Vibration of a Nonlinear System During Acceleration Through Resonance

1948 ◽  
Vol 15 (1) ◽  
pp. 21-24
Author(s):  
R. B. Meuser ◽  
E. E. Weibel
Keyword(s):  
Nonlinear System ◽  
Linear Systems ◽  
Critical Speed ◽  
Wave Force ◽  
Generalized Solution ◽  
Sine Wave ◽  
Mass System ◽  
Linear Damping ◽  
Mathematical Machine

Abstract During acceleration of a machine through a critical speed, displacements and stresses may attain large values. For linear systems F. M. Lewis (1), and J. G. Baker (2) have studied different aspects of this problem, the former analytically, the latter by mathematical-machine methods. This paper presents a generalized solution obtained on the mechanical analyzer (3) for the effect of an accelerated sine-wave force on a spring-mass system having linear plus cubic elasticity and linear damping. The range of accelerations covered applies to electrically driven reciprocating machines and to other rapid starting units. Some interesting effects of nonlinearity on displacements and forces are pointed out.

Analysis of Piecewise Linear Systems With Displacement and Time Regions by Vector Fields

1999 ◽  
Author(s):  
Mikio Nakai ◽  
Shinji Murata ◽  
Seiji Hagio
Keyword(s):  
Linear Systems ◽  
Vector Fields ◽  
Matrix Representation ◽  
Piecewise Linear ◽  
Generalized Solution ◽  
State Variables ◽  
Piecewise Linear Systems ◽  
Restoring Forces ◽  
Pass Through ◽  
Solution Methodology

Abstract A generalized solution methodology based on piecewise linear vector fields is proposed for piecewise linear systems with singular regions or asymmetric restoring forces which vary spatially and temporally. In matrix representation for these systems, state variables in each region can be explicitly expressed as a function of the time the orbit spends between two boundaries or the time the orbit takes to pass through the boundary. The time can be determined by the Brent method, and periodic solutions can then be obtained. Analytical solutions are validated on a system with 3-regions of displacement and 2-regions of time, a circumferential vibration of gear meshing system, by using the newly developed numerical method.

Nonlinear System Identification in Offshore Structural Reliability

1995 ◽  
Vol 117 (3) ◽  
pp. 171-177 ◽  
Author(s):  
P. D. Spanos ◽  
R. Lu
Keyword(s):  
System Identification ◽  
Nonlinear System ◽  
Structural Reliability ◽  
Transfer Functions ◽  
Nonlinear System Identification ◽  
Simulated Data ◽  
Wave Force ◽  
Ocean Waves ◽  
Offshore Structures ◽  
Analysis And Design

Nonlinear forces acting on offshore structures are examined from a system identification perspective. The nonlinearities are induced by ocean waves and may become significant in many situations. They are not necessarily in the form of Morison’s equation. Various wave force models are examined. The force function is either decomposed into a set of base functions or it is expanded in terms of the wave and structural kinematics. The resulting nonlinear system is decomposed into a number of parallel no-memory nonlinear systems, each followed by a finite-memory linear system. A conditioning procedure is applied to decouple these linear sub-systems; a frequency domain technique involving autospectra and cross-spectra is employed to identify the linear transfer functions. The structural properties and the force transfer parameters are determined with the aid of the coherence functions. The method is verified using simulated data. It provides a versatile and noniterative approach for dealing with nonlinear interaction problems encountered in offshore structural analysis and design.

scholarly journals Brain Activation in Primary Motor and Somatosensory Cortices during Motor Imagery Correlates with Motor Imagery Ability in Stroke Patients

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Linda Confalonieri ◽  
Giuseppe Pagnoni ◽  
Lawrence W. Barsalou ◽  
Justin Rajendra ◽  
Simon B. Eickhoff ◽  
...  
Keyword(s):  
Motor Imagery ◽  
Brain Activity ◽  
Premotor Cortex ◽  
Region Of Interest ◽  
Wave Force ◽  
Sine Wave ◽  
Lower Percentage ◽  
Imagery Ability ◽  
Motor Execution ◽  
Stroke Patients

Aims. While studies on healthy subjects have shown a partial overlap between the motor execution and motor imagery neural circuits, few have investigated brain activity during motor imagery in stroke patients with hemiparesis. This work is aimed at examining similarities between motor imagery and execution in a group of stroke patients. Materials and Methods. Eleven patients were asked to perform a visuomotor tracking task by either physically or mentally tracking a sine wave force target using their thumb and index finger during fMRI scanning. MIQ-RS questionnaire has been administered. Results and Conclusion. Whole-brain analyses confirmed shared neural substrates between motor imagery and motor execution in bilateral premotor cortex, SMA, and in the contralesional inferior parietal lobule. Additional region of interest-based analyses revealed a negative correlation between kinaesthetic imagery ability and percentage BOLD change in areas 4p and 3a; higher imagery ability was associated with negative and lower percentage BOLD change in primary sensorimotor areas during motor imagery.

scholarly journals Assessment of Effects of a Delay Block and a Nonlinear Block in Systems with Chaotic Behavior Using Lyapunov Exponents

