bluuebunny/crossref_metadata_2025_split huggingface dataset:
Van der Pol Mode Stability via Hill’s Equation
Authors: Storti Duane W. , Reinhall Per G. , Sliger David M. 
Published: February 2021

Abstract
The critical variational equation governing the stability of symmetric phase-locked modes for a pair of identical van der Pol oscillators with linear coupling is presented and shown to be equivalent to a Hill’s equation whose periodic coefficient involves the van der Pol limit cycle. We identify the countable set of resonances corresponding to the instability of the in-phase mode and present power series expansions for the Hill determinants which bound these resonances. An additional stability surface is associated with the transformation to Hill’s standard form and corresponds to the time-dependent damping coefficient having zero mean. We present a Padé approximant for this zero mean damping surface which is uniformly effective throughout the parameter range. Power series are also presented for the intersection of the resonance boundaries with the zero mean damping surface and the periodic solutions which occur on the intersection curves. Padé approximants computed from the power series for the intersection curves provide an improved estimate for the growth of the resonances as ε increases.
Nonlinear Regenerative Machine Tool Vibrations
Authors: Stépán Gábor , Kalmar-Nagy Tamas 
Published: February 2021

Abstract
The existence and the nature of the Hopf bifurcation is presented in the delay-differential equation model of the so-called regenerative machine tool vibration. The relevant nonlinearity is considered at the cutting force dependence on the chip thickness. The delayed terms show a special algebraic structure in the nonlinear part of the equation of motion. This results in a surprisingly simple and useful analytical formula in the end of the lengthy calculation based on center manifold reduction in the corresponding infinite dimensional phase space. The result gives a simple way to estimate the domain of attraction of the stable stationary cutting as well as an estimation of that technological parameter domain, where the cutting is globally stable.
Rotor Instability Due to Coupled Effect of Lateral and Torsional Modes and Improper Bearing Design
Authors: Zhang Yatao , Nyqvist Jari 
Published: February 2021

Abstract
This paper deals with a special subsynchronous vibration problem, namely rotor instability caused by partly coupled effect of torsional and bending modes and partly improper bearing design. A theoretical model is presented to investigate such complicated vibration problem. The analysis shows that a single bending or torsional vibration analysis is not enough to predict the stability of a geared rotor system, which includes a turbine, a gear, a generator, several bearings, a squeeze film damper and stators. Either a bearing design, which gives stability in single lateral vibration analysis, cannot guarantee the stability if a torsional vibration mode is involved. This indicates that the bearing design plays much more significant role in a geared rotor system. The theoretical model has been successfully applied to a steam turbine set, which experienced such kind of subsynchronous vibration, by modifying the original bearing design.
The Estimation of Rotor Unbalance
Authors: Lees A. W. , Friswell M. I. 
Published: February 2021

Abstract
A method is presented to determine the state of unbalance of a rotating machine. The only requirement of the procedure is a good numerical model for the rotor and an approximate model for the bearing behaviour. No assumptions are made concerning the operational mode shape of the rotor and the influence of the supporting structure is included in a consistent manner. For simplicity the analysis is presented in a single plane orthogonal to the rotor axis, but no difficulty is foreseen in extending the method to two planes. Examples are given for a two bearing system with both constant and varying bearing coefficients.
Spontaneous Sidebanding at Subharmonic Peaks of Rotordynamic Nonlinear Response
Authors: Ehrich Fredric , Berthillier Marc 
Published: February 2021

Abstract
One of the authors has shown in previous papers (Enrich, 1995; Ehrich, 1996) that, when high speed rotors are operated in the transcritical range with the rotor located eccentrically in its rotor/stator clearance with the rotor in intermittent contact with the stator, a nonlinear response, at speeds both slightly above and slightly below the critical speed, is induced. The response at a particular speed will include significant components at an asynchronous frequency which is approximately equal to the natural frequency of the system. In particular, when the speed (normalized by the natural frequency) S is approximately (J+1)/J, the dominant frequency (normalized by the natural frequency) F is precisely J/(J+1) times S or approximately 1 (where values of the whole number J &lt; 1 give the subcritical set of speeds and values J &gt; 1 give the supercritical set of speeds). The phenomenon has been termed spontaneous sidebanding.
Observations of similar asynchronous responses noted in a Campbell diagram of the rotordynamic response of an actual high speed rotor clustered around a subharmonic response peak at a rotational speed twice the natural frequency suggest that the phenomenon is also possible at any subharmonic pseudo-critical response peak. In this more general case, we would expect that at rotational speeds in the vicinity of the M th subharmonic pseudo-critical normalized speed where S is approximately (MJ+1)/J and the dominant normalized frequency F is precisely J/(MJ+1) times S or approximately 1 [where values of the whole number J &lt; 1 give the sub(pseudo)critical set of speeds and values J &gt; 1 give the super(pseudo)critical set of speeds].
A simple numerical model of the nonlinear system verifies that these asynchronous responses are indeed possible. Operation of the model at a rotational speed approximately double the natural frequency yields data which closely reproduce the asynchronous response seen in the actual machine.
Static and Dynamic Analysis of Multileaf Foil Journal Bearings Considering Misalignment Effects
Authors: Reddy D. Sudheer Kumar , Swarnamani S. , Prabhu B. S. 
Published: February 2021

