Geodesic
Investigation of the transient responses of a beam on an elastic polymeric foundation
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 1, pp. 97-105 Cet article a éte moissonné depuis la source Math-Net.Ru

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The negative impact of vibrations on various devices and mechanisms can be significant, so it is important to take this factor into account when designing, operating and maintaining various equipment and engineering systems. Various methods and technologies can be used to protect against the negative effects of vibrations. Special damping materials are often used. This research paper is devoted to the analysis of the effectiveness of vibration reduction taking into account the physical parameters of elastic polymeric materials. To conduct the study, a mathematical model describing motion of the beam resting on an elastic polymeric foundation is constructed. The model is based on a system of nonlinear differential equations. An algorithm was developed and applied for the numerical solution of this system of equations. Numerical experiments were carried out for the study of the system reaction to different cases of accelerations. As a result, the deflection structure for materials with different physical characteristics were obtained. These results can serve as a starting point for a deeper study of materials and creation of more complex structures.
Keywords: transient responses, elastic polymeric foundation, nonlinear differential equation, Galerkin method. 
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A. D. Kashcheeva; A. A. Zamyshlyaeva. Investigation of the transient responses of a beam on an elastic polymeric foundation. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 1, pp. 97-105. http://geodesic.mathdoc.fr/item/VYURU_2024_17_1_a8/

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