Evaluation of the non-linear dynamic response to harmonic excitation of a beam with several breathing cracks

The aim of this article is to present a technique capable of evaluating the dynamic response of a beam with several breathing cracks perpendicular to its axis and subjected to harmonic excitation. The method described is base d on the assumption of periodic response and that cracks open and close con tinuously. In this way, a non-linear system of algebraic equations can be d efined and solved iteratively, with the advantage over direct numerical int egration of the equation of motion of being easier and therefore faster to compute. In this article, the vibrational response to harmonic force of a cantilever beam with cracks of different size and location is analyzed using this "ha rmonic balance" approach and the results are compared with those obtained t hrough numerical integration. (C) 2000 Academic Press.