Twenty years of computational methods for harmonic response analysis of non-proportionally damped systems

Twenty years ago, accurate harmonic response analysis of non-proportionally damped systems required the solution of a complex eigenvalue problem and modal superposition of complex modes. In order to avoid the computational effort of complex modal superposition, several approximate methods were proposed and accuracy of each such technique was studied extensively. In the past twenty years, while the search for appropriate approximate techniques for each different application continued, more rigorous methods were also developed. In this paper, the progress in computational methods for harmonic response analysis of nonproportionally damped systems is reviewed, emphasis being placed on a powerful technique which was first extended to structural modification analysis and then to harmonic response analysis of systems with non-linearities