Frequency equations of small oscillations mixed systems of the coupled discrete and continuous subsystems

Abstract

In this paper, by using examples of mixed systems of the coupled discrete subsystem of rigid bodies and continuous subsystem, the method of obtaining; of small oscillations frequency equations are presented. Small oscillations frequency equations of coupled deformable body and holonomic conservative systems are obtained. By using numerical experiment connections between own small oscillations circular frequencies of the mixed system and subsystem of the rigid bodies and deformable body are studied and analyzed. By using MathCAD program graphical presentations of a set of small oscillations circular frequencies of the deformable body with "perturbations"caused on interaction of subsystem small oscillations of rigid bodies. By using examples, analogy between frequency equations of some classes of these systems is identified. Special cases of discretization and continualization of coupled subsystems with corresponding sets of proper circular frequencies and frequency equations of small oscillations are analyzed.