Ingeniería ◽  
2017 ◽  
Vol 22 (2) ◽  
pp. 240
Author(s):  
Pablo César Rodríguez Gómez ◽  
Maikoll Andres Rodriguez Nieto ◽  
Jose Jairo Soriano Mendez
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Linear Systems ◽  
Lyapunov Exponents ◽  
Chaotic Behavior ◽  
Structural Characteristics ◽  
Largest Lyapunov Exponent ◽  
Nonlinear Characteristic ◽  
Feedback Systems ◽  
Contour Plots

Context: Because feedback systems are very common and widely used, studies of the structural characteristics under which chaotic behavior is generated have been developed. These can be separated into a nonlinear system and a linear system at least of the third order. Methods such as the descriptive function have been used for analysis.Method: A feedback system is proposed comprising a linear system, a nonlinear system and a delay block, in order to assess his behavior using Lyapunov exponents. It is evaluated with three different linear systems, different delay values and different values for parameters of nonlinear characteristic, aiming to reach chaotic behavior.Results: One hundred experiments were carried out for each of the three linear systems, by changing the value of some parameters, assessing their influence on the dynamics of the system. Contour plots that relate these parameters to the Largest Lyapunov exponent were obtained and analyzed.Conclusions: In spite non-linearity is a condition for the existence of chaos, this does not imply that any nonlinear characteristic generates a chaotic system, it is reflected by the contour plots showing the transitions between chaotic and no chaotic behavior of the feedback system.Language: English  

Identification and control of nonlinear systems using PieceWise Auto-Regressive eXogenous models

2019 ◽  
Vol 41 (14) ◽  
pp. 4050-4062
Author(s):  
Zeineb Lassoued ◽  
Kamel Abderrahim
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Linear Systems ◽  
Experimental Results ◽  
Pole Placement ◽  
Nonlinear Behaviour ◽  
Auto Regressive ◽  
Identification Approach ◽  
Arbitrary Precision ◽  
And Control

In this paper, we consider the problems of nonlinear system representation and control. In fact, we propose a solution based on PieceWise Auto-Regressive eXogenous (PWARX) models since these models are able to approximate any nonlinear behaviour with arbitrary precision. Moreover, the identification and control approaches of linear systems can be extended to these models because the parameters of each sub-model are linearly related to the output. The proposed solution is based on two steps. The first allows to represent the nonlinear system by a PWARX model using the identification approach. The second consists in designing a controller for each sub-model using the pole placement strategy. Simulation and experimental results are presented to illustrate the performance of the proposed approach.

Non-linear disturbance observer-based adaptive composite anti-disturbance control for non-linear systems with dynamic non-harmonic multisource disturbances

2017 ◽  
Vol 40 (12) ◽  
pp. 3458-3465 ◽  
Author(s):  
Zheng Wang ◽  
Jianping Yuan
Keyword(s):  
Linear Systems ◽  
Disturbance Observer ◽  
Control Structure ◽  
Non Linear ◽  
Linear Damping ◽  
Non Linear Systems ◽  
Complex Features ◽  
The Stability ◽  
Linear Disturbance ◽  
Adaptive Composite

In this paper, an adaptive composite anti-disturbance control structure is constructed for a class of non-linear systems with dynamic non-harmonic multisource disturbances. The key point of this paper is that a kind of non-harmonic disturbance, which has non-linear internal dynamics and complex features, is involved. A non-linear exogenous system is employed to describe the dynamic non-harmonic disturbances and several useful assumptions are introduced. By introducing a non-linear damping term, a novel adaptive non-linear disturbance observer is constructed. Based on the disturbance/uncertainty estimation and attenuation (DUEA) schemes, a composite anti-disturbance control structure is synthesized. Meanwhile, a new sufficient condition is derived and the stability of the closed-loop system is proved. Several illustrative examples are employed to demonstrate the effectiveness of the proposed method.

scholarly journals Modal Appropriation for Use with In-Operation Modal Analysis

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
M. Abdelghani ◽  
D. J. Inman
Keyword(s):  
Experimental Data ◽  
Phase Shift ◽  
Modal Analysis ◽  
Impulse Response ◽  
Simulated Data ◽  
Wave Force ◽  
Sine Wave ◽  
Subspace Method ◽  
Characteristic Frequencies ◽  
System Output

We propose in this paper a numerical modal appropriation method for use with in-operation modal analysis (INOPMA). The key idea is to realize that the correlation sequence of the system output is the sum of decaying sinusoids with a certain phase shift and therefore it may be considered as an impulse response. The method is based on performing a numerical convolution of a single sine wave force with the system output correlation sequence. The steps are then similar to the classical modal appropriation method, although the characteristic frequencies are different. This approach is validated and compared to a subspace method on simulated data as well as on experimental data and it is shown that INOPMA outperforms the subspace method.

scholarly journals Parametric Excitation of a Nonlinear System

1965 ◽  
Vol 32 (4) ◽  
pp. 899-902 ◽  
Author(s):  
W. K. Tso ◽  
T. K. Caughey
Keyword(s):  
Nonlinear System ◽  
Linear Systems ◽  
Parametric Excitation ◽  
Higher Order ◽  
Non Linear ◽  
Non Linear Systems

A study has been made on the parametric excitation of a nonlinear system with hardening springs. In the parametric excitation of linear systems, the only subharmonic predicted is a subharmonic of order 1/2. However, in the parametric excitation of non-linear systems, it is shown that higher order subharmonics can exist, depending both on the amplitude and frequency of the parametric excitation.

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