the Ritz technique, yielding natural frequencies and mode shapes for coupled axial, radial, and circumferential deformations. This treatment is applicable to “disks” of arbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings, and shells. The solutions so obtained converge in the limiting cases to the values expected from the classical theories, and to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the technologically-important range, the natural frequencies of certain in- and out-of-plane modes can be close to one another, or even identically repeated.
Translating Webs With Roller Misalignment: Part I — Model and Equilibrium
Authors: Mockensturm Eric , Mote C. D.
Published: February 2021

The literature on thin, narrow axially moving materials is diverse and mature. However, few investigators have studied the behavior of thin, wide translating continua. This paper and a sequel evaluate the effect of out-of-plane, roller misalignment on the equilibrium and dynamic behavior of wide, axially moving, paper and textile webs. In this paper, a fully nonlinear shell theory that incorporates transverse shear strains is developed and used to determine the equilibrium deformation caused by roller misalignment. This model allows for consideration of large, possibly intentional, roller misalignment. The equations of equilibrium are reduced by assuming the web is deformed into a right helicoid. The resulting nonlinear, ordinary, differential equations are solved both numerically and analytically, employing perturbation. It is found that the longitudinal, membrane stress increases with the magnitude of roller misalignment. However, in a web with free longitudinal edges, the lateral, membrane stress is compressive for any roller misalignment. The translation speed acts, by way of centrifugal tensioning, to increase the lateral, membrane stress. Example results highlight other important conclusions concerning the equilibrium response of webs to out-of-plane roller misalignment.
On a Computational Method for Finding the Fixed Points of a Map
Authors: Guttalu Ramesh S.
Published: February 2021

One of the problems arising in the analysis of periodic nonlinear dynamical systems is to determine multiple equilibria and periodic solutions. These may be formulated in terms of finding zeros of a nonlinear vector function. The iterative methods commonly employed for this purpose concentrate on locating a single zero from a given initial guess. The homotopic and continuation methods are also used for locating multiple zeros but they primarily have been used to follow a single solution branch with a parameter variation. The purpose of this paper is to explore a method based on a differential equation for finding multiple zeros. The equilibria of this differential equation correspond with the zeros of a given vector function. Since the equilibria is asymptotically stable, they can be obtained by examining a large number of trajectories. For this purpose, the cell-to-cell mapping is ideally suited for finding the equilibria, and hence the zeros of a nonlinear vector function. Preliminary results for finding multiple fixed points of a highly nonlinear map are provided in this paper.
Coupling Between Modes of the Asymmetrically-Forced Stretched String
Authors: Bayly Philip V. , Murphy Kevin D.
Published: February 2021

A stretched string that is harmonically forced in one plane may exhibit motion in a perpendicular plane. Previous studies (see Bajaj and Johnson (1992)) have shown that if only one mode is directly excited in the plane of the excitation, the steady-state motion in the perpendicular plane will contain large amplitude motion only in the same mode. In other words, large amplitude, non-planar oscillations may occur only for n:n (e.g., 1:1 or 2:2) coupling. In this paper, it is shown that this result is not true for situations in which the mean force applied to the string is non-zero. A bias force, in combination with harmonic excitation at the second resonant frequency leads to out-of-plane motion of the first mode of the string. This 2:1 resonance is predicted by first-order averaging and is also seen in simulations and experiments.
Effect of Elastomeric Isolator on Dynamic Response of an Exhaust System
Authors: Muju Sandeep , Lane John
Published: February 2021

Elastomeric isolators are typically used as connectors between the body-side and exhaust-side hangers to modulate the vibrational excitation input from the exhaust system into the vehicle underbody, Fig. 1. The dynamic response of these isolators must be properly tuned to avoid any interior cavity boom or structural vibration transmission.

This paper studies the effect of elastomeric properties of the isolator material on the dynamic response of the exhaust system and the transmitted force response. A simplified geometry for an exhaust system is considered. The solution procedure developed may be used for an arbitrary number of isolators. In order to separate the coupling effect of multiple isolators, the effect of a single isolator is studied in detail. The problem solution is developed for a generic functional form for the dynamic stiffness of the isolator. The resulting system of equations leads to a nonlinear transcendental equation for an eigenvalue problem. Based on the available experimental data for typical isolators a functional form of dynamic stiffness is considered. The resulting solution reveals the influence of the elastomeric isolators on the dynamic characteristics of a typical exhaust system. Further, the frequency response of the force transmitted is also obtained. This procedure may be used to either predict the effect of a particular isolator for varying ambient conditions (temperature, preload, vibration amplitude) and/or may be used to tune the properties of an isolator to best suit a particular application.
Applications of the Causality Condition to Acoustic Reflections
Authors: McDaniel J. Gregory
Published: February 2021

