Estimating Damping of Real Structures

Described in this paper is a method to obtain equivalent modal viscous damping ratios from stiffness and energy dissipation properties of structural components. Specifically, modal viscous damping ratios are computed as the weighted sum of component energy ratios (ratio of energy dissipated to peak potential energy per cycle of motion) weighted by the ratios of component to total peak potential energies. Component energy ratios may be estimated from vibration studies of the individual components or similar structures made exclusively of the component materials. Component potential energies may be computed from component stiffness matrices and modal deflections. A great simplification is that total peak potential energy may be computed as half the natural circular frequency squared for mode shapes normalized such that the generalized mass equals unity. Modal viscous damping ratios are computed for four example structures all having reinforced concrete frames with gypsum wallboard partitions. Damping ratios predicted and measured vary from 2% to 5%.