Uncertain frequency response analysis of clamp-pipe systems via the coordinate transformed polynomial chaos expansion

Abstract

The frequency response function (FRF) that links structural responses and external excitations is required to realize the dynamic analysis of a clamp-pipe system. Due to random geometry and stiffness parameters, the FRF becomes a stochastic quantity that is represented by a surrogate model based on the polynomial chaos expansion (PCE) in this paper. Considering that an FRF trajectory is mainly controlled by resonance and anti-resonance frequencies, a reference frequency coordinate characterized by the controlling frequencies associated with a nominal value of input random variables is first determined. By reserving the original amplitude, an FRF sample is projected to the reference coordinate through a linear transform. Then, a PCE surrogate model with coefficients estimated by the Gauss-quadrature scheme is obtained, and the utility of an inverse transform allows one to obtain the predicted FRF result in the original domain. Together with estimations on the confidence intervals and extreme boundary results, engineering applications are demonstrated by the uncertain FRF analysis of straight and L-shape clamp-pipe systems.