The causality condition, which states that the response of a passive system cannot preceed its cause, places mathematical constraints on the complex Fourier transform of the response. For minimum-phase-shift systems, these constraints take the form of Hilbert transform relations between the magnitude and phase of the Fourier transform. These relations have historically had a profound impact on the design of electrical circuits, as evidenced in Bode’s text Network Analysis and Feedback Amplifier Design. The present work presents new applications in the area of structural acoustics which show how the mechanical impedance of a passive fluid-loaded structure can sometimes be inferred from the magnitude of its acoustic reflection coefficient. The approach is demonstrated on a one-dimensional problem in which an incident acoustic wave reflects from a passive structure. An equivalent form of the Hilbert transform, known as the Wiener-Lee transform, is used for the numerical calculations. If the reflection coefficient is minimum-phase-shift, then its phase can be uniquely computed from its magnitude. In this work, it is shown that the minimum-phase-shift property of the reflection coefficient actually depends on the real part of the mechanical impedance of the structure. Therefore, in an inversion problem where one attempts to infer the mechanical impedance given the magnitude of reflection, additional assumptions about the structure must be made in order to arrive at a unique answer. In cases where one attempts to design a passive structure with a specified reflection coefficient magnitude, the causality condition yields a mechanical impedance which corresponds to a minimum-phase-shift reflection coefficient.
Practical Signal Analysis: Do Wavelets Make Any Difference?
Authors: Newland David E.
Published: February 2021

Signal decomposition by time-frequency and time-scale mapping is an essential element of most diagnostic signal analysis. Is the wavelet method of decomposition any better than the short-time Fourier transform and Wigner-Ville methods? This paper explores the effectiveness of wavelets for diagnostic signal analysis. The author has found that harmonic wavelets are particularly suitable because of their simple structure in the frequency domain, but it is still difficult to produce high-definition time-frequency maps. New details of the theory of harmonic wavelet analysis are described which provide the basis for computational algorithms designed to improve map definition.
Parameter Adaptation With Automatically Selected Co-Ordinates From Measured Eigenvectors As a Way to a Validated FE Model
Authors: Zehn Manfred W. , Schmidt Gerald , Martin Oliver
Published: February 2021

This paper considers an algorithm on the basis of parameter adaptation for mass and stiffness embedded in the eigenvalue problem solver. The algorithm is intended for large finite element (FE) models. The errors, which can be reduced by the procedure described in this paper, occur due to detailed features, which would require an unduly fine mesh to be included in the model, or in uncertainties in the description of mechanical behaviour, material properties, etc. Another source for errors are model reduction techniques (superelement technique) necessary for the application of the model structure in an automatic control circuit (smart structures).

It is a well-known fact that the natural frequencies can be measured much more accurately than mode shapes, for mode shapes can only be measured for accessible regions and normally for translational degrees of freedom (DOF). Therefore the algorithm uses only measured natural frequencies (frequency differences) and the calculated mode shape vectors to determine the parameter changes. In a new approach it is also possible to select automatically, or by experience, those co-ordinates from the measured mode shape vectors that correspond to points with high sensitivity or other very reliable points. An interface system designed to exchange data between the experimental modal analysis system (EMA) and the FE program ensures, that the measured and calculated mode shape vectors are orthonormalised in the same way and the points of the FE mesh correspond to the pick up points for the measurement. Examples of industrial parts at the end of the paper illustrate how the procedure works and what influence we can obtain by inclusion of some co-ordinates of measured mode shape vectors.
On Updating of Finite Element Model Using Optimization Method
Authors: Luber Wolfgang G.
Published: February 2021

An error localization and update method is presented which examines the elastic and dynamic behavior of the structure by means of deflections stemming from a discrete load case and from normal mode shapes of the structure respectively as well as the information of the change of natural frequencies. The main objective of the study is to provide an economical and reliable error localization method for aeronautical structures. A finite element model of the elastic structure must be available before testing the real structure to determine the optimal positioning of sensors. The error localization is based on sensitivity methods and on nonlinear mathematical optimization codes. Displacements for selected load cases and normal modes are taken as constraints. Minimum sizing changes with respect to the initial structure is used as objective function. Numerical examples with different structures show that the proposed methods can accurately detect the variations in stiffness in certain cases.
Automatic Selection of Parameters for Updating Procedures
Authors: Imamovic N. , Ewins D. J.
Published: February 2021

