EIGENVALUE PROBLEM OF MDOF NON-PROPORTIONAL COMPLEX DAMPING SYSTEM AND TRANSFER FUNCTION BY MODE SUPERPOSITION [Translated Paper]

Abstract

First, we present a method for obtaining the eigenvalues and eigenvectors of a multi-degree-of-freedom system with nonproportional complex damping. These eigenvalues and eigenvectors are complex and appear in conjugate pairs, corresponding to the number of masses, with forward waves and their conjugate backward waves. By leveraging the orthogonality of the eigenvectors, we show that the seismic transfer function for each mass can be expressed as a superposition of the transfer functions of the complex modes of the forward wave, exhibiting conjugate symmetry. Similarly, using the orthogonality of the real eigenvectors, we derive an approximate transfer function by superimposing the transfer functions of the real modes. Finally, numerical calculations using a simple model are performed to validate the proposed complex eigenvalue analysis method and the transfer function based on complex modes. Additionally, we discuss the reliability of the transfer function derived from real modes.