Abstract:
This paper studies mechanical systems with rapidly oscillating elements. We suggested a method to obtain limiting equations of such systems when the oscillation frequency tends to infinity. We considered a mechanical system with an arbitrary number of degrees of freedom subject to rapid periodic vibrations with zero mean. Its motion can be described by second-order equations. Also we obtained an explicit form of the limiting equations of motion written in the form of 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.