ASYMPTOTIC SOLUTIONS FOR NONLINEAR-SYSTEMS WITH HIGH DEGREES OF NONLINEARITY

A method is proposed for the recurrent construction of the periodic so lution of a substantially non-linear conservative system with a single degree of freedom which is close to a vibration impact system. It is assumed that the restoring force is a power function of the deflection . A quantity which is the inverse of this exponent is regarded as a sm all parameter. The method is based on the asymptotic representation (i n a certain weak sense) of this non-linearity in powers of a small par ameter) using normalization and Laplace transformation procedures. Thi s approach leads to differential equations containing generalized delt a-functions of the unknown variable and derivatives of these functions of as high an order as desired.