@incollection{cha-rou-20-aa-unldyn, title = {Uncertain Nonlinear Dynamic Problems}, author = {Chakraverty, Snehashish and Rout, Saudamini}, booktitle = {Affine Arithmetic Based Solution of Uncertain Static and Dynamic Problems}, series = {Synthesis Lectures on Mathematics {\&} Statistics}, year = 2020, pages = {125-150}, doi = {10.1007/978-3-031-02424-5_7}, comment = {Finds eigenvalues of matrices of affine forms.}, 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 $M(\lambda)x = 0$, for all $\lambda$, and contains two unknowns viz. the eigenvalue parameter ($\lambda$) and the ``nontrivial'' vector(s) ($x$) (known as eigenvector) corresponding to it.} }