A mathematical model and data visualization of contact interaction between a plate and a beam under the action of external transverse load and external additive color noise is constructed. The construction is in a stationary temperature field, the effect of which is taken into account according to the theory of Duhamel Neumann by solving the three-dimensional and two-dimensional heat conduction equations by the finite difference method, the heat exchange between the plate and the beam is not taken into account. The plate is subject to the Kirchhoff model, and the beam to the Euler- Bernoulli model. The mathematical model takes into account the physical nonlinearity of the elastically deformable material. Contact interaction is taken into account according to the theory of Kantor. The system of differential equations is reduced to the Cauchy problem by the Bubnov-Galerkin method in higher approximations in spatial variables. The Cauchy problem is solved by the Runge-Kutta method of the fourth order of accuracy. To solve the physically nonlinear problem, at each time step, an Birger iterative procedure was applied. The visualization of the results of a numerical experiment was carried out using the methods of nonlinear dynamics and using wavelet analysis. The numerical results of the effect of color noise on the contact interaction between the plate and the beam are given. It has been established that red additive noise has a more significant effect on the oscillation pattern of the lamellar-beam structure in comparison with pink and white noise.

data visualization, plate, beam, contact interaction

Yakovleva Tatyana Vladimirovna,  yan-tan1987@mail.ru,  Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny Novgorod; Yuri Gagarin State Technical University of Saratov

Bazhenov Valentin Georgievich,  bazhenov@mech.unn.ru,  Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny Novgorod

Krysko Vadim Anatolyevich,  tak@san.ru,  Yuri Gagarin State Technical University of Saratov