A Modified Newmark Scheme for Simulating Dynamical Behavior of MDOF Nonlinear Systems

Abstract Background In general, diagnostics can be defined as the procedure of mapping the information obtained in the measurement space to the presence and magnitude of faults in the fault space. These measurements, and especially their nonlinear features, have the potential to be exploited to detect changes in dynamics due to the faults. Purpose We have been developing some interesting techniques for fault diagnostics with gratifying results. Methods These techniques are fundamentally based on extracting appropriate features of nonlinear dynamical behavior of dynamic systems. In particular, this paper provides an overview of a technique we have developed called Phase Space Topology (PST), which has so far displayed remarkable effectiveness in unearthing faults in machinery. Applications to bearing, gear and crack diagnostics are briefly discussed.

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THE CONTROL OF STOCHASTIC COMPLEX DAMPED NONLINEAR SYSTEMS

International Journal of Modern Physics C ◽

10.1142/s0129183107011303 ◽

2007 ◽

Vol 18 (08) ◽

pp. 1263-1275 ◽

Cited By ~ 5

Author(s):

QUN HE ◽

YONG XU ◽

GAMAL M. MAHMOUD ◽

WEI XU

Keyword(s):

Lyapunov Exponent ◽

Nonlinear Systems ◽

Time Evolution ◽

Excellent Agreement ◽

Random Noise ◽

Dynamical Behavior ◽

Random Phase ◽

Phase Plot ◽

Periodic Attractors ◽

Map Analysis

The aim of this paper is to continue our investigations by studying complex damped nonlinear systems with random noise. The effect of random phase for these systems is examined. The interested system demonstrates unstable periodic attractors when the intensity of random noise equals zero, and we show that the unstable dynamical behavior will be stabilized as the intensity of random noise properly increases. The phase plot and the time evolution are carried out to confirm the obtained results of Poincaré map analysis and top Lyapunov exponent on the dynamical behavior of stability. Excellent agreement is found between these results.

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Changes in the dynamical behavior of nonlinear systems induced by noise

Physics Reports ◽

10.1016/s0370-1573(99)00043-5 ◽

2000 ◽

Vol 323 (1) ◽

pp. 1-80 ◽

Cited By ~ 78

Author(s):

P Landa

Keyword(s):

Nonlinear Systems ◽

Dynamical Behavior

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Changes in the dynamical behavior of nonlinear systems induced by high-frequency vibration or by noise

Foundations of Engineering Mechanics - Regular and Chaotic Oscillations ◽

10.1007/978-3-540-45252-2_14 ◽

2001 ◽

pp. 323-372

Author(s):

Polina S. Landa

Keyword(s):

Nonlinear Systems ◽

High Frequency ◽

Dynamical Behavior ◽

High Frequency Vibration

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Convergence and Stability of a Parametric Class of Iterative Schemes for Solving Nonlinear Systems

Mathematics ◽

10.3390/math9010086 ◽

2021 ◽

Vol 9 (1) ◽

pp. 86

Author(s):

Alicia Cordero ◽

Eva G. Villalba ◽

Juan R. Torregrosa ◽

Paula Triguero-Navarro

Keyword(s):

Nonlinear Systems ◽

Dynamical Behavior ◽

Order Convergence ◽

Hammerstein Integral Equation ◽

Iterative Schemes ◽

The Third ◽

The Family ◽

The Stability ◽

Theoretical Results ◽

Parametric Class

A new parametric class of iterative schemes for solving nonlinear systems is designed. The third- or fourth-order convergence, depending on the values of the parameter being proven. The analysis of the dynamical behavior of this class in the context of scalar nonlinear equations is presented. This study gives us important information about the stability and reliability of the members of the family. The numerical results obtained by applying different elements of the family for solving the Hammerstein integral equation and the Fisher’s equation confirm the theoretical results.

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