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The purpose of this thesis is to study the failure prediction of structures subjected to random vibrations. First, the most relevant and fundamental theory in random vibrations is presented. A known method to efficiently calculate RMS von Mises stress in a random vibration environment is re-derived. Next, two practical case studies are presented: a cantilever beam and a rocket launcher payload subjected to random vibrations are analyzed using ANSYS. From this analysis, the expected frequency of the response and the root mean square (RMS) response for the displacement and stress are calculated. The statistical quantities obtained from the random vibration analysis, such as the expected frequency and RMS stress response, are used to determine the probability of the first-passage failure as well as the fatigue life.

The purpose of this thesis is to study the failure prediction of structures subjected to random vibrations. First, the most relevant and fundamental theory in random vibrations is presented. A known method to efficiently calculate RMS von Mises stress in a random vibration environment is re-derived. Next, two practical case studies are presented: a cantilever beam and a rocket launcher payload subjected to random vibrations are analyzed using ANSYS. From this analysis, the expected frequency of the response and the root mean square (RMS) response for the displacement and stress are calculated. The statistical quantities obtained from the random vibration analysis, such as the expected frequency and RMS stress response, are used to determine the probability of the first-passage failure as well as the fatigue life.