Incremental time-space finite strip method for non-linear structural vibrations

Abstract

Based on an incremental Hamilton's principle a versatile and systematic computer method for analyzing non-linear structural vibrations is developed. The method can be regarded as an incremental harmonic balance method associated with a finite strip procedure in the time-space domain. Only linearized equations in terms of frequency increment, amplitude increments, etc. have to be formulated and solved in each incremental step. This method is applicable to highly non-linear problems and may be generalized to related non-linear periodic structural motions. A typical time-space finite strip for beam problems is worked out and examples for a wide variety of vibration problems including free and forced vibrations, super- and sub-harmonic resonances, and complicated phenomena such as internal resonance are computed.