Parameters of the periodic response of a system with friction-affected constraints and harmonic excitation
A single degree of freedom system acted upon by a harmonic force is investigated with several friction-affected constraints. Because of the dependence of friction on the joint reactions and of special effects (as sticking and slipping) induced by friction, it is possible to obtain the solution by numerical and iterative methods. The system is a determinate structure, and no other circumstances necessitate to take into account deformations of the system's parts. The friction coefficients are assumed to be functions of the relative velocities of the parts in question. Author applies in the course of the numerical solution of the differential equations a so-called stopping check: if for a moment \(t_ i\) \(q(t_ i)=0\) (\(q\) is the generalized coordinate) stopping occurs; if \(\ddot q(t_ i)=0\) the system sticks; if \(\ddot q(t_ i)\neq 0\), the system slips. In the case of sticking, the time delay is calculated, when again motion begins. It is shown how the sticking properties and motion resistances due to friction can be calculated. Response of the system is called to be periodic and having constant amplitude, when relative period and amplitude changes remain about a prescribed error. A special numerical example (using a special velocity dependence of the kinetic friction coefficients) shows a number of possible peculiarities, because complexity of the task doesn't allow to take general statements. Important conclusions are drawn; the most important is: an ``equivalent'' damping cannot be given generally, and abandoning of the friction makes impossible the precise study of this motion.
scientific article; zbMATH DE number 63823