A study of the modal strain energy method for viscoelastically damped structures

The modal strain energy (MSE) method has been proposed to estimate the moda l loss factors or modal damping ratios of structures with viscoelastic damp ers. There are certain assumptions made in deriving the MSE method, such as the computation of the modal loss factor directly from the ratios of the i maginary and real parts of the eigenvalues, and the neglect of the influenc e of the imaginary mode shapes, etc. These assumptions may result in overes timating the modal damping,ratios of viscoelastically damped structures whe n the added damping is high. In this study, the effect of the assumptions m ade by the MSE method is investigated, and modified formulations of the MSE method are derived. The modified MSE method removes the assumptions made i n the original MSE method. Furthermore, earthquake responses of a complex s tiffness system and a linear viscous damping system, of which the modal dam ping ratios are estimated by the MSE method, are compared. Study results: i ndicate that the difference arising from the assumptions becomes significan t when the damping ratio is larger than 20%. For the illustrated non-propor tionally damped system, the effect of imaginary mode shapes on the MSE meth od can be neglected when the damping ratio is smaller than 20%. It is then concluded that, for most engineering applications with design damping ratio s smaller than 20%, the conventional linear viscous damping model with the MSE method may result in solutions in good agreement with those obtained by the more rigorous complex stiffness model.