Plenary Lecture

Plenary Lecture

Modeling of Vibrations of Lumped and Continual Mechanical Systems by Ordinary Differential Equations

Professor Jan Awrejcewicz
Technical University of Lodz
Department of Automation and Biomechanics
Lodz, Poland

Abstract: Example taken from mechanical engineering, i.e. dynamics of a triple physical pendulum exhibiting a plane motion (lumped system) and dynamics of a cylindrical shell with the circular cross section (continual system ) are studied. In the first case the Lagrange’a equations are used to derive the governing second order ODEs, whereas in the second case strongly nonlinear PDEs are reduced to a truncated set of ODEs via FDM (Finite Difference Method) and the higher order Bubnov-Galerkin approximations.
Mathematical modeling of triple pendulum includes details, taking into account some characteristic features (for example, real characteristics of joints built by the use of roller bearings) as well as some imperfections (asymmetry of the forcing) of the real system. Parameters of the model are obtained by a combination of the estimation from experimental data and direct measurements of the system's geometric and physical parameters. A few versions of the model of resistance in the joints are tested in the identification process. Good agreement between both numerical simulation results and experimental measurements have been obtained and presented. Some novel features of our real system chaotic dynamics have been reported.
In the case of the circular cylindrical shell dynamics the problems related to its regular, bifurcational and chaotic dynamics are illustrated and discussed, as well as it’s local (global) stability loss versus control parameters. In addition, the convergence and validity of the applied numerical algorithms are studied.
The lecture includes movies and animations of regular and chaotic dynamics of the analysed systems.

Brief Biography of the Speaker:
Jan AWREJCEWICZ received the M.Sc. and Ph.D. degrees in the field of Mechanics from the Technical University of Lodz in 1977 and 1981, respectively. He received also his bachelor's degree in Philosophy in 1978 from the University of Lodz, and DSc. degree in Mechanics from the Technical University of Lodz in 1990. He is an author or co-author of abort 500 publications in scientific journals and conference proceedings, monographs (37), text books (2), edited volumes (3), conference proceedings (11), journal special issues (11), other books (8) and other short communications and unpublished reports (225). He is now the Head of Department of Automatics and Biomechanics, and the Head of Ph.D. School on 'Mechanics' associated with the Faculty of Mechanical Engineering of the Technical University of Lodz. In 1994 he earned the title of Professor from the President of Poland, Lech Walesa, and in 1996 he obtained the golden cross of merit from the next President of Poland, Aleksander Kwasniewski. He is a contributor to 50 different research journals and to 150 conferences. During his scientific travel he visited 60 different countries. His papers and research cover various disciplines of mathematics, mechanics, biomechanics, automatics, physics and computer oriented science (more details at

WSEAS Unifying the Science