scholarly journals NONLINEAR DYNAMICS OF THE CONTACT INTERACTION OF A THREE-LAYER PLATE-BEAM NANOSTRUCTURE IN A WHITE NOISE FIELD

2018 ◽  
Vol 6 (2) ◽  
pp. 294-300
Author(s):  
T. V. Yakovleva ◽  
◽  
V. A. Krysko-jr ◽  
V. A. Krysko ◽  
◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
White Noise ◽  
Contact Interaction ◽  
Noise Field

scholarly journals Investigation of the Effect of Additive White Noise on the Dynamics of Contact Interaction of the Beam Structure

2019 ◽  
Author(s):  
Ольга Салтыкова ◽  
Olga Saltykova ◽  
Александр Кречин ◽  
Alexander Krechin
Keyword(s):  
Nonlinear Dynamics ◽  
White Noise ◽  
Contact Interaction ◽  
Geometric Nonlinearity ◽  
Chaotic Dynamics ◽  
Kutta Method ◽  
Beam Structure ◽  
Runge Kutta Method ◽  
Additive White Noise ◽  
The Finite Difference Method

The purpose of this work is to study and scientific visualization the effect of additive white noise on the nonlinear dynamics of beam structure contact interaction, where beams obey the kinematic hypotheses of the first and second approximation. When constructing a mathematical model, geometric nonlinearity according to the T. von Karman model and constructive nonlinearity are taken into account. The beam structure is under the influence of an external alternating load, as well as in the field of additive white noise. The chaotic dynamics and synchronization of the contact interaction of two beams is investigated. The resulting system of partial differential equations is reduced to a Cauchy problem by the finite difference method and then solved by the fourth order Runge-Kutta method.

On the maximum of random fields represented by stochastic integrals over circles

1987 ◽  
Vol 24 (03) ◽  
pp. 574-585 ◽  
Author(s):  
Enzo Orsingher
Keyword(s):  
White Noise ◽  
Upper Bound ◽  
Random Fields ◽  
Stochastic Integrals ◽  
Noise Field ◽  
Fixed Radius

In this paper we obtain an upper bound for the maximum of random fields of the form , where CP denotes circles of fixed radius and dW(P′) is a plane white noise field. The results presented are obtained by means of successive steps involving Slepian's lemma for random fields, inequalities on Brownian fields and planar stochastic integrals.

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