Uncertain Nonlinear Dynamic Problems

Abstract

Nonlinear dynamic problems from various fields of science and engineering lead to nonlinear eigenvalue problems. In this chapter, we focus on the solutions of nonlinear eigenvalue problems with uncertainty. A nonlinear eigenvalue problem is a generalization of a linear eigenvalue problem viz. standard eigenvalue problem or generalized eigenvalue problem to the equations that depend nonlinearly on the eigenvalues. Mathematically, a nonlinear eigenvalue problem is generally described by an equation of the form M(λ)x = 0, for all λ, and contains two unknowns viz. the eigenvalue parameter (λ) and the “nontrivial” vector(s) (x) (known as eigenvector) corresponding to it.