Efficient computation of frequency response for non-proportional damped systems

Frequency response analysis is required in many structural dynamic applications. For large-scale problems, the cost of performing a frequency response analysis within a frequency interval of interest can be computationally very expensive and prohibitive, because the evaluation of the structural response for each excitation frequency requires solving a system with complex coefficients. For such purposes, a new method for the frequency response analysis of a non-proportional damped system in the frequency interval [0,ω_max] is established. We first determine the lower-order modes in the interval [0, ω_max/ψ] and retain the quantity, where ψ is an optional parameter which is greater than zero and less than 1. The default value of ψ is set to 0.5. We then approximate the unknown higher-order mode contributions by using partial sums of the constructed convergent power series of excitation frequency. The number of items in the partial sum is determined adaptively by an iterative algorithm performed at ω_max. The resulting analytical expression for the frequency response is applied to the frequency interval [0,ω_max]. Consequently, the frequency response analysis can be fulfilled simply by changing the excitation frequency in the analytical expression. Although the proposed method is derived based on the state space approach, its implementation is transformed to the original space to reduce the computational effort and storage space. The accuracy and effectiveness of the proposed method are illustrated and validated by two numerical examples.