bluuebunny/crossref_metadata_2025_split huggingface dataset:
Dynamics of a Free Play Type of Nonlinearity System Under Deterministic and Random Excitations
Authors: Orabi Ismail I. 
Published: March 2021

Abstract
The dynamics of nonlinear structures under harmonic and random excitations is studied. The harmonic excitation is modeled by periodic loadings while the random excitations is modeled by segments of stationary Gaussian white noise processes. Transient responses of a single-degree-of-freedom model is studied to illustrate the characteristic of nonlinear responses. A free play type of nonlinearity is considered. The effects of nonlinearities on the overall dynamics of structure is investigated. The linearization technique is used to calculate the response statistics. To check the accuracy of the linearization technique, the results are compared with Monte-Carlo digital simulations and good agreement are observed.
Parametric Vibrations in a Magneto-Thermo-Elastic Layer of Finite Thickness
Authors: Wauer Jörg 
Published: March 2021

Abstract
The dynamic behavior of a magneto-thermo-elastic planar layer subjected to a bias magnetic field is examined. The magnetic field acts parallel to the layer surfaces and is composed of a constant and a harmonically oscillating part. In particular, the small coupled magneto-thermo-elastic vibrations superimposed on the basic steady state response due to the stationary magnetic excitation are analyzed. Attention is focused on the influence of the pulsating part of the bias magnetic field on the governing variational equations to prove the stability of the basic state. In general, the stability equations describing the perturbations of the magnetic, thermal and elastic field properties are coupled in a special form and also the parametric excitation acts in a non-classical manner. Hence the variety of possible parametric resonances seems to be limited.
Dynamic Analysis of Non-Uniform Beams With Time Dependent Elastic Boundary Conditions
Authors: Lee Sen Yung , Lin Shueei Muh 
Published: March 2021

Abstract
The dynamic response of a non-uniform beam with time dependent elastic boundary conditions is studied by generalizing the method of Mindlin-Goodman and utilizing the exact solutions of general elastically restrained non-uniform beams given by Lee and Kuo. The time dependent elastic boundary conditions for the beam are formulated. A general form of change of dependent variable is introduced and the shifting polynomials of the third order degree, instead of the fifth order degree polynomials taken by Mindlin-Goodman, are selected. The physical meaning of these shifting polynomial functions are explored. Finally, the limiting cases are discussed and several examples are given to illustrate the analysis.
The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques
Authors: Tong X. , Tabarrok B. 
Published: March 2021

Abstract
In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.
Development and Application of Interpolated Cell Mapping to the Lorenz Equations
Authors: Tongue Benson H. , White Matt T. 
Published: March 2021

Abstract
The Interpolated Cell Mapping strategy is extended to allow an analysis of the Lorenz equations. Both cell size and mapping time are varied in order to identify optimal solutions. A higher-order interpolation method for Interpolated Cell Mapping is developed and compared to numerical integration. Regions of state space with high levels of spatial deformation are found and are seen to correspond to areas that are dense with basin boundaries.
Smoothing Technique for Rub or Looseness-Related Rotor Dynamic Problems
Authors: Goldman Paul , Muszynska Agnes 
Published: March 2021

Abstract
The lateral vibration response of a rotor, experiencing periodic contact with a nonrotating machine component, is considered. In the case of an inelastic impact, this causes a piecewise, step-changing stiffness of the system. Applying to the rotor model a specially developed variable transformation which smooths discontinuities, and applying then an averaging technique, a variety of imbalance-related resonant regimes of rotor lateral motion are obtained, and their stability is analyzed. The developed analytical algorithm has a high potential as a valuable research tool for investigating local nonlinear effects in rotor systems.
Nonlinear Vibration Characteristics With Large Unbalance of Turbogenerators Rotor Systems
Authors: Lu Songyuan , Wei Gao 
Published: March 2021

Abstract
Some catastrophic vibration failures of turbogenerators shaft system have occurred in China and abroad. But, since the researches on nonlinear vibration characteristics of real engineering rotor-bearing system were not thoroughgoing in the past years, so the accurate and quantity analysis on particular accidents is still impossible. However, to understand the nonlinear vibration characteristics with large unbalance is engineering important for accident analysis, investigation and for precautions against the failures.
This paper employed a new transfer matrix-time marching approach, and made researches on calculation for nonlinear vibration caused by large vibration at the generator rotor and low pressure rotor of 200MW turbogenerators made in China.
By this study, some new and important conclusions concerned transient process while much mass escaped from turbogenerators rotor at operation condition have been obtained. They can provide valuable suggestions to the accident analysis, the design of large turbogenerators shaft and operation technology of the power plants, and these conclusions will be the foundation for the further researches on the destruction mechanism of turbogenerators forced by nonlinear vibration.
Effects of Experimental Procedures on Narmax Model Estimation
Authors: McCabe Sarah A. , Davies Patricia 
Published: March 2021