Abstract
In the present work the analysis of gas lubricated multileaf journal bearing has been presented. The two dimensional compressible Reynolds equation was solved to establish the pressure field in the clearance space of the bearing. Elastic deformation equation is coupled with the Reynolds equation to get the foil deflections and change in film thickness. The effect of bearing misalignment on foil bearing performance characteristics has been presented. The problem has been formulated using incremental finite element method. The effect of bearing misalignment on static performance characteristics like load carrying capacity, frictional torque, minimum film thickness and on dynamic characteristics in terms of stiffness and damping coefficients have been presented.
Vibrations: Noises Produced by Rotors and Eddy Current Probes
Authors: Nguyen The Tam , Bigret Roland 
Published: February 2021

Abstract
• The rotating equipment monitoring, protection and diagnostic system is based mainly on the knowledge of bearing structure vibrations and shaft relative vibrations. The vibration measurements are performed respectively by seismic transducers and proximity probe transducers.
• Measured signals are affected by uncertainties, the most significant sources of which could be mechanical and electrical runout.
• These uncertainties are mentioned by well known standards which recommend or dictate general rules but do not give any advice or procedure in view of reaching the main objective, that is to optimize the efficiency of the monitoring, protection and diagnostic system to improve machine reliability.
• This paper gives two examples showing the effect of inaccuracies, due to noise, on the interpretation of the machine vibrations.
• One validation procedure identifying true noise will be given, using the rotor slow roll principle.
• Noise suppression will be presented requiring sampling and resampling of time domain signals taken on a non synchronous mode. A newly designed software will be used.
• Mechanical runout could induce inacurracies on rotors low speed balancing.
• Noises could create harmful forces on the rotor in a magnetic bearing system.
• Modern manufacturing techniques can minimize mechanical runout in order to avoid noise suppression which could generate additional incaccuracies.
Whirl Speeds and Unbalance Response of Rotor-Bearing Systems Using Finite Dynamic Elements
Authors: Yang Bo-Suk , Hwang Hyung-Sub , Oh Sae-Kyoo 
Published: February 2021

Abstract
The conventional finite element model for rotor-bearing system are formed using shape functions which are based on static displacements, and can lead some errors in analysis of general rotor dynamics problems. A procedure is presented for dynamic modeling of rotor-bearing system which consist of finite dynamic shaft elements, rigid disk, and bearing element. A finite dynamic element model including the effects of rotary inertia, gyroscopic moments, axial force, and axial torque is developed using the frequency dependent shape function. The natural whirl speeds, stability, and unbalance response of rotor system are calculated on several cases and compared with the conventional finite elements.
Design of Liquid Seals for Centrifugal Compressors
Authors: Kirk R. Gordon , Baheti S. K. 
Published: February 2021

Abstract
The use of liquid ring type oil seals in centrifugal compressors was essential for high pressure applications dating back to the early 1960’s. The analysis of high pressure oil seals was first documented in the literature in the mid 1970’s following a series of compressor instability problems that made it clear that a better understanding of how seals influence the overall rotor stability was necessary. To produce compressor designs at higher speeds requires that an adequate method of predicting the oil seal influence on rotor dynamic stability be available for the designer. With the enhanced capability of personal computers and improved finite element models of the oil film thermal and hydrodynamic solutions, it is now possible to more accurately predict the dynamic characteristics of the oil seals. This paper presents a series of predicted results from a currently available advanced state of the art computer analysis for high pressure oil seals. The evaluation of several high pressure compressor seal designs illustrate the current capability for analytical predictions for various seal bore geometries. Conclusions and recommendations for the design of liquid ring seals are presented, which can give the compressor designer guidance for application to future high performance compressor liquid seal designs.
Fly Rod Performance and Line Selection
Authors: Hoffmann Jon A. , Hooper Matthew R. 
Published: February 2021

Abstract
The stiffness, first mode natural frequency and deflection profile can be used to describe the performance of a fly rod. A finite element model has been developed which predicts the performance parameters of fly rod blanks as a function of the geometry and material properties of the blanks. The results of the model compare favorably with experimental results. The model was used to evaluate the effects of changes of design parameters on rod performance. The natural frequency of a rod or a rod blank is a function of the stiffness to mass ratio and the mass distribution of the rod. An empirical equation that predicts the natural frequency of a rod or a rod blank as a function of the mass of the tip section, location of the center of gravity of the tip section and rod stiffness is presented. The line weight rating for fly rods was found to be a function of the stiffness and frequency of the rods. For the first time, an empirical method for the selection of a line weight that matches the performance characteristics of a rod is presented.
A New Microslip Model for Bending Response and Hysteresis Loss of a Multiwire Strand
Authors: Jayakumar C. V. , Sathikh S. , Jebaraj C. 
Published: February 2021

