Limitation on the method of strained coordinates for vibrations with weak grazing unilateral contact

Abstract

The NNM (Nonlinear normal modes) have recently been investigated with the method of strained coordinates for spring mass models with some springs with piecewise linear stiffness. The N d.o.f. case and the mathematical validity of the method for large time were rigorously proved. The time validity is related to the nature of contact. For grazing contact, this method and also the multiscale expansion lose nonlinear features. For a small piecewise linear stiffness, we show that this method is less precise for a weak unilateral grazing contact. Thus, the validity of the asymptotic expansion for large time can not be improved and the method has to be modified.