Abstract
The nonlinear autoregressive moving average model with exogenous inputs (NARMAX model) is a convenient digital representation that can be used to simulate a large class of nonlinear vibratory systems. However, the process of identifying the model structure and estimating the model term coefficients can be prohibitively computationally intensive. Most identification techniques start with a model structure containing all possible terms and then use an algorithm to determine the significance of each term and reduce the model size by eliminating insignificant terms. For many physical systems of interest (such as those with high order dynamics or multi-inputs/multi-outputs), the size of the model can exceed the available computational resources. It therefore becomes necessary to apply all available knowledge of the physical system to eliminate terms from the initial model structure and reduce this task to manageable proportions. To explore the utility of this identification method, it was used to identify the NARMAX model for a numerically generated single degree of freedom system. The identified model was used to simulate the system; a comparison is made between the numerically integrated response and the NARMAX simulated response. However, it is one thing to test system identification techniques by applying them to numerically generated data and quite another to use data which has been measured from a physical system. Not only are there differences between the ideal model of the system and the physical system, the measurement process introduces other changes to the data such as sampling effects, quantization effects, filtering effects, and measurement induced noise. In order to determine what effects on the model identification process are introduced by each step in the measurement process, the numerically integrated data was successively modified to simulate the effects of filtering and quantization (which introduces measurement noise) and the model identification process was performed on this altered data. These newly identified models were again used to simulate the system for purposes of comparison. Finally, the model identification process is applied to data measured from a physical system and the resulting model is evaluated for the purpose of simulation.
Identification of Nonlinear Systems Parameters Using Polyspectral Measurements and Analysis
Authors: Hajj Muhammad R. , Nayfeh Ali H. , Popovic Pavol 
Published: March 2021

Abstract
Experimental and analytical techniques that characterize nonlinear modal interactions in structures are used to quantify parameters in representative nonlinear systems. The subject of the experimental study is a three-beam frame. Subharmonic resonances and interaction between widely spaced modes are exploited to determine nonlinear parameters in models that represent these interactions. The phases of the auto-bispectra of the response of this structure appear in the analytical solutions of the representative models. Values of these phases could thus aid in determining other unknown parameters of nonlinear systems.
Applications of Time-Frequency Analysis to Structures With Internal Resonance
Authors: Dippery Kyle D. , Smith Suzanne Weaver 
Published: March 2021

Abstract
Time-frequency analysis is an approach to characterizing the nature of signals whose frequency content changes over time. Although the primary applications of this field have, to date, been in the area of communications and signal analysis, it is becoming known in the field of structural dynamics. This paper explores the application of two straightforward time-frequency techniques to several structures that exhibit internal resonance. In particular, the systems analyzed exhibit simple modal interactions and, in one case, a transition to chaos. While other methods exist for analysis of these types of behaviors, larger systems with more complex resonances maybe better analyzed with time-frequency techniques.
The Nonlinear Vibration Analysis of a Clamped-Clamped Beam by a Reduced Multibody Method
Authors: Kovacs A. P. , Ibrahim R. A. 
Published: March 2021

Abstract
The nonlinear response characteristics for a dynamic system with a geometric nonlinearity is examined using a multibody dynamics method. The planar system is an initially straight clamped-clamped beam subject to high frequency excitation in the vicinity of its third natural mode. The model includes a pre-applied static axial load, linear bending stiffness and a cubic in-plane stretching force. Constrained flexibility is applied to a multibody method that lumps the beam into N elements for three substructures subjected to the nonlinear partial differential equation of motion and N-1 linear modal constraints. This procedure is verified by d’Alembert’s principle that leads to a discrete form of Galerkin’s method. A finite difference scheme models the elastic forces. The beam is tuned by the axial force to obtain fourth order internal resonance that demonstrates bimodal and trimodal responses in agreement with low and moderate excitation test results. The continuous Galerkin method is shown to generate results conflicting with the test and multibody method. A new checking function based on Gauss’ principle of least constraint is applied to the beam to minimize modal constraint error.
A Study of Bifurcations in Periodic Systems
Authors: Guttalu Ramesh S. , Flashner Henryk 
Published: March 2021

Abstract
An approach for analysis of stability and bifurcations of multivariable nonlinear systems with periodically varying coefficients is formulated using the notion of point mapping (period to period mapping). Analytical expressions of the point mapping and its dependence on system’s parameters are obtained using a recursive procedure. The procedure yields coefficients of a multinomial expansion of the point mapping up to an arbitrary order of state variables and parameters. Analytical stability and bifurcation conditions can be then expressed as functional relations between system parameters. In addition, parametric expressions for bifurcated solutions of different periods are also obtained. The proposed approach is demonstrated in a study of parametric stability and bifurcation of a nonlinear Mathieu’s equation. Analytical conditions for bifurcation as well as expressions for bifurcation to harmonic and subharmonic solutions are derived. The results are compared to direct integration computation that are considered to be an “exact solution”. It is shown that, unlike perturbation analysis, the proposed method provides very accurate solution even for large values of the parameters. Moreover, unlike most existing methods, the approach presented here is applicable to multiple degree-of-freedom systems with multiple parameters. Most existing analysis methods apply mainly to single degree-of-freedom systems and their extension to higher dimensions is difficult and computationally cumbersome.
Experiments on a Rocking Block
Authors: Fielder William T. , Virgin Lawrence N. , Plaut Raymond H. 
Published: March 2021

