Mathematical Modeling of Hydroelastic Interaction Between Stamp and Three-Layered Beam Resting on Winkler Foundation
The purpose of the article is to develop the mathematical model of bending oscillations of a three-layered beam, resting in Winkler foundation and interacting with a vibrating stamp through a thin layer of viscous incompressible liquid. The three-layered beam with incompressible lightweight filler by using broken normal hypothesis was considered. The bending oscillations equation of three-layered beam resting on Winkler foundation and interacting with vibrating stamp through viscous liquid layer is obtained. On the basis of plane hydroelasticity problem solution, the laws of the three-layered beam deflections and pressure in the liquid along the channel are found. The frequency dependent functions of the beam deflections amplitude distribution and liquid pressure along the channel are constructed. The obtained results allow to define oscillations resonance frequencies and to study tense-deformed state of three-layered beam, as well as, hydrodynamic parameters of viscous liquid interacting with vibrating stamp and three-layered beam, resting on Winkler foundation. The study was funded by Russian Foundation for Basic Research (RFBR) according to the projects № 18-01-00127-a and № 19-01-00014-a.
KeywordsHydroelasticity Three-layered beam Winkler foundation Viscous liquid Oscillations Vibrating stamp
The study was funded by Russian Foundation for Basic Research (RFBR) according to the projects № 18-01-00127-a and № 19-01-00014-a.
- 2.Gorshkov, A.G., Starovoitov, E.I., Yarovaya, A.V.: Mechanics of Layered Viscoelastoplastic Structural Elements. Fizmatlit, Moscow (2005). (in Russian)Google Scholar
- 3.Krylov, A.N.: On Analysis of Beams Lying on Elastic Base. Izd-vo AN SSSR. Leningrad (1931). (in Russian)Google Scholar
- 4.Pleskachevskii, Y.M., Starovoitov, E.I., Leonenko, D.V.: Mechanics of Three-Layer Beams and Plates Connected with an Elastic Foundation. Fizmatlit, Moscow (2011). (in Russian)Google Scholar
- 15.Velmisov, P.A., Ankilv, A.V.: Dynamic stability of plate interacting with viscous fluid. Cybern. Phys. 6(4), 262–270 (2017)Google Scholar
- 17.Ageev, R.V., Mogilevich, L.I., Popov, V.S., Popova, A.A., Kondratov, D.V.: Mathematical model of pulsating viscous liquid layer movement in a flat channel with elastically fixed wall. Appl. Math. Sci. 8(159), 7899–7908 (2014)Google Scholar
- 27.Ergin, A., Kutlu, A., Omurtag, M.H., Ugurlu, B.: Dynamics of a rectangular plate resting on an elastic foundation and partially in contact with a quiescent fluid. J. Sound Vib. 317(1–2), 308–328 (2008)Google Scholar
- 34.Gorshkov, A.G., Morozov, V.I., Ponomarev, A.T., Shklyarchuk, F.N.: Aerogidroelasticity of Designs. Fizmathlit, Moscow (2000). (in Russian)Google Scholar
- 35.Loitsyanskii, L.G.: Mechanics of Liquid and Gas. Drofa, Moscow (2003). (in Russian)Google Scholar