Abstract
A new hypothesis for wire-core slip is devised to predict bending stiffness for an initially tensioned helical wire strand. In this model, the Coulomb friction stick-gross slip hypothesis and the Coulomb friction Hertzian contact microslip hypothesis are combined to form a system of two springs in series. This results in a low bending stiffness as found normally in experiments as well as in practice. The hysteresis loss and the bending stiffness predicted are compared with those available in literature. The agreement is encouraging.
Flexural Vibrations of Thick Cylindrical Panels
Authors: Hamidzadeh H. R. 
Published: February 2021

Abstract
Harmonic vibrations of thick viscoelastic cylindrical panels are investigated. The medium is considered to be a homogeneous, isotropic, linear viscoelastic, thick cylindrical panel of infinite extent. In the development of an analytical solution, the two dimensional elastodynamic theory is employed and the material damping is considered by introducing complex elastic moduli. The panels end conditions do not allow the displacement along the tangential direction; however, the radial displacements are not constrained. The displacements on the surface of the panel are formulated in terms of boundary stresses and their harmonic responses due to the radial and tangential boundary stresses are determined. Displacements and stresses in both the radial and tangential direction for each of the normal modes in the medium are computed. This is achieved by utilizing an algorithm for the Bessel functions of complex argument and fractional order. The algorithm is numerically stable for a wide range of exciting frequencies, circumferential mode numbers, and loss factors.
Nonlinear Vibrations in an Elastic Structure Subjected to Vertical Excitation and Coupled With Liquid Sloshing in a Rectangular Tank
Authors: Ikeda Takashi 
Published: February 2021

Abstract
The nonlinear coupled vibrations of an elastic structure and liquid sloshing in a rectangular tank, partially filled with liquid, are investigated. The structure containing the tank is vertically subjected to a sinusoidal excitation. In the theoretical analysis, the resonance curves for the responses of the structure and liquid surface are presented by the harmonic balance method, when the natural frequency of the structure is equal to twice the natural frequency of one of the sloshing modes. From the theoretical analysis, the following predictions have been obtained: (a) Due to the nonlinearity of the fluid force, harmonic oscillations appear in the structure, while subharmonic oscillations occur on the liquid surface, (b) the shapes of the resonance curves markedly change depending on the liquid depth, and (c) when the detuning condition is slightly deviated, almost periodic oscillations and chaotic oscillations appear at certain intervals of the excitation frequency. These were qualitatively in good agreement with the experimental results.
Three-to-One Internal Resonances in Parametrically Excited Hinged-Clamped Beams
Authors: Chin Char-Ming , Nayfeh Ali H. 
Published: February 2021

Abstract
The nonlinear planar response of a hinged-clamped beam to a parametric excitation of either its first mode or its second mode is investigated. The analysis accounts for mid-plane stretching, a static axial load, a restraining spring at one end, and modal damping. For a range of axial loads, the second natural frequency is approximately three times the first natural frequency and hence the first and second modes may interact via a three-to-one internal resonance. The method of multiple scales is used to attack directly the governing nonlinear integral-partial-differential equation and associated boundary conditions and derive two sets of four first-order nonlinear ordinary-differential equations describing the modulation of the amplitudes and phases of the first two modes in the case of principal parametric resonance of either the first or the second mode. Periodic motions and periodically and chaotically modulated motions of the beam are determined by investigating the equilibrium and dynamic solutions of the modulation equations. For the case of parametric resonance of the first mode, trivial and two-mode solutions are possible, whereas for the case of parametric resonance of the second mode, trivial, single-, and two-mode solutions are possible. The two-mode equilibrium solutions of the modulation equations may undergo either a supercritical or a subcritical Hopf bifurcation, depending on the magnitude of the axial load. In the region of dynamic solutions, some phenomena are documented, including period-doubling bifurcations and blue-sky catastrophes.
On the Effects of Imperfections and Mistuning on the Performance of Subharmonic Vibration Absorbers
Authors: Chao Chang-Po , Shaw Steven W. 
Published: February 2021

