Geodesic
Dynamics of a Crankshaft Mechanism under the Pressure of a Viscous Gas
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected issues of mathematics and mechanics, Tome 310 (2020), pp. 237-266

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We study an initial–boundary value problem with free boundary for one-dimensional equations of viscous gas dynamics. The problem models the motion of a crankshaft mechanism under gas pressure. It is assumed that the gas fills a cylinder, which is modeled by the interval $[0,1]$. A variable point $a(t)\in [0,1]$ models a piston moving inside the cylinder. The piston is assumed to be connected to a planar three-link crankshaft mechanism. We also assume that a velocity distribution on the boundary of the cylinder and a density distribution on gas inflow segments are given. The gas motion is described by the one-dimensional Navier–Stokes equations of viscous compressible fluid dynamics. It is required to determine the joint motion of the gas and crankshaft mechanism. We prove that this problem has a weak renormalized solution.
Mots-clés : viscous gas
Keywords: inhomogeneous boundary conditions, weak solutions, crankshaft mechanism. 
@article{TM_2020_310_a17,
     author = {P. I. Plotnikov and J. Soko{\l}owski},
     title = {Dynamics of a {Crankshaft} {Mechanism} under the {Pressure} of a {Viscous} {Gas}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {237--266},
     publisher = {mathdoc},
     volume = {310},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2020_310_a17/}
}
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P. I. Plotnikov; J. Sokołowski. Dynamics of a Crankshaft Mechanism under the Pressure of a Viscous Gas. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected issues of mathematics and mechanics, Tome 310 (2020), pp. 237-266. http://geodesic.mathdoc.fr/item/TM_2020_310_a17/