Dynamic study of an elastic system with two degrees of freedom

Authors

  • Vladimir Dragos Tataru
  • Mircea Bogdan Tataru

Keywords:

dynamic study, constraint forces, numerical integration methods, elastic mechanical system

Abstract

In the paper is presented the dynamic survey of an elastic mechanical system which consists of two rigid solids linked to each other by a cylindrical joint. One of the two rigid solids is linked through an elastic linear spring to another rigid solid which is supposed to be fixed. We aim to study the movement of this elastic mechanical system under the action of forces. In order to do this in this paper is presented a numerical method which requires the writing of the differential equations of motion under matrix form. Finally, a computing program is elaborated with the help of which the differential equations of motion are integrated using numerical integration methods. In this way it is determined the variation with respect to time of the k

References

VÂLCOVICI V., B?LAN ?t., VOINEA R., Mecanica Teoretic?, Editura Tehnic?, Bucharest, 1968.

VOINEA R., VOICULESCU D., CEAU?U V., Mecanica, Editura Didactic? ?i Pedagogic?, Bucharest, 1983, pp. 351–355.

STAICU, ?t., Aplica?ii ale calculului matriceal în mecanica solidelor, Editura Academiei R.S.R., Bucharest, 1983.

ANGELES, J., LEE, S.K., The formulation of dynamical equations of holonomic mechanical systems using a natural orthogonal complement, Journal of Applied Mechanics, 55, 1, pp. 243–244, 1988.

PAPASTRAVIDIS, J.G., On the transitivity equations of rigid-body dynamics, Journal of Applied Mechanics, 59, pp. 955–962, 1992.

BLAJER, W., A projection method approach to constrained dynamic analysis, Journal of Applied Mechanics, 59, 3, pp. 643–649, 1992.

BLAJER, W., BESTLE, D., SCHIEHLEN, W., An orthogonal complement matrix formulation for constrained multibody systems, Journal of Mechanical Design, 116, 2, pp. 423–428, 1994.

MU?AT, S.D., Ecua?ii de tip Euler pentru solidul rigid deduse din ecua?iile lui Lagrange, XIXth National Conference of Solid Mechanics, Târgovi?te, Romania, 1995, Vol. 2, pp. 219–226.

STAICU, ?t., Mecanica Teoretic?, Editura Didactic? ?i Pedagogic? Bucure?ti R.A., Bucharest, 1998.

BAU?IC, F., Mecanica Teoretic?. Dinamica. Mecanica Analitic?, Editura Conspress, Bucharest, 2004.

BRATU, P., Mecanica Teoretic?, Editura Impuls, Bucharest, 2006.

STAICU, ?t., Dynamics of the spherical 3-UPS/S parallel mechanism with prismatic actuators, Multibody System Dynamics, 22, 2, pp. 115–132, 2009.

KAMMAN, J.W., HOUSTON, R.L., Dynamics of constrained multibody systems, Journal of Applied Mechanics, 51, 4, pp. 899–903, 1984.

PAPASTAVRIDIS, J.G., Maggi’s equations of motion and the determination of constrained reactions, Journal of Guidance, Control and Dynamics, 13, 2, pp. 213–220, 1990.

NIKRAVESH, P.E., Systematic reduction of multibody equations of motion to a minimal set, International Journal of Non-Linear Mechanics, 25, 2, pp. 143–151, 1990.

BLAJER, W., On the determination of joint reactions in multibody mechanisms, Journal of Mechanical Design, 126, 2, pp. 341–350, 2004.

HOUSTON, R.L., Methods of analysis of constrained multibody systems, Mechanics of Structures and Machines, 17, 2, pp. 135–143, 1989.

Published

2016-09-10