This paper describes a new model updating approach based on the standard sensitivity method combined with a new method for automatic selection of updating parameters. It is no longer necessary to select specific updating parameters and to proceed with a global optimisation using these selected parameters. The new method for automatic selection allows the analyst to select any number of updating parameters. The method is based on an assessment of the contribution for each updating parameter to the rank of the sensitivity matrix, and the final selection of updating parameters is performed iteratively by removing the updating parameters which contribute least so long as the rank of the sensitivity matrix is outside a specified value. This solution procedure is performed at every iteration during updating and this ensures that the sensitivity matrix is well conditioned throughout the whole updating process. The technique can be applied to both the modal- and response-based updating approaches. The application of the method is demonstrated on a number of real engineering structures rather than using simulated experimental data.
Evaluation of Different Strategies in the Parametric Identification of Dynamic Models
Authors: Fregolent Annalisa , D’Ambrogio Walter
Published: February 2021

In the present paper, two different updating techniques are compared: the FRU-IT method, based on the minimisation of the force residual through a deterministic approach, and the GAME-UP method based on the minimisation of the output residual, using genetic algorithms. FRU-IT method, as most of the deterministic approaches presented in the literature, is strongly affected by measurement errors, that propagate in the solution and require sophisticated regularisation techniques. The use of genetic algorithms, that find the solution in a heuristic way by simulating an evolution process and require only the definition of fitness indicators, allows to bypass this problem. Results, obtained by solving an experimental test case, confirm that the use of genetic algorithms is a valid alternative to traditional methods.
Friction Phenomena Related to Drum Brake Squeal Instabilities
Authors: Hultén Johan O.
Published: February 2021

Several experiments and analyses have carried out in the field of brake squeal and there are many suggestions to be found in the literature as to the cause of brake squeal. In this paper a mathematical model for friction-induced vibration and noise generation is used to study the influence of these different squeal excitation types.

Squealing brakes are excited by the friction forces in the interface between the drum and the linings. This friction and its interaction with the brake structure can be modeled in many different ways. In this paper, different self-excitation types identified in the literature are tested — each one having the potential of generating instabilities.

The drum brake model used for the analysis is two-dimensional, and consists of a drum and two shoes with linings. The same brake geometry and material properties are used for all computations, which means that the influence of each mechanism can be estimated.

The results from this analysis show that, among the friction models analyzed, the constant coefficient of friction model gives the largest contribution to the instability level of squealing drum brakes. The contribution from the negative μ-velocity slope is shown to be minor.

For the constant coefficient of friction model, there are different excitation types. Among these, lining deformation induced instabilities are shown to generate large instabilities, follower forces show a negligible contribution to the instabilities generated and self-locking is shown to be impossible for the brake analyzed.
A Perturbation Analysis of Nonlinear Squeal Vibrations in Aircraft Braking Systems
Authors: Gordon James T.
Published: February 2021

A perturbation analysis of nonlinear squeal vibrations in aircraft braking systems is presented. The multiple-time-scale technique is used to obtain equations for the limit cycle amplitude and frequency of general autonomous self-excited systems with Coulomb friction, nonlinear stiffness and damping. Coulomb friction terms are shown to modify the amplitude equation to yield perturbations and a universal unfolding of the fundamental Hopf pitchfork bifurcation. The solution method is applied to a nonlinear squeal model in which nonlinear mechanical and material properties of the brake heat stack produce the destabilizing mechanism. The analysis shows that stable and unstable limit cycles can exist for a given constant brake friction coefficient.
Wheel Suspension Related Disc Brake Judder
Authors: Jacobsson Helena
Published: February 2021

Brake judder can be explained as a dynamical amplification of brake torque variation (BTV) when passing through a critical speed of a vehicle. The BTV arises owing to different geometrical defects e.g. disc thickness variation (DTV), disc runout and dynamical effects. DTV is usually the most important source of these fluctuations.

