@incollection{cha-21-aa-struct,
  title = {Affine Approach in Solving Linear Structural Dynamic Problems with Uncertain Parameters},
  editor = {Snehashish Chakraverty},
  booktitle = {New Paradigms in Computational Modeling and Its Applications},
  chapter = {8},
  publisher = {Academic Press},
  pages = {97-121},
  year = 2021,
  isbn = {978-0-12-822133-4},
  doi = {10.1016/B978-0-12-822133-4.00003-7},
  author = {S. Rout and Snehashish Chakraverty},
  comment = {Uses AA to compute eigenvalues},
  abstract = {The present chapter proposes an affine approach for computing the linear structural dynamic problems having uncertain and nonprobabilistic model parameters with the help of affine arithmetic operations. The solutions of linear dynamic problems of structures lead to eigenvalue problems, viz., generalized and standard eigenvalue problems. When there is a deficiency of large data, the material and geometric properties of the said problems may be considered as intervals due to uncertainty. The error explosion problem occurs in interval arithmetic, which leads to wide-ranging results. In this case, affine arithmetic may be developed to handle the uncertainty with ease. Using this affine arithmetic, we have included a new procedure for solving standard as well as generalized interval eigenvalue problems having uncertainty in the form of closed intervals. Several numerical examples related to various applications of structural dynamic problems have been worked out to illustrate the reliability and efficiency of the present approach.}
}