Session: MSNDC-04-02 Nonlinear Dynamics of Structures

Paper Number: 97326

97326 - Analysis of a Hysteretic Relay Oscillator Chain 

The dynamical behavior of a hysteretic relay oscillator chain is investigated in this paper. The continuous-time hybrid system is transformed into a discrete map, which describes the evolution of the state variables at the transitions of the relay elements. The advantage of the discrete map is that the switching time and the states at the transitions can be efficiently calculated by analytical expressions. The energy growth rate, energy distribution, and evolution of the dominant states of the chain oscillator are studied using the discrete map. We find that, for the low degree of freedom chains, the growth of the total kinetic energy is proportional to the two-thirds power of the switching time. For the high degree of freedom chains, the growth of the kinetic energy is irregular and strongly dependent on the initial conditions. A synchronized oscillation of the kinetic energy can be observed after the initial transient fluctuations in the kinetic energy distribution in the degrees of freedom. The kinetic energy is evenly distributed in the degrees of freedom, except for the last degree of freedom, where the kinetic energy is much smaller. The dominant states of the relay elements, which have the most significant influence on the system's dynamical behavior, show an alternating pattern.

Presenting Author: Janos Lelkes Budapest University of Technology and Economics, Faculty of Mechanical Engineering, Department of Fluid Mechanics

Presenting Author Biography: Janos Lelkes is a Ph.D. student at the Budapest University of Technology and Economics. Janos holds a BS degree in mechatronics and an MS degree in Mechanical engineering. His research interests include nonlinear dynamics, aeroelasticity, and wave energy.

Authors:

Janos Lelkes Budapest University of Technology and Economics, Faculty of Mechanical Engineering, Department of Fluid Mechanics
Tamas Kalmar-Nagy Department of Fluid Mechanics, Faculty of Mechanical Engineering, Budapest University of Technology and Economics