Investigation of Bending Vibrations in Voigt–Kelvin Bars with Regard for Nonlinear Resistance Forces
We present a procedure aimed at the qualitative investigation of the solution of a mathematical model of bending vibrations of viscoelastic bodies under the action of dissipative forces and nonlinear resistance forces in a bounded domain. This procedure is based of the general approaches of the theory of nonlinear boundary-value problems and the application of the Galerkin method and enables one to substantiate the correctness of the solution of the model and use approximate methods for its investigation.
KeywordsGalerkin Method Transverse Vibration Vibration System Qualitative Investigation Dissipative Force
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- 1.V. I. Erofeev, V. V. Kazhaev, and N. P. Semerikova, Waves in Rods. Dispersion. Dissipation. Nonlinearity [in Russian], Fizmatlit, Moscow (2002).Google Scholar
- 2.P. Ya. Pukach, “Mixed problem for a strongly nonlinear equation of the vibration mode of a beam in a bounded domain,” Prykl. Probl. Mekh. Mat., Issue 4, 59–69 (2006).Google Scholar
- 3.A. M. Slipchuk, “Investigation of the influence of compressive (tensile) forces on the nonlinear transverse vibrations of a beam,” Visn. Nats. Univ. “L’viv. Politekh.” Ser. Optymiz. Vyrobn. Prots. Tekh., Kontr. Mashynobud. Pryladobud., No. 713, 191–196 (2011).Google Scholar
- 4.B. I. Sokil, A. P. Senyk, I. I. Nazar, and M. B. Sokil, “Transverse vibrations of a nonlinearly elastic medium and the d’Alembert method for their investigation,” Visn. Nats. Univ. “L’viv. Politekh.” Ser. Dynam., Mitsn. Proekt. Mashyn Prylad., No. 509, 105–110 (2004).Google Scholar