Limit Equations of Motion for Mechanical Systems with Vibrating Elements / A. A. Markeeva and M. A. Levin. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 5. P. 23-33 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 112-121].

Mechanical systems with vibrating elements are studied. A method of finding the limit equations for such systems is proposed when the oscillation frequency tends to infinity. A mechanical system with an arbitrary number of degrees of freedom is considered. This system is subject to rapid periodic vibrations with zero mean. Its motion can be described by second-order equations. An explicit form of limit equations of motion is obtained as a system of first-order differential equations.

Key words: mechanical systems with vibrating elements, limiting equations, convergence of solutions, pendulum with a vibrating suspension point.