Analysis and computer simulation of linear and nonlinear mechanical vibratory systems subjected to continuous and piecewise constant force

This dissertation is devoted to a systematic study of the behavior of linear and nonlinear vibratory systems subjected to continuous and piecewise constant excitations with a new approach to approximate and numerical solutions of dynamic problems.;Analytical solutions of closed form are derived for some of the dynamical systems under the exertion of piecewise constant forces. Detailed theoretical and numerical analyses of the oscillatory properties of the dynamical systems are presented.;With the introduction of a new piecewise constant argument, (Nt) /N, the gap between the two categories of dynamical systems of continuous and piecewise constant functions is filled. A technique based on piecewise-constant function is presented. Approximate and numerical solutions to nonlinear oscillatory problems are conveniently obtained with the technique. The numerical results provided by the technique are accurate with good convergence in comparison with those of commonly used numerical methods.;Periodic and chaotic behavior of some nonlinear dynamical systems are analyzed with a quantitative analysis based on periodicity ratio, which reveals the behavior of a dynamical system and is developed as an effective criterion for diagnosis of periodic and chaotic motions. The piecewise-constant technique and the concept of periodicity ratio have been applied to a dynamical analysis of a Froude pendulum which has been modeled both as a weakly and a highly nonlinear system.