Eigenvalue uncertainty in stressed structures.

Abstract

A method is presented for calculating the statistics of the natural frequencies and mode shapes of vibration for a structure acted upon by an external static loading which results in the structure being stressed for eigenvalue analysis. The analytical tools presented apply to the probabilistic eigenvalue problem, and it is apparent that structural parameter uncertainty will significantly influence all aspects of the structure's response. The treatment of a sample problem serves the purpose of furthering understanding for the importance of considering structural parameters as random variables.