Nonlinear differential equations solution with time variable stiffness

The main object of this thesis is the mathematical study of the dynamic behavior of the rotor-AMB described by non-linear differential equations with quadratic and cubic nonlinearities and time-varying stiffness. The non-linear rotor-AMB system with time-varying stiffness subjected to multi-external excitations or multi-parametric excitations or single-external and single- tuned excitation or multi-external and multi- tuned excitations and multi- external, -parametric and -tuned excitations (as a general case) are studied. The method of multiple time scales is applied to solve the non-linear ordinary differential equations up to the second order approximation. All possible resonance cases are investigated from this approximation. The stability of the steady state solution is determined applying Lyapunov's first method. The numerical solutions are focused on both the effect of different parameters and the behavior of the system at resonant conditions. The variations of the response due to the change of various parameters are investigated and studied. Simulation results are achieved using MATLAB 7.0 and MAPLE 13.0 programs.

Autorentext

H. S. Bauomy received his B.S. degree in Mathematics from Zagazig University, EGYPT, in 2000. He then received his M.S.c and Ph.D. degrees from Zagazig University, in 2007 and 2011, respectively. his research interests include Differential equations, Non-linear dynamical systems, Numerical Analysis and Vibration control.