Abstract
The concept of similar normal mode is used to study the free oscillations of a class of strongly non-linear, two degree of freedom undamped systems. By using the so-called balancing diagrams, the bifurcations of normal modes can be conveniently studied for different forms of stiffness non-linearities. Consequently, the stability of the resulting free motions is analytically examined and the theoretical results are checked by numerical integration of the equations of motion.
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