Dynamics of Oscillator With Soft Impacts

2001 ◽  
Author(s):  
František Peterka
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Mechanical System ◽  
Linear Model ◽  
Piecewise Linear ◽  
Impact Oscillator ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear System ◽  
New Phenomena ◽  
The Impact

Abstract The impact oscillator is the simplest mechanical system with one degree of freedom, the periodically excited mass of which can impact on the stop. The aim of this paper is to explain the dynamics of the system, when the stiffness of the stop changes from zero to infinity. It corresponds to the transition from the linear system into strongly nonlinear system with rigid impacts. The Kelvin-Voigt and piecewise linear model of soft impact was chosen for the study. New phenomena in the dynamics of motion with soft impacts in comparison with known dynamics of motion with rigid impacts are introduced in this paper.

ANALYTICAL SOLUTIONS OF SYSTEMS WITH PIECEWISE LINEAR DYNAMICS

2010 ◽  
Vol 20 (02) ◽  
pp. 509-518 ◽  
Author(s):  
Y. KOMINIS ◽  
T. BOUNTIS
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Piecewise Linear ◽  
Time Intervals ◽  
Linear Dynamics ◽  
Piecewise Linear System ◽  
Nonautonomous Dynamical Systems ◽  
Autonomous Component ◽  
Physical Phenomena ◽  
Linear Periodic System

A class of nonautonomous dynamical systems, consisting of an autonomous nonlinear system and an autonomous linear periodic system, each acting by itself at different time intervals, is studied. It is shown that under certain conditions for the durations of the linear and the nonlinear time intervals, the dynamics of the nonautonomous piecewise linear system is closely related to that of its nonlinear autonomous component. As a result, families of explicit periodic, nonperiodic and localized breather-like solutions are analytically obtained for a variety of interesting physical phenomena.

EFFECT OF ELEVATED TEMPERATURE ON CONCRETE STRUCTURES BY BOUNDARY ELEMENTS

2012 ◽  
Vol 09 (01) ◽  
pp. 1240014 ◽  
Author(s):  
PETR P. PROCHAZKA ◽  
TAT S. LOK
Keyword(s):  
Elevated Temperature ◽  
Boundary Element Method ◽  
Nonlinear System ◽  
Time Dependent ◽  
System Of Equations ◽  
Systems Of Equations ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear System ◽  
Long Time ◽  
Large Systems

Extreme elevation of temperature principally threatens tunnel linings and may cause fatal disaster; the recovery of it may take a long time and significant traffic troubles. System of equations is to be described and solution in terms of boundary element method (BEM) is suggested. Moreover, a technique of time-dependent eigenparameters enables one to apply parallel computations and converts the strongly nonlinear system to pseudo-linear one using the influence and polarization tensors. Consequently, instead of repeated solution of large systems of equations, the multiplication of pre-calculated influence matrices has to be carried out instead. In order to properly create the above-outlined procedure, internal cells are selected in the regions primarily connected by the change of temperature. Some examples follow the theory.

scholarly journals A Modified Lindstedt–Poincaré Method for a Strongly Nonlinear System with Quadratic and Cubic Nonlinearities

1996 ◽  
Vol 3 (4) ◽  
pp. 279-285 ◽  
Author(s):  
S.H. Chen ◽  
Y. K. Cheung
Keyword(s):  
Nonlinear System ◽  
Present Method ◽  
Nonlinear Oscillations ◽  
Perturbation Expansion ◽  
Nonlinear Characteristics ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear System ◽  
Strongly Nonlinear Oscillations ◽  
Quadratic And Cubic Nonlinearities

A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.

scholarly journals Iterative Ensemble Smoother as an Approximate Solution to a Regularized Minimum-Average-Cost Problem: Theory and Applications

SPE Journal ◽  
2015 ◽  
Vol 20 (05) ◽  
pp. 962-982 ◽  
Author(s):  
Xiaodong Luo ◽  
Andreas S. Stordal ◽  
Rolf J. Lorentzen ◽  
Geir Nævdal
Keyword(s):  
Nonlinear System ◽  
Average Cost ◽  
History Matching ◽  
Estimation Problem ◽  
Matching Problem ◽  
Strongly Nonlinear ◽  
System A ◽  
Ensemble Smoother ◽  
Strongly Nonlinear System ◽  
Iterative Ensemble Smoother

Summary The focus of this work is on an alternative implementation of the iterative-ensemble smoother (iES). We show that iteration formulae similar to those used by Chen and Oliver (2013) and Emerick and Reynolds (2012) can be derived by adopting a regularized Levenberg-Marquardt (RLM) algorithm (Jin 2010) to approximately solve a minimum-average-cost (MAC) problem. This not only leads to an alternative theoretical tool in understanding and analyzing the behavior of the aforementioned iES, but also provides insights and guidelines for further developments of the smoothing algorithms. For illustration, we compare the performance of an implementation of the RLM-MAC algorithm with that of the approximate iES used by Chen and Oliver (2013) in three numerical examples: an initial condition estimation problem in a strongly nonlinear system, a facies estimation problem in a 2D reservoir, and the history-matching problem in the Brugge field case. In these three specific cases, the RLM-MAC algorithm exhibits comparable or better performance, especially in the strongly nonlinear system.

scholarly journals Steady state response of a nonlinear system

1980 ◽  
Vol 3 (3) ◽  
pp. 535-547 ◽  
Author(s):  
Sudhangshu B. Karmakar
Keyword(s):  
Steady State ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Linear System ◽  
Linear Model ◽  
Series Solution ◽  
Steady State Response ◽  
State Response ◽  
Equivalent Linear Model

This paper presents a method of the determination of the steady state response for a class of nonlinear systems. The response of a nonlinear system to a given input is first obtained in the form of a series solution in the multidimensional frequency domain. Conditions are then determined for which this series solution will converge. The conversion from multidimensions to a single dimension is then made by the method of association of variables, and thus an equivalent linear model of the nonlinear system is obtained. The steady state response is then found by any technique employed with linear system.

Impact Severity in Drive Line Systems With Backlash

2009 ◽  
Author(s):  
Stijn Boere ◽  
Amit Shukla ◽  
Rob Fey ◽  
Henk Nijmeijer
Keyword(s):  
Linear System ◽  
Numerical Simulations ◽  
Transient Response ◽  
Piecewise Linear ◽  
Transient Behavior ◽  
Degree Of Freedom ◽  
Peak Acceleration ◽  
Step Input ◽  
Piecewise Linear System ◽  
The Impact

Numerical simulations are used to study the transient behavior of a four degree-of-freedom, rotational piecewise linear system. This study focusses on the impact between bodies in a system with backlash as a result of a sudden step input and the associated transient response. The subsequent Single Sided Impacts and Double Sided Impacts are studied as a function of the amplitude of the step input and the size of the backlash. Transitions have been observed between Double Sided Impact regions and Single Sided Impact regions which agree with earlier findings. However, in this paper a more complete overview of the boundaries is given. The severity of the impacts is quantified with the peak-to-peak acceleration of the impacting bodies. Increasing the size of the step input increases the severity of the impacts. However, increasing backlash size leads to an extremum in impact severity. This is a possible explanation for seeming contradictions in literature.

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