SOME PROBLEMS IN NONLINEAR MECHANICS

Abstract

The aim of this thesis, which consists of five chapters is to study some problems in non-linear mechanics, which governed by a set of coupled second order ordinary non-linear differential equations.

The study is concentred on:

- Finding the approximate

resonances conditions and

solutions in the presence of internal

without (ch.l, ch.2) by employing one

of the perturbation techniques.

- Finding the steady state solutions (periodic solutions).

- Examini11g the stability of the steady state solutions by applyl.11g the v0riational method and Routh-Hurwith Criterion. - Graphical representations of the results. The first chapter is devoted to the principal parametric resonance of the first mode without internal resonances and in the

presence of all possible

two-degree-of-freedom with

internal resonances, for system havl.ng

quadratic and cubic nonlinearities

subjected to parametric excitation.

The second chapter is concerned with the combination parametric resonance without internal resonances and in the presence of all ossible internal resonances, to the system mentioned i11 chapter one. In chapters three and four, the nonlinear system of three rods

under horizontal kinematic excitation, Fig.(6), in which the horizontal rod I is connected by means of two articulated joints (points A and B) with two identical elements II, stiffly connected