An efficient method for calculating the frequency response of a proportional damping system over a given frequency interval

•The Sturm sequence number is applied to adaptively determine the number of low-order 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 terms in the partial sum is determined by the highest excitation frequency only.•The resulting expression is valid for the entire frequency interval of interest.•The computational cost is significantly reduced. The computational cost of the frequency response within the frequency interval may be high for large-scale structures. An efficient method for calculating the frequency response of a proportional damping system over a given frequency interval which starts from zero is proposed. The Sturm sequence number is used to adaptively determine the number of low-order modes that need to be calculated. The complementary part of the contribution of the calculated low-order modes is approximated by the partial sum of the power series that is proven to converge. The number of terms in the sum is adaptively determined only by the highest excitation frequency. The resulting frequency response expression is valid for the entire frequency interval. One numerical example is presented to demonstrate the high accuracy and effectiveness of this method.