Abstract
The first passage problem in random vibration has been successfully solved for a wide range of single degree of freedom nonlinear systems subjected to both parametric and external broad band excitations. The solution method is numerical and has been shown to be both accurate and efficient. Two example problems are given and discussed. The first is a parametrically excited Duffing oscillator obtained from the single mode expansion of a pin-ended beam-column subjected to simultaneous wide-band axial and transverse loading and undergoing large transverse displacement. The second is a simple oscillator incorporating the Bouc-Wen model for hysteretic behavior.
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