Design of TMD for damped linear structures using the dual criterion of equivalent linearization method

• This paper deal with design of TMD in case of damped linear structure.
• The idea is based on improved equivalent linearization method with dual criterion.
• We