Efficient computation of frequency response for non-proportional damped systems

•An optional parameter greater than zero and less than 1 is introduced.•Only the lower-order modes in an interval depending on the parameter need to be calculated.•Construct a convergent power series and use its partial sum to approximate the contributions of truncated modes.•Adaptively determine the terms in the partial sum using only the right end of the frequency interval only.•Derive an analytical expression valid for the entire frequency interval of interest.