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Regularity of Solutions to Dynamic Contact Problems

Barboteu M., Sofonea M.

Machine Dynamics Research

2010

Vol. 34, No. 1

5-13

We investigate the regularity in time of solutions of two dynamic frictionless contact problems. The first problem describes the vibration of a mass-spring system and the second one concerns the contact of an elastic rod. In both models the contact is described with normal compliance. We show that the regularity of the normal compliance function determines the regularity of the solution.

Free longitudinal vibrations of an elastically connected double – rod system

Oniszczuk Z.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

2005

z. 65 [222]

303-310

In this work, the theoretical longitudinal vibration analysis of an elastically connected double-rod system is presented. The double-rod system is the model of a complex continuous system, which is composed of two straight, uniform elastic rods attached together by a Winkler elastic layer. The motion of the system is described by a coupled set of two non-homogeneous partial differential equations, which can be solved by using the classical mathematical methods. Solutions of undamped free vibrations are formulated by applying the modal expansion method. Two infinite sequences of the natural frequencies and corresponding mode shape functions expressing synchronous and asynchronous vibrations of the system are determined. The initial-value problem is considered to find the final form of free vibrations.