The Unsteady Contact Interaction Problem of an Absolutely Rigid Body and a Membrane
This article investigates the vertical impact of an absolutely rigid body (indenter) on a membrane. The supersonic (initial) and subsonic stages of unsteady interaction are considered. The solution at the initial stage of contact interaction is reduced to solving a differential equation. A resolving system of equations was obtained for the problem at subsonic stage. The Green’s function for the membrane is found and a numerical-analytical algorithm is constructed to solve the system. The unknown functions calculation results are presented in the graph form.
KeywordsSuperposition method Transient function Laplace and fourier integral transforms Membrane Absolutely rigid body Unsteady contact problem
The authors would like to acknowledge the financial support of the Russian Foundation for Basic Research (project № 19-08-01023 A).
- 1.Gorshkov, A.G., Medvedsky, A.L., Rabinsky, L.N., Tarlakovsky, D.V.: Waves in Continuum Media. Fizmatlit, Moscow (2004). (in Russian)Google Scholar
- 2.Gorshkov, A.G., Tarlakovsky, D.V.: Dynamic Contact Problems with Moving Boundaries. Fizmatlit, Moscow (1995). (in Russian)Google Scholar
- 3.Mikhailova, E.Y., Tarlakovskii, D.V., Fedotenkov, G.V.: Transient Contact Problem for Liquid Filled Concentric Spherical Shells and a Rigid Barrier. In: Proceedings of the First International Conference on Theoretical, Applied and Experimental Mechanics, 385–386 (2018)Google Scholar
- 4.Fedotenkov, G.V., Mikhailova, E.Y., Kuznetsova, E.L., Rabinskiy, L.N.: Modeling the unsteady contact of spherical shell made with applying the additive technologies with the perfectly rigid stamp. Int. J. Pure Appl. Math. 111(2), 331–342 (2016)Google Scholar