Abstract
The stability of the periodic solutions is examined in Part 4. Here, it is shown that we have to conclude the stability of periodic solutions of the equations of motion with multi-degree-of-freedom by solving the complex eigenvalue problem. Meanwhile, in order to get approximate periodic solutions we usually have to solve nonlinear algebraic equations with applying iteration procedure such as Newton-Raphson procedure, because they cannot be solved algebraically. However there are some cases in which they are solved algebraically, and we can get approximate solutions for nonlinear free and forced vibrations and determine the boundary regions of instability for subharmonic oscillations and parametric excitations.
