Sliding of a solid body supported by a round platform on a horizontal plane with orthotropic friction. Part 1. Regular load distribution

Motion of a thin elliptic plate under symmetric and asymmetric orthotropic friction forces

“…where m is a mass of the plate, ρ is a mass density of the plate, e is an ellipse eccentricity, p is a value of uniformly distributed pressure, g is the acceleration of free fall. Let's find integration ranges in (8). We introduce angle Ψ = π 2 + ϑ − ϕ (see fig.…”

“…Tables 1 and 2 show the way how equations (13) are divided into several parts. Thus, finally, we achieve equations for friction force projections in the case of instantaneous velocity center lies outside area covered by the plate in the following form: 6,8,13,14 velocities are directed to all 4 quadrants.…”

“…Thus, we should solve equations (22) and (24) to find ϑ * , δ * . Furthermore, because there is a strict dependence of plate motion on interrelations between inertia moment and friction coefficients (see, for example, [8]) we should all the time check solution in both regions. Let's get back to system (5).…”

“…We attempt to finalize our work done during last years. We investigated a circular area with symmetric orthotropic friction and uniform pressure distribution in [8], an elliptic area with symmetric orthotropic friction and uniform pressure distribution in [12] and linear pressure distribution in [11], a mass point with asymmetric friction in [9], a mass point and elliptic plate with asymmetric friction in [20] and a ring with asymmetric friction in [10].…”

“…We attempt to finalize the work we have done during the last few years. We investigated a circular area with symmetric 2 O Silantyeva and N Dmitriev orthotropic friction and uniform pressure distribution in [18], an elliptic area with symmetric orthotropic friction and uniform pressure distribution in [19], linear pressure distribution in [20], a mass point with asymmetric friction in [21], a mass point and elliptic plate with asymmetric friction in [22] and a ring with asymmetric friction in [23]. In these works, we considered different analytic approaches to find out the friction force and friction moment and finally came to the idea that the method presented in the current paper was most suitable for studying the asymmetry of friction.…”