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This chapter considers the effect of nonlinearities on the dynamic response of structures. As with the nonlinear static analysis, an incremental/iterative approach is developed; here, however, we must also discretize the time. The computer methods established will be applicable to most dynamics problems; in the analysis, however, the emphasis is on vibrations, and we consider the two cases of free vibration and forced vibration. For structural applications, the dominant behavior is linear elastic, therefore we treat the nonlinearities as perturbations on this behavior. This will allow us to effect some simplified solutions.
KeywordsFree Vibration Chaotic Motion Tangent Stiffness Force Frequency Tangent Stiffness Matrix
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