Measurements have been made on a passenger car with heavy DTV on one of its front brakes. The eigen frequency of the wheel suspension was found to be 14 Hz, corresponding to a first order critical speed of 95 km/h. These measurements qualitatively verify the brake model with a maximum caliper vibration amplitude close to 100 km/h followed by a slowly decreasing amplitude.
The Stability of Ejected Beams
Authors: Renshaw Anthony
Published: February 2021

This paper examines the free vibration and stability of an Euler-Bernoulli beam ejected from or, equivalently, drawn into an orifice at an arbitrary angle relative to gravity. A stability boundary for this system is presented in terms of two dimensionless, time varying parameters, one describing the beam bending stiffness and the other indicating the axial tension induced by gravity. This stability boundary is the limit of positive definiteness of a Lyapunov functional for the system. The Lyapunov functional is the Jacobi integral of the system, which qualifies as a Lyapunov functional for many gyroscopic systems. The ejected beam system is gyroscopic when the time varying coefficients in the system equation are held constant. It is also shown that initially, the free vibration problem for the ejected beam has the same vibration modes shapes as an ordinary cantilever beam but that the magnitude and period of vibration grow as the square root of time.
Analysis of Resonances and Instabilities in Elliptical Gear Systems
Authors: Lai Ming-Jun , Seireg Ali A.
Published: February 2021

Two types of elliptical gears, namely first-order and second-order oval elliptical gears, are studied in this paper. The dynamic behavior of such gears is investigated by considering the effect of the eccentricity ratio and the corresponding transmission function, the time-varying mesh stiffness, time-varying mesh inertia, mesh damping as well as the operating speed and external load. The influence of the system parameters on the different resonance and instability conditions is also investigated. The results are compared with those for the circular gears with the same center distance, number of teeth and mesh stiffness and show that the elliptical gears can exhibit better dynamic performance than the circular gears under such conditions. Within the kinematic constraint for the angle of obliquity of the elliptical gears, it is shown that the larger the eccentricity is in their useful range of operation, the more advantageous such gears can be. It is found from the analysis of the dynamic magnification of the tooth load at the primary resonance that a zero magnification occurs for the circular gears with sinusoidal mesh stiffness fluctuation when the ratio of the amplitude of input torque fluctuation to its average value equals the fluctuation ratio of the mesh stiffness. A minimum magnification is also found for the two types of elliptical gears when the mesh stiffness fluctuation is similarly tuned to the torque fluctuation.
Dynamic Modeling of the Three-Degrees-of-Freedom Planar Platform-Type Manipulator
Authors: Mohamed Maher G. , Attia Hazem A.
Published: February 2021

In this paper, the dynamic Modeling of the planar three-degrees of freedom platform-type manipulator is presented. A kinematic analysis is carried out initially, to evaluate and correct the initial coordinates and velocities. The dynamic model of the manipulator is formulated using a two-step transformation. Initially, the dynamic formulation is written in terms of the Cartesian coordinates of a dynamically equivalent system of particles. Since a particle does not have rotational motion, the differential equations of motion are derived by applying Newton’s second law to study the translational motion of the particles. A system of nine primary particles replaces the whole manipulator and the system mass matrix is derived. The equations of motion are then transformed to a more manipulator oriented variables; relative joint coordinates. This leads to efficient solution and integration of the equations of motion. Since the multibody system under consideration contains two independent closed kinematic loops, each of the two closed loops is cut at a suitable joints in order to produce a reduced open loop system with additional constraint equations. When the two cut joints are reassembled, the defined relative joint coordinates are no longer independent. They are related by the cut joint constraints. The constraint forces associated with the cut joint constraints are expressed in terms of Lagrange multipliers. Both cut joint constraints and constraint forces are then introduced into the equations of motion for the reduced open loop system to produce the resulting equations of motions of manipulator. A numerical example is presented and a computer program is developed.
Harmonic and Transient Response Analyses for a Transmission Mechanism With Flexible Support
Authors: Hongzhao Liu , Appleton E. , Zhixiao Su , Shengning Zhang , Weiqing Cao
Published: February 2021

The dynamic responses to harmonic and transient excitation for a multiple-point meshing mechanism with flexible support have been studied. First, the system’s frequency transfer functions were developed and steady-state outputs to a cosine excitation were obtained by both frequency-response and Laplace transformation methods. It is shown that by the appropriate choice of design parameters, the dynamic torque in the basic shaft for a given frequency excitation can, in theory, be reduced to zero. The system’s responses to step, impulsive, and ramp function excitation are also analysed. Furthermore, The maximum torques in the torsional bar and basic shaft are discussed which is an essential consideration for the strength design of these key elements.
Dynamic Analysis of Multibody Rotor-Bearing System
Authors: Mohiuddin M. A. , Khulief Y. A.
Published: February 2021

