Measurement of the multivalued phase curves of a strongly nonlinear system by fixed frequency tests

2020 ◽  
Vol 90 (11) ◽  
pp. 2543-2560
Author(s):  
Genbei Zhang ◽  
Chaoping Zang ◽  
Michael I. Friswell
Keyword(s):  
Nonlinear System ◽  
Fixed Frequency ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear System

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.

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.

Response statistics of strongly nonlinear system to random narrowband excitation

2006 ◽  
Vol 291 (3-5) ◽  
pp. 1261-1268
Author(s):  
Xiaoli Yang ◽  
Wei Xu ◽  
Zhongkui Sun
Keyword(s):  
Nonlinear System ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear System

scholarly journals Periodic Solution of the Strongly Nonlinear Asymmetry System with the Dynamic Frequency Method

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 676 ◽  
Author(s):  
Zhiwei Zhang ◽  
Yingjie Wang ◽  
Wei Wang ◽  
Ruilan Tian
Keyword(s):  
Nonlinear System ◽  
Numerical Solutions ◽  
Harmonic Balance Method ◽  
Conservative System ◽  
Balance Method ◽  
Frequency Method ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear System ◽  
Derivatives Of ◽  
Dynamic Frequency

In this article, we present a new accurate iterative and asymptotic method to construct analytical periodic solutions for a strongly nonlinear system, even if it is not Z2-symmetric. This method is applicable not only to a conservative system but also to a non-conservative system with a limit cycle response. Distinct from the general harmonic balance method, it depends on balancing a few trigonometric terms (at most five terms) in the energy equation of the nonlinear system. According to this iterative approach, the dynamic frequency is a trigonometric function that varies with time t, which represents the influence of derivatives of the higher harmonic terms in a compact form and leads to a significant reduction of calculation workload. Two examples were solved and numerical solutions are presented to illustrate the effectiveness and convenience of the method. Based on the present method, we also outline a modified energy balance method to further simplify the procedure of higher order computation. Finally, a nonlinear strength index is introduced to automatically identify the strength of nonlinearity and classify the suitable strategies.

scholarly journals The Poincaré method for an oscillator with quadratic nonlinearity

2004 ◽  
Vol 26 (1) ◽  
pp. 23-30
Author(s):  
Nguyen Van Dinh ◽  
Tran Duong Tri
Keyword(s):  
Nonlinear System ◽  
Free Oscillation ◽  
Second Harmonic ◽  
Oscillation Period ◽  
Quadratic Nonlinearity ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear System

In [2], to evaluate free oscillation period of an undamped oscillator with large cubic restoring nonlinearity, a modified Poincare method has been proposed. There, in the neighborhood of the free oscillation of interest, the strongly nonlinear system under consideration is assumed to be near certain linear one with unknown (to be evaluated) frequency. In the present paper, we deal with the case of quadratic non-linearity. An additional modification is introduced consisting in the elimination of constant derivation and second harmonic terms. The results obtained show that the domain of application of the Poincare method can be enlarged.

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