Abstract
A rigid, slender, rectangular block is an apparently simple example of a stability problem. In a static sense, the upright position remains stable providing the restoring moment due to gravity is sufficient to offset any applied overturning moment. Rotated about either corner, the block will overturn if a critical angle is exceeded. However, if the (quiescent) block is subjected to a horizontal (dynamic) base excitation, and assuming that no sliding, bouncing, or out-of-plane motion occurs, a typical block may either: (i) remain stationary relative to the base, (ii) rock, or (iii) overturn.
The conditions under which overturning occurs are of particular interest here, i.e., the boundary between categories (ii) and (iii) above. Combinations of forcing parameters, i.e., magnitude and frequency of the sinusoidal excitation, are categorized according to whether, and how quickly, overturning occurs. The transition when the block changes from rotation about one corner to the other, the energy loss at impact, and large-angle geometric effects are the sources of nonlinearity in this problem.
Based on numerical integration, and taking great care to accurately model the impact condition, it is shown that transient rocking prior to overturning exhibits an extreme sensitivity and dependence on certain system parameters. A number of counter-intuitive features are observed. Some elementary experiments conducted on a relatively slender, rigid block placed on a shake table confirm some of the simulation results, but also point out the modeling difficulties encountered in such inherently sensitive systems.
On Integrating Factors and a Perturbation Method
Authors: van Horssen W. T. 
Published: March 2021

Abstract
In this paper the fundamental concept (due to Euler, 1734) of how to make a first order ordinary differential equation exact by means of integrating factors, is extended to n-th order (n ≥ 2) ordinary differential equations and to systems of first order ordinary differential equations. For new classes of differential equations first integrals or complete solutions can be constructed. Also a perturbation method based on integrating factors can be developed. To show how this perturbation method works the method is applied to the well-known Van der Pol equation.
Optimal Structural Control: A Reliability-Based Approach
Authors: Kaspari D. C. , Spencer B. F. , Sain M. K. 
Published: March 2021

Abstract
This paper develops probabilistically-based optimal control strategies which focus on minimizing the extreme responses of a structure subject to stochastic excitation. A performance function is chosen that is directly related to the failure probability for the structure. Optimization is performed over a parameterized class of controllers, subject to a probabilistic constraint on the available control effort. System uncertainty is modelled parametrically and is incorporated into the optimization algorithm. First and second order reliability methods (FORM/SORM) are employed for calculation of the required probabilities. A numerical example using a two story structure subject to seismic excitation is provided to illustrate the approach. The probability estimates based on the FORM/SORM approach are compared with Monte Carlo simulation (MCS) to demonstrate the efficiency and accuracy of the FORM/SORM approach.
Fuzzy Control of Nonlinear Systems in the Presence of Noise
Authors: Casciati F. , Faravelli L. 
Published: March 2021

Abstract
Imprecise linguistic descriptions of system conditions can be used as the basis for activating control forces. In this paper, one discusses the aspects of the application of fuzzy control to civil engineering problems. Attention is focused on the presence of noise in the sensor reading and in the time delay. The results of numerical examples studying nonlinear systems subjected to random excitations are presented to illustrate some peculiar features of fuzzy control.
On the Control of Chaos in Extended Structures
Authors: Barratt Carl 
Published: March 2021

Abstract
A mechanism is proposed for synchronizing the vibrations of an externally forced array of Duffing oscillators with nearest-neighbor viscoelastic coupling. The parameters of the individual oscillators and the couplings are chosen such that, in the absence of control, the oscillators vibrate chaotically and incoherently. The proposed control scheme brings the elements into synchrony with each other in a few tens of cycles of the external forcing function. It is robust, maintaining the desired state in the presence of noise. It is general in that it works with any form of external forcing. A modification of the mechanism is used to control the forced chaotic vibrations of a single Duffing oscillator allowed to vibrate out of the vertical plane.
Optimal Paths, Caustics, and Boundary Layer Approximations in Stochastically Perturbed Dynamical Systems
Authors: Maier Robert S. , Stein Daniel L. 
Published: March 2021

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

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

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

Abstract
The sliding of two surfaces with respect to each other involves many interacting phenomena. In this paper a simple model is presented for the dynamic interaction of two dry sliding surfaces. This model consists of a beam on elastic foundation acted upon by a series of moving linear springs, where the springs represent the asperities on one of the surfaces. The coefficient of friction is constant. Although a nominally steady-state solution exists, an analysis of the dynamic problem indicates that the steady solution is dynamically unstable for any finite speed. Eigenvalues with positive real parts give rise to self-excited motion which continues to increase with time. The mechanism responsible for the instability is a result of the interaction of certain complex modes of vibration (which result from the moving springs) with the friction force of the moving springs. It is expected that these vibrations play a role in the behavior of sliding members with dry friction.