Modal analysis of mechanical systems with impact non-linearities: Limitations to a modal superposition

This paper presents an attempt to generalize the modal superposition formula to mechanical systems with impact type non-linearities following the procedure introduced for smooth non-linearities. The study is restricted to simple one- and two-degree-of-freedom systems with a unilateral constraint on one of the degrees of freedom, for which the response can be analytically determined. Generalized frequencies, modes and masses are built in the procedure. The results obtained for various sets of parameters point out some limitations to the validity of a general modal superposition formula. (C) 2000 Academic Press.