Non-Gaussian additive and multiplicative noise-induced chaos in the lateral vibration of a viscoelastic plate: A fully analytic approach

2020 ◽  
pp. 107754632097137
Author(s):  
Ali Reza Asnafi
Keyword(s):  
Analytical Approach ◽  
Multiplicative Noise ◽  
Chaotic Behavior ◽  
Viscoelastic Plate ◽  
Equation Of Motion ◽  
Lateral Vibration ◽  
Bounded Noise ◽  
Noise Characteristics ◽  
Additive And Multiplicative Noise ◽  
Non Gaussian

In this study, the chaotic behavior of a viscoelastic plate under integrated non-Gaussian additive and multiplicative bounded noise is investigated with an analytical approach. First, the governing equation of motion of the system was derived by introducing a set of dimensionless parameters. After that, the modified version of Melinkov’s function in terms of statistical indices was obtained, and then, for a spectrum of bounded noises, the boarder curves of chaotic areas were obtained. The model of sine/cosine Wiener was chosen for the bounded noise which enables the researcher to produce a range of wide and narrowband noises. For the case that the excitation is only additive, or only multiplicative, and that both excitations exist simultaneously, the effect of variations in structural properties and noise characteristics on the chaos area were investigated. It was shown that at frequencies close to the natural frequency of the corresponding linear system, narrowband excitations affected the chaotic behavior more than the wideband ones and vice versa. To validate the results, a numerical simulation was also made.

scholarly journals Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1329
Author(s):  
Lev Ryashko ◽  
Dmitri V. Alexandrov ◽  
Irina Bashkirtseva
Keyword(s):  
Multiplicative Noise ◽  
Nonlinear Dynamical Systems ◽  
Stochastic Theory ◽  
Slow Variable ◽  
Theoretical Description ◽  
Mathematical Study ◽  
Stochastic Generation ◽  
Nonlinear Dynamical ◽  
Additive And Multiplicative Noise ◽  
And Shifts

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.

scholarly journals GPS Signal Detection under Multiplicative and Additive Noise

2012 ◽  
Vol 66 (4) ◽  
pp. 479-500 ◽  
Author(s):  
P. Huang ◽  
Y. Pi ◽  
I. Progri
Keyword(s):  
Signal Detection ◽  
Urban Areas ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Power Level ◽  
Signal Propagation ◽  
Signal Acquisition ◽  
Detection Scheme ◽  
Additive And Multiplicative Noise ◽  
Gps Signal Acquisition

In some Global Positioning System (GPS) signal propagation environments, especially in the ionosphere and urban areas with heavy multipath, GPS signal encounters not only additive noise but also multiplicative noise. In this paper we compare and contrast the conventional GPS signal acquisition method which focuses on handling GPS signal acquisition with additive noise, with the enhanced GPS signal processing under multiplicative noise by proposing an extension of the GPS detection mechanism, to include the GPS detection model that explains detection of the GPS signal under additive and multiplicative noise. For this purpose, a novel GPS signal detection scheme based on high order cyclostationarity is proposed. The principle is introduced, the GPS signal detection structure is described, the ambiguity of initial PseudoRandom Noise (PRN) code phase and Doppler shift of GPS signal is analysed. From the simulation results, the received GPS signal at low power level, which is degraded by additive and multiplicative noise, can be detected under the condition that the received block of GPS data length is at least 1·6 ms and sampling frequency is at least 5 MHz.

An equation of motion for a thick viscoelastic plate

1992 ◽  
Vol 13 (5) ◽  
pp. 477-486 ◽  
Author(s):  
Yang Zheng-wen ◽  
Yang Ting-qing
Keyword(s):  
Viscoelastic Plate ◽  
Equation Of Motion

Vibrations and Dynamic Response of Viscoelastic Plates on Nonperiodic Elastic Supports

1977 ◽  
Vol 99 (2) ◽  
pp. 404-409 ◽  
Author(s):  
K. Nagaya
Keyword(s):  
Elastic Plate ◽  
Correspondence Principle ◽  
Impact Load ◽  
Viscoelastic Model ◽  
Viscoelastic Plate ◽  
Equation Of Motion ◽  
Bending Moments ◽  
Elastic Supports ◽  
The Laplace Transform ◽  
Continuous Plate

This paper discusses the vibration and transient response problems of nonperiodically elastic supported viscoelastic continuous plate. The three-element viscoelastic model is adopted in the analysis. The solution for the plate is obtained from the correspondence principle by applying the Laplace transform to the constitutive equation and the equation of motion for the elastic plate. Expressions of displacements and bending moments for an impact load are obtained, and the results for the viscoelastic plate are compared with those for the elastic plate.

scholarly journals A THEORETICAL APPROACH FOR PARETO–ZIPF LAW

2008 ◽  
Vol 19 (08) ◽  
pp. 1175-1181
Author(s):  
ÇAĞLAR TUNCAY
Keyword(s):  
Theoretical Approach ◽  
Analytical Approach ◽  
Multiplicative Noise ◽  
Zipf Law ◽  
Fragmentation Processes

We suggest an analytical approach for the Pareto–Zipf law, where we assume random multiplicative noise and fragmentation processes for the growth of the number of citizens of each city and the number of the cities, respectively.

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