Abstract
The article presents a mathematical simulation of interaction between a plate and a beam locally supporting the plate in its center. The system is exposed to an external transverse load and external additive colored noise (pink, red, white). The structure is located in a steady temperature field, accounted for in the Duhamel-Neumann theory by solving 3D (plate) and 2D (beam) heat conduction equations, using finite difference method (FDM). Heat transfer between the plate and the beam is disregarded. Kirchhoff simulation was used for the plate and the Euler–Bernoulli simulation was used for the beam. The mathematical simulation accounts for physical nonlinearity in elastically deformable materials. B. Y. Kantor’s theory is applied to simulate contact interaction. The differential equation set is reduced to the Cauchy problem, using the highest-approximation Bubnov–Galerkin methods or spatial-variable FDM. The Cauchy problem is solved using the fourth-order Runge–Kutta or Newmark method. I. A. Birger’s iterative procedure is used at each time step for analyzing a physically nonlinear problem. Numeric results are analyzed using the methods of nonlinear dynamics (signal patterning, phase portraits, Poincaré sections, Fourier and Wavelet power spectra, analysis of the Lyapunov exponents using the Wolf, Kantz, and Rosenstein methods). The convergence of the methods is studied. Different methods are used to obtain reliable results. Numerical results on the effect of colored noise on plate–beam interaction are presented. Additive red noise shows more significant effect on the vibrations and the plate–beam interaction than white and pink noises.
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The Russian Science Foundation (project No. 15- 19-10039-P) financially supported this work.
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Bazhenov, V.G., Yakovleva, T.V., Krysko, V.A. (2020). Mathematical Simulation of the Plate–Beam Interaction Affected by Colored Noise. In: Altenbach, H., Eremeyev, V., Pavlov, I., Porubov, A. (eds) Nonlinear Wave Dynamics of Materials and Structures. Advanced Structured Materials, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-030-38708-2_4
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