Abstract
As an application of the general technique presented in a companion paper, the complex modes of nonproportionally damped close-coupled two-degree-of-freedom system are approximated through second-order perturbation. Assuming the nonproportionality to be either moderate or weak, the pseudo natural frequencies, modal damping ratios, and complex “modes” are expressed in terms of natural frequencies and mode shapes of the counterpart undamped 2DOF system, and of respective damping ratios of the two single-degree-of-freedom (SDOF) subsystems. The effects of damping nonproportionality are contained in eight nondimensional perturbation coefficients. These perturbations depend only on the ratio of masses, ratio of natural frequencies, and damping ratios of the two SDOF subsystems. The approximate explicit formulas avoid the complications of Ferrari's classical solution for the quartic characteristic equation. Parametric studies illustrate the convenient use of the present formulas as well as check their accuracy.
