On the Role of Nonlinearity in the Dynamic Behavior of Rubber Components

1986 ◽  
Vol 59 (5) ◽  
pp. 740-764 ◽  
Author(s):  
J. Harris ◽  
A. Stevenson
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Behavior ◽  
Material Composition ◽  
Geometrical Design ◽  
Linear Spring ◽  
Case Design

Abstract This paper has discussed the transmissibility behavior of rubber mounts with reference to nonlinearity originating from the material composition and from the geometrical design. It has been shown that in many cases, linear assumptions can be made, provided the limitations of these assumptions are understood. In this case, design can proceed as for a linear spring. Finally, there is some indication of how the nonlinear behavior can be exploited to advantage in the design of novel suspension components.

A Multi-Mode Approach for the Nonlinear Vibrations of Circular Cylindrical Shells

2001 ◽  
Author(s):  
Francesco Pellicano ◽  
Marco Amabili ◽  
Michael P. Païdoussis
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Vibrations ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Symbolic Manipulation ◽  
Comparison Functions ◽  
Circular Cylindrical Shells ◽  
Multi Mode

Abstract The nonlinear vibrations of simply supported, circular cylindrical shells, having geometric nonlinearities is analyzed. Donnell’s nonlinear shallow-shell theory is used, and the partial differential equations are spatially discretized by means of the Galerkin procedure, using a large number of degrees of freedom. A symbolic manipulation code is developed for the discretization, allowing an unlimited number of modes. In the displacement expansion particular care is given to the comparison functions in order to reduce as much as possible the dimension of the dynamical system, without losing accuracy. Both driven and companion modes are included, allowing for traveling-wave response of the shell. The fundamental role of the axisymmetric modes, which are included in the expansion, is confirmed and a convergence analysis is performed. The effect of the geometric shell characteristics, radius, length and thickness, on the nonlinear behavior is analyzed.

Sources and Propagation of Nonlinearity in a Vibration Isolator With Geometrically Nonlinear Damping

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
J. C. Carranza ◽  
M. J. Brennan ◽  
B. Tang
Keyword(s):  
Vibration Isolation ◽  
Nonlinear Behavior ◽  
High Amplitude ◽  
Nonlinear Damping ◽  
Single Frequency ◽  
Geometrically Nonlinear ◽  
Harmonic Force ◽  
Isolation System ◽  
Linear Spring ◽  
Harmonic Components

In this paper, the behavior of a single degree-of-freedom (SDOF) passive vibration isolation system with geometrically nonlinear damping is investigated, and its displacement and force transmissibilities are compared with that of a linear system. The nonlinear system is composed of a linear spring and a linear viscous damper which are connected to a mass so that the damper is perpendicular to the spring. The system is excited by a harmonic force applied to the mass or a displacement of the base in the direction of the spring. The transmissibilities of the nonlinear isolation system are calculated using analytical expressions for small amplitudes of excitation and by using numerical simulations for high amplitude of excitation. When excited with a harmonic force, the forces transmitted through the spring and the damper are analyzed separately by decomposing the forces in terms of their harmonics. This enables the effects of these elements to be studied and to determine how they contribute individually to the nonlinear behavior of the system as a whole. For single frequency excitation, it is shown that the nonlinear damper causes distortion of the velocity of the suspended mass by generating higher harmonic components, and this combines with the time-varying nature of the damping in the system to severely distort the force transmitted though the damper. The distortion of the force transmitted through the spring is much smaller than that through the damper.

CNN DYNAMICS REPRESENTS A BROADER CLASS THAN PDEs

2002 ◽  
Vol 12 (10) ◽  
pp. 2051-2068 ◽  
Author(s):  
M. GILLI ◽  
T. ROSKA ◽  
L. O. CHUA ◽  
P. P. CIVALLERI
Keyword(s):  
Difference Scheme ◽  
Dynamic Behavior ◽  
Topological Equivalence ◽  
Continuous Space ◽  
Nonlinear Networks ◽  
Space Discretization ◽  
Spatio Temporal ◽  
The Relationship ◽  
Similar Dynamic

The relationship between Cellular Nonlinear Networks (CNNs) and Partial Differential Equations (PDEs) is investigated. The equivalence between discrete-space CNN models and continuous-space PDE models is rigorously defined. The key role of space discretization is explained. The problem of the equivalence is split into two subproblems: approximation and topological equivalence, that can be explicitly studied for any CNN model. It is known that each PDE can be approximated by a space difference scheme, i.e. a CNN model, that presents a similar dynamic behavior. It is shown, through several examples, that there exist CNN models that are not equivalent to any PDEs, either because they do not approximate any PDE models, or because they have a qualitatively different dynamic behavior (i.e. they are not topologically equivalent to the PDE that they approximate). This proves that the spatio-temporal CNN dynamics is broader than that described by PDEs.

scholarly journals Two-phase flow in Hele-Shaw cells: numberical studies of sweep efficiency in a five-spot pattern

1988 ◽  
Vol 29 (4) ◽  
pp. 375-400 ◽  
Author(s):  
Leonard W. Sahwartiz ◽  
Anthony J. Degregoria
Keyword(s):  
Dimensionless Parameter ◽  
Viscosity Ratio ◽  
Nonlinear Behavior ◽  
Boundary Integral ◽  
Porous Media Flow ◽  
Sweep Efficiency ◽  
Two Phase ◽  
Production Wells ◽  
Range Of Values