A multibody formulation of a rotor-bearing system of interconnected flexible and rigid components is presented. The elastic shaft is modelled by the finite element method where shear stiffness, torsional stiffness and the gyroscopic effects are considered. An application to a large-scale rotor-bearing system is presented. Complex modal transformations were invoked to obtain a reduced-order dynamic model. The dynamic responses due step and impulse excitations were obtained using both the full-order and the reduced-order models. Comparisons are presented to verify the validity and accuracy of the reduced-order modal form.
Parameter Identification for Multibody Dynamic Systems
Authors: Serban Radu , Freeman Jeffrey S. , Negrut Dan
Published: February 2021

This paper presents a parameter identification technique for multibody dynamic systems, based on a nonlinear least-square optimization procedure. The procedure identifies unknown parameters in the differential-algebraic multibody system model by matching the acceleration time history of a point of interest with given data. Derivative information for the optimization process is obtained through dynamic sensitivity analysis. Direct differentiation methods are used to perform the sensitivity analysis. Examples of the procedure are presented, applying the technique both to perfect data; i.e. data produced by the assumed model with the optimal choice of parameters, and to experimental data; i.e. data measured on the real system and thus subject to noise and modelling imperfections.
Reduction of Forced Vibration Response by Optimum Balance of Linkage and Optimum Design of System
Authors: Zhang She-min , Morita Nobuyoshi , Torii Takao
Published: February 2021

This paper proposes a new method to reduce the forced vibration response of frame of linkage. It is that the root-mean-square (RMS) value of binary maximum (Bmax) of forced vibration response at a series of angular velocities is taken as the objective function, and the counterweight mass parameters of links and the stiffness factors are used as design variables. Then, it is found out that the responses are related not only to the Bmax value of shaking forces, but also to the shape of curve of shaking forces. The calculation results are compared with those of two other methods used in the reduction of forced vibration response by optimized balance of linkages, and it is shown that the new method can significantly reduce the responses of frame of linkage.
Effects of Noise on Measured Ritz Vectors
Authors: Zimmerman David C. , Cao Timothy T.
Published: February 2021

Ritz vectors offer many advantages over the traditional mode shapes in the areas of model reduction and structural dynamic simulation. Building upon the recent development of an experimental method to extract Ritz vectors from measured dynamic response data, these vectors were also demonstrated to offer great potential in the areas of finite element model correlation and structural damage detection. In this paper, a Monte Carlo simulation is performed to study the accuracy and stability of Ritz vectors extracted from this new procedure using noise corrupted response data. The statistical variation of Ritz parameters and modal parameters extracted from the same data is made to assess the sensitivity of Ritz vector extraction to measured noise.
Structural Dynamics and Damage Detection of Foam-Rigidized Deployable Aerospace Structures
Authors: Main John A. , Smith Suzanne Weaver , Chapman Alexander L. , Hobbs Kenneth Patrick
Published: February 2021

The basic advantage of deployable structures, their compact stowed size relative to their final deployed size, presents a significant advantage to the aerospace designer. Extremely large structures that stow into very small volumes for launch are particularly feasible with one particular type of deployable, the inflated structure. However, it is difficult to advocate the use a purely inflated structure for an orbital mission because of the risk of micrometeor puncture.

Rigidizing the structure in some fashion addresses this fragility issue. Design and operational issues with respect to foam-rigidized aerospace structures are investigated in this paper. The structures are fabricated from flexible Kapton film that is formed into a cylindrical shell. The shell is injected with a hardening urethane foam to form a composite strut.

The results of both static and dynamic tests of four test coupons cut from foam rigidized struts are presented. The experimentally determined structural properties are then input into a finite–element model to gain insight into the dynamic behavior of a realistic inflated–rigidized structure.

As with all structures touted for aerospace use, the survivability of foam–rigidized structures in the orbital environment is of interest. This issue is investigated by damaging the test coupons in a controlled fashion and then again experimentally evaluating the static and dynamic material properties. These properties are used for sections of the finite–element model to represent damage to the structure. An evaluation of the possibility of vibration–based damage assessment is included.
Order Reduction of Identified Interval Model for Systems With Uncertain Parameters
Authors: Lew Jiann-Shiun , Lim Kyong B.
Published: February 2021

