The motion of an absolutely rigid biaxial trolley with an elastic body along a double rail curvilinear track

The research deals with the unsteady motion of an elastic body located on an absolutely rigid trolley moving on the elastic rollers along an arbitrary curvilinear track with two equidistant guide rails. The track is defined by the equations of bending and torsion of its midline. The contact between the trolley and the rails is carried out through the nonlinear elastic rollers of rear drive axle, rigidly connected with the trolley, and those of the front axle, coupled with it in the middle by the spherical hinge. We developed a new nonlinear mathematical model for calculating the relative and portable motions of a trolley with an elastic body along the surface and defined contact reactions and overloads. Initially, we conducted a geometric modeling of kinematic motion of a biaxial trolley, where the distance between the axes is considered to be small in comparison with the curvature radius of the trolley centerline. Next, we obtained the relations allowing us to further consider the curvature of the midline between the axes of the trolley. Then, we described dynamics of the relative motion of an elastic body on the trolley by finite deformations in the quadratic approximation. Finally, we worked out equations of system motion taking into account the nonlinear elasticity and damping of the rollers, on which the trolley slides along the surface at a predetermined speed or under a given traction.

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