An analytical technique, namely the method of multiple scales, is applied to solve the
differential equations of free oscillations with even nonlinearities in a mass-spring system. Unlike
other perturbation methods, the method of multiple scales is effective in determining the transient
response as well as determining the approximation to the frequency of the nonlinear system. In
this paper, the periodic solutions of the even nonlinear differential equations have been obtained by
using the method of multiple scales. Compared with the numerical examples, the approximate
solutions are in good agreement with exact solutions. The numerical and analytical solutions have
clearly shown that there exists the so-called drift phenomenon in the free oscillations of systems
with even nonlinearities without any external excitation.
DIFFERENTIAL EQUATIONS OF STABILITY AND FREE OSCILLATIONS OF A THREE-LAYER PLATE SUPPORTED BY RIGIDITY RIBS