This paper addresses the issue of modeling a system with parametric uncertainty via a reduced-order interval model. A system with parametric uncertainty is represented by intervals of transfer function coefficients obtained directly from time-domain response data. An approach based on the sensitivity of a performance specification to the identified uncertain parameters is developed for efficiently analyzing the identified interval model. This approach can significantly reduce the computational effort required by interval system techniques and hence simplify its robust control design. A torque converter clutch system with friction uncertainty is given to fix ideas.
A Method for Identification of Powerplant Joint Properties Using FRF Data and FEM Model
Authors: Takahashi Yukitaka , Suzuki Toshibumi , Tsukahara Masayoshi
Published: February 2021

Vibration characteristics of a powerplant, an important parameter to evaluate the booming noise and the durability of each parts of an automobile is a major field of simulation analysis using the finite element method (FEM). Overall vibration characteristics, however, depend heavily on the joint properties when it comes to the analysis of complicated structures like a powerplant where a number of parts are incorporated. Among other characteristics, it is extremely difficult to conduct accurate identification of the damping characteristics of the joint area, which had been the result of inaccurate analyses.

This paper reports a newly established method to solve these problems through the application of frequency response function (FRF) data and FEM models. Also described is the result of application of the method to the evaluation of a transversely-mounted in-line four-cylinder engine in a front-wheel drive layout. The application revealed that the joint properties can be identified fairly accurately, which in turn allows reliable prediction of vibration level.
“Errors-in-Variables” Identification Techniques Applied to Modal Analysis
Authors: Guillaume Patrick
Published: February 2021

The present paper introduces maximum likelihood “errors-in-variables” identification techniques in the field of experimental modal analysis. The nonparametric (i.e. the estimation of the FRF’s) as well as the parametric case (i.e. the estimation of the modal parameters) are considered.
Numerical Algorithms for Subspace State Space System Identification (N4SID)
Authors: Van Overschee Peter , De Moor Bart , Favoreel Wouter
Published: February 2021

We present the basic notions on subspace identification algorithms for linear systems. These methods estimate state sequences or extended observability matrices directly from the given data, through an orthogonal or oblique projection of the row spaces of certain block Hankel matrices into the row spaces of others. The extraction of the state space model is then achieved through the solution of a least squares problem. These algorithms can be elegantly implemented using well-known numerical linear algebra algorithms such as the LQ- and singular value decomposition. The paper aims at giving an overview of the methodologies used in time domain subspace identification. A short overview of frequency domain subspace identification results is also presented.
Garteur Group on Ground Vibration Testing: Results From the Test of a Single Structure by 12 Laboratories in Europe
Authors: Balmès Etienne , Wright Jan R.
Published: February 2021

In an effort to assess state of the art methodologies for the experimental determination of modal characteristics, 12 European groups, most of them working in the area of aircraft ground vibration tests for flutter certification, participated in a GAR-TEUR action group whose main activity was to have independent tests of a single representative structure. Design considerations for the common structure are first detailed. Estimates of frequency response functions and modal characteristics are then compared and show a level of consistency that is much higher than those reported in previous similar exercises.
The Wide World of Translating Webs
Authors: Mote C. D. , Mockensturm Eric
Published: February 2021

Our webs are wide, very thin, two-dimensional, continua arising commonly as a material in transport in machine systems. Though they are thin, webs often require modeling as plates or shells, albeit very thin and flexible ones, because even small bending stiffness distinguishes their behaviors from membranes in critical ways. Technological applications generating interest in web mechanics include the manufacture and handling of paper where wide sheets are transported by rollers at the highest possible speed, thereby maximizing productivity. Material handling problems of a similar type also arise with tissues, films, magnetic media, textiles, fabrics, polymer sheets, and the like. In a technical world pressing for ever higher speeds of stable transport, the web instabilities of wrinkling and flutter commonly bound the productivity of a technological process. These instabilities can result in permanent damage or rupture of the material and disruption of the manufacturing process. Consequently, the presentation today addresses some findings on webs that relate to their modeling, the prediction and causes of wrinkling, and the effect of roller misalignment on web behavior during transport. To allow us to maintain this focus, the rich collection of works on membrane structures, including modeling of inflated membranes, space structures and fiber reinforced membranes will not be part of our discussion. For attention to interesting membrane developments readers might examine Reissner (1938), Steigmann and Pipkin (1989), Jenkins and Leonard (1991), Li and Steigmann (1993), and Haseganu and Steigmann (1994). The most important topic of web flutter caused by air flows over the web surfaces will not be addressed, though recent experimental findings can be found in Chang and Moretti (1992) and Nguyen (1993). Theories modeling the flow and web in these coupled problems tend to underestimate the flutter speeds. This problem area is one of great importance.