Dynamic characteristics and frequency response function for frame with dampers with uncertain design parameters

Abstract

ABSTRACTThe influence of uncertain design parameters on dynamic characteristics and the frequency response function is considered in this paper. A structure with dampers modeled as a shear frame is analyzed. The dampers properties of dampers are described by fractional derivatives. The design parameters of the considered structure change only in a specified range and the interval analysis is taken into account in calculating the lower and upper bounds of dynamic characteristics. Several methods are used to obtain the limit values of objective functions: the vertex method and the method of approximation using the first- and the second-order Taylor series expansion. The vertex method is adopted as a comparative method. Two examples are presented in order to illustrate the considered methods. In the case of large uncertainties, the obtained results differ from those obtained by means of the vertex method. Therefore, a new method using the second-order Taylor series expansion is proposed. The method consists of a sequence of changes of only one parameter and requires much fewer combinations when the number of uncertain design parameters is high.