Interval analysis of frequency response functions of structures with uncertain parameters

This paper proposes an interval finite element (IFE) method for the frequency response function (FRF) of structures with uncertain parameters. The element-by-element (EBE) method is first extended to dynamic systems to formulate the IFE equation. Subsequently, the Fourier transform is applied on the interval dynamic equation to convert it into a system of linear equations. The structural FRF is obtained by solving the linear equations using the Brouwer's fixed point theorem. During the interval calculation, a special treatment of matrix multiplication is employed to reduce the overestimation. Finally, the transient response of dynamic system under harmonic loading can be obtained by the inverse Fourier transform. Numerical examples are presented and the results are compared with the vertex solutions and the direct IFE solutions to demonstrate the effectiveness of the proposed EBE–IFE method.