TY - EJOU
AU - Rout, S.
AU - Chakraverty, S.
TI - Solving Fully Fuzzy Nonlinear Eigenvalue Problems of Damped Spring-Mass Structural Systems Using Novel Fuzzy-Affine Approach
T2 - Computer Modeling in Engineering \& Sciences
PY - 2019
VL - 121
IS - 3
SN - 1526-1506
AB - The dynamic analysis of damped structural system by using finite element
method leads to nonlinear eigenvalue problem (NEP) (particularly, quadratic eigenvalue
problem). In general, the parameters of NEP are considered as exact values. But in actual
practice because of different errors and incomplete information, the parameters may have
uncertain or vague values and such uncertain values may be considered in terms of fuzzy
numbers. This article proposes an efficient fuzzy-affine approach to solve fully fuzzy
nonlinear eigenvalue problems (FNEPs) where involved parameters are fuzzy numbers
viz. triangular and trapezoidal. Based on the parametric form, fuzzy numbers have been
transformed into family of standard intervals. Further due to the presence of interval
overestimation problem in standard interval arithmetic, affine arithmetic based approach
has been implemented. In the proposed method, the FNEP has been linearized into a
generalized eigenvalue problem and further solved by using the fuzzy-affine approach.
Several application problems of structures and also general NEPs with fuzzy parameters
are investigated based on the proposed procedure. Lastly, fuzzy eigenvalue bounds are
illustrated with fuzzy plots with respect to its membership function. Few comparisons are
also demonstrated to show the reliability and efficacy of the present approach.
KW - Fuzzy nonlinear eigenvalue problem
KW - fuzzy set theory
KW - affine arithmetic
KW - interval overestimation problem
KW - triangular fuzzy number
KW - trapezoidal fuzzy number
KW - fuzzy-affine approach
DO - 10.32604/cmes.2019.08036