@inproceedings{zhu-che-08-aa-dynstruc,
  author = {Zhu, Zeng Qing and Chen, J.J.},
  title = {Dynamic Response Analysis for Structures with Interval Parameters Based on Affine Arithmetic},
  booktitle = {Advanced Materials Research},
  year = 2008,
  month = jun,
  volume = {44-46},
  pages = {157--164},
  publisher = {Trans Tech Publications Ltd},
  doi = {10.4028/www.scientific.net/AMR.44-46.157},
  comment = {Structural engineering},
  abstract = {This paper aims to study the uncertainty of the MDOF structural dynamic response, taking   not only the interval characteristics of structural physical parameters and geometric dimension, but   also the interval characteristics of applied load simultaneously . By means of the description of the   interval parameters of uncertain structure with affine forms, the interval structural dynamic equation   is studied, and an improved affine arithmetic based on interval division is presented, where   correlations between the interval elements in eigenvalue and responses equations are considered,   independent uncertain parameters are transformed to affine forms, and the solution of eigenvalue and   response equations are transformed into the corresponding certain ones. With general affine   arithmetic, the eigenvalue of each order and response bounds are determined by searching for the   maximum and minimum in the solutions. Finally, some mathematical examples and a further engineering application confirm the feasibility and validity of this approach.}
}