Affine Approach to Solve Nonlinear Eigenvalue Problems of Structures with Uncertain Parameters

摘要

Various science and engineering problems involve uncertainty with respect to parameters due to different causes. The uncertain parameters may be contemplated as closed intervals. Uncertain material parameters of structural vibration problems may produce interval mass matrices and interval stiffness matrices. In general, dynamic problems with interval uncertainty lead to generalized interval eigenvalue problems. Further, the inclusion of damping factor may transform the problem to a nonlinear interval eigenvalue problems, viz., quadratic and/or cubic eigenvalue problems. In this respect, affine arithmetic may be used to handle the uncertainties due to the overestimation problem occurred in some of the cases of interval arithmetic. Accordingly, this manuscript aims to deal with solving the nonlinear eigenvalue problems with interval parameters using affine arithmetic. Numerical examples have been worked out to illustrate the reliability and efficiency of the present approach.