Analytic Study of Linear and Nonlinear Mode Localization

1993 ◽  
Vol 60 (2) ◽  
pp. 555-557 ◽  
Author(s):  
A. F. Vakakis
Keyword(s):  
Nonlinear Systems ◽  
Analytical Method ◽  
Normal Modes ◽  
Nonlinear Stiffness ◽  
Mode Localization ◽  
Weakly Coupled ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems ◽  
Exact Analytical Method ◽  
Vibrating Systems

The localization of the normal modes of weakly coupled vibrating systems is examined with a new exact, analytical method. Both linear and nonlinear systems are considered and the mode localization is examined by means of “balancing diagrams.” This study complements previous studies of the author and co-workers on investigating mode localization in systems with nonlinear stiffness elements.

Mathematical modeling of conversion of non-Gaussian random processes, signals and noise in linear and nonlinear systems

2018 ◽  
pp. 66-78
Author(s):  
V. M. Artyushenko ◽  
V. I. Volovach
Keyword(s):  
Mathematical Modeling ◽  
Nonlinear Systems ◽  
Random Processes ◽  
Mathematical Transformation ◽  
Positive And Negative Feedback ◽  
Non Linear Systems ◽  
Linear And Nonlinear ◽  
Non Gaussian ◽  
Linear And Nonlinear Systems ◽  
Inertial Systems

The questions connected with mathematical modeling of transformation of non-Gaussian random processes, signals and noise in linear and nonlinear systems are considered and analyzed. The mathematical transformation of random processes in linear inertial systems consisting of both series and parallel connected links, as well as positive and negative feedback is analyzed. The mathematical transformation of random processes with polygamous density of probability distribution during their passage through such systems is considered. Nonlinear inertial and non-linear systems are analyzed.

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