| Abstract: | Based on an incremental Hamilton's principle a versatile and systematic computer method for analysing non-linear structural vibrations is developed in this paper. The essence of the proposed 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 such as dynamic stability, flutter and some motions of a rotating body, etc. To show the effectiveness and versatility of this method, 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. Comparisons with previous results are also made. |