Abstract
A pair of centrifugal pendulum vibration absorbers (CPVA’s) riding on half-order epicycloidal paths have recently been found to be very effective at reducing torsional vibration levels in a rotating system that is subjected to a harmonic external torque. Previous analyses of this system have assumed perfectly manufactured and exactly tuned paths for the absorber masses. The primary goal of this study is to explore the effects that manufacturing and other imperfections and intentional mistunings have on the performance of this absorber system. To this aim, the equations of motion are first derived for a simplified model. The basic system has two and a half degrees of freedom with a one-to-one internal resonance and two-to-one resonant external excitation. Utilizing the method of averaging, the steady-state solutions are obtained and used to evaluate the absorber performance via two performance indices: the rotor acceleration and the applicable range of the disturbing torque. Finally, some guidelines are provided for designers in terms of how one should choose and/or control intensional mistuning and imperfections of the absorber paths.
Phase Space Transport in a Class of Multi-Degree of-Freedom Systems
Authors: Chen Shyh-Leh , Shaw Steven W. 
Published: February 2021

Abstract
In this paper we describe some recent advances in the basic theory and applications of phase space transport in nonlinear dynamic systems. These methods offer both qualitative and quantitative information about the behavior of solutions near homoclinic and heteroclinic motions in nonlinear dynamical systems. Applications of these ideas are found in fluid mixing and the escape of solutions from potential energy wells under the action of disturbances, for example, in models of ship capsize. In this work the theory is extended to a certain class of higher-order systems in which several time scales are involved. In addition, a new analytical estimate is derived and used for the rate of transport in the case of two-dimensional Poincare maps. Extensive simulation results from a specific ship dynamics model are used to demonstrate and verify these results.
Two Groups of Chaotic Vibrations in a Single-Degree-of-Freedom Maglev System
Authors: Xu Zhixiang , Tamura Hideyuki 
Published: February 2021

Abstract
In this paper, a single-degree-of-freedom magnetic levitation dynamic system, whose spring is composed of a magnetic repulsive force, is numerically analyzed. The numerical results indicate that a body levitated by magnetic force shows many kinds of vibrations upon adjusting the system parameters (viz., damping, excitation amplitude and excitation frequency) when the system is excited by the harmonically moving base. For a suitable combination of parameters, an aperiodic vibration occurs after a sequence of period-doubling bifurcations. Typical aperiodic vibrations that occurred after period-doubling bifurcations from several initial states are identified as chaotic vibration and classified into two groups by examining their power spectra, Poincare maps, fractal dimension analyses, etc.
Experimental Identification Technique of Nonlinear Beams in Time Domain
Authors: Yasuda Kimihio , Kamiya Keisuke 
Published: February 2021

Abstract
In previous papers the authors proposed a new experimental identification technique applicable to elastic structures. The proposed technique is based on the principle of harmonic balance, and can be classified as the frequency domain technique. The technique requires the excitation force to be periodic. This is in some cases a restriction. So another technique free from this restriction is of use. In this paper, as a first step for developing such techniques, a technique applicable to beams is proposed. The proposed technique can be classified as the time domain one. Two variations of the technique are proposed, depending on what methods are used for estimating the parameters of the governing equations. The first method is based on the usual least square method. The second is based on solving a minimization problem with constraints. The latter usually yields better results. But in this method, an iteration procedure is used, which requires initial values for the parameters. To determine the initial values, the first method can be used. So both methods are useful. Finally the applicability of the proposed technique is confirmed by numerical simulation and experiments.
Vibration Isolation and Damping for Bucking Bars
Authors: Cherng John G. , Ge Tong , Peng Sheng-Lih 
Published: February 2021

Abstract
Bucking bars are used with pneumatic percussive rivet tools for airplanes, ships, and heavy vehicle constructions. The rivet is actually flattened by the bucking bar instead of the riveting hammer when the force is transmitted to the contact point between the rivet stem and the bucking bar. It has been proven that the operator who is holding the backing bar receives higher level of vibration than the person who is operating the rivet hammer. However, more attention has been given to the design modifications of the rivet hammer than the bucking bars which may due to the economic reasons. (The price of hammer is 50 to 100 times higher than the bucking bars’ price.) In this paper, the vibration characteristics of the bucking bars, the applications of vibration isolation and damping to the bucking bars, the optimum mass distribution calculated by a two degree-of-freedom model and the comparative results of the conventional bucking bar and ergonomically modified bucking bars are presented.
Mounting Stiffness Effects in “Free-Free” Modal Tests
Authors: Wolf Joseph A. 
Published: February 2021

Abstract
The fundamental issue confronting a vibration test engineer is how to obtain the best representation for the natural frequencies and corresponding mode shapes of a mechanical system. In the case of a structure such as a vehicle that has rigid body degrees of freedom, a vibration test requires some sort of artificial support system. The purpose of this work is to quantify the influence of this support system using two example structures: a one-degree-of-freedom oscillator, and a uniform beam on two types of supports. In all cases, the actual influence of the supports on the modal test results is greater than one would estimate a priori. It is hoped that these results, which have been derived from exact solutions, will provide insight for designing test supports for more complex structures.