Computation of frequency responses and their sensitivities for undamped systems

•The Sturm sequence number is applied to adaptively determine the number of the lowest modes that need to be calculated.•The complementary part of contribution of the computed modes is approximated by a partial sum of a convergent power series.•The number of items in the partial sum are adaptively determined by the highest excitation frequency only.•The resulting expressions are efficient for the entire range of excitation frequencies of interest.•The proposed method can significantly reduce the computational cost.