AbstractThe unsteady Hele-Shaw problem is a model nonlinear system that, for a certain parameter ranger, exhibits the phenomenon known as viscous fingering. While not directly applicable to multiphase porous-media flow, it does prove to be an adequate mathematical model for unstable dieplacement in laboratory parallel-plate devices. We seek here to determine, by use of an accurate boundary-integral frount-tracking scheme, the extent to which the simplified system captures the canonical nonlinear behavior of displacement flows and, in particular, to ascertain the role of noise in such systems. We choose to study a particular pattern of injection and production “wells.” The pattern chosen is the isolated “five-spot,” that is a single source surrounded by four symmetrically-placed sinks in an infinite two-dimensional “reservoir.” In cases where the “pusher” fluid has negligible viscosity, sweep efficiency is calculated for a range of values of the single dimensionless parameter τ, an inverse capillary number. As this parameter is reduced, corresponding to increased flow rate or reduced interfacial tension, this efficiency decreases continuously. For small values of τ, these stable displacements change abruptly to a regime characterized by unstable competing fingers and a significant reduction in sweep efficiency. A simple stability argument appears to correctly predict the noise level required to transit from the stable to the competing-finger regimes. Published compilations of experimental results for sweep efficiency as a function of viscosity ratio showed an unexplained divergence when the pusher fluid is less viscous. Our simulations produce a similar divergence when, for a given viscosity ratio, the parameter τ is varied.

scholarly journals Nonlinear Dynamics of Sea Clutter

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Timothy R. Field ◽  
Simon Haykin
Keyword(s):  
Cross Section ◽  
Shape Parameter ◽  
Stochastic Dynamics ◽  
Nonlinear Behavior ◽  
Sea Clutter ◽  
Sea State ◽  
Theoretical Derivation ◽  
Radar Scattering ◽  
Points Of View

We review experimental evidence for the nonlinearity of sea clutter and the role of the z-parameter or Mann-Whitney rank-sum statistic in quantifying this nonlinear behavior in the context of a hybrid AM/FM model for sea clutter, viewed as a cyclostationary process. An independent theoretical derivation of the stochastic dynamics of radar scattering in a sea clutter environment, in terms of a pair of coupled stochastic differential equations for the received envelope and radar cross-section (RCS), enables the identification of nonlinearity in terms of the shape parameter for the RCS. We are led to conclude that, from both experimental and theoretical points of view, the dynamics of sea clutter are nonlinear with a consistent degree of nonlinearity that is determined by the sea state.

scholarly journals Predictability and Information Theory. Part II: Imperfect Forecasts

2005 ◽  
Vol 62 (9) ◽  
pp. 3368-3381 ◽  
Author(s):  
Timothy DelSole
Keyword(s):  
Information Theory ◽  
Mutual Information ◽  
Dimensional Space ◽  
Nonlinear Behavior ◽  
Potential Predictability ◽  
Low Dimensional ◽  
Lower Dimensional Space ◽  
True System ◽  
Normally Distributed

Abstract This paper presents a framework for quantifying predictability based on the behavior of imperfect forecasts. The critical quantity in this framework is not the forecast distribution, as used in many other predictability studies, but the conditional distribution of the state given the forecasts, called the regression forecast distribution. The average predictability of the regression forecast distribution is given by a quantity called the mutual information. Standard inequalities in information theory show that this quantity is bounded above by the average predictability of the true system and by the average predictability of the forecast system. These bounds clarify the role of potential predictability, of which many incorrect statements can be found in the literature. Mutual information has further attractive properties: it is invariant with respect to nonlinear transformations of the data, cannot be improved by manipulating the forecast, and reduces to familiar measures of correlation skill when the forecast and verification are joint normally distributed. The concept of potential predictable components is shown to define a lower-dimensional space that captures the full predictability of the regression forecast without loss of generality. The predictability of stationary, Gaussian, Markov systems is examined in detail. Some simple numerical examples suggest that imperfect forecasts are not always useful for joint normally distributed systems since greater predictability often can be obtained directly from observations. Rather, the usefulness of imperfect forecasts appears to lie in the fact that they can identify potential predictable components and capture nonstationary and/or nonlinear behavior, which are difficult to capture by low-dimensional, empirical models estimated from short historical records.

Nonlinear Stability of Thermoelastic Sliding Contact

2005 ◽  
Vol 74 (3) ◽  
pp. 595-598
Author(s):  
Jason D. Miller ◽  
D. Dane Quinn
Keyword(s):  
Multiple Scales ◽  
Dynamical Behavior ◽  
Stable State ◽  
Nonlinear Behavior ◽  
Sliding Contact ◽  
Stability Criteria ◽  
Multiple Scales Analysis ◽  
Two Equilibria

A model for sliding contact of a thermoelastic rod is considered and is subjected to a multiple scales analysis to uncover its nonlinear behavior near a neutrally stable state. The analysis reveals a combination of the contact resistance and frictional intensity that describes the generic unfolding of this critical state and its associated bifurcations. In particular, the system can describe how two equilibria coalesce in a saddle-node bifurcation and generalizes stability criteria that have been presented previously in the literature for this model. Moreover, this analysis describes the role of the initial deformation of the rod on its long-term dynamical behavior.

Nonlinear behavior of vocal fold vibration: The role of coupling between the vocal folds

1999 ◽  
Vol 13 (4) ◽  
pp. 465-476 ◽  
Author(s):  
Antoine Giovanni ◽  
Maurice Ouaknine ◽  
Bruno Guelfucci ◽  
Ping Yu ◽  
Michel Zanaret ◽  
...  
Keyword(s):  
Vocal Fold ◽  
Nonlinear Behavior ◽  
Vocal Folds ◽  
Vocal Fold Vibration
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