bluuebunny/crossref_metadata_2025_split huggingface dataset:
In-Plane Vibration Modes of Arbitrarily Thick Disks
Authors: Tzou Kevin I. , Wickert Jonathan A. , Akay Adnan 
Published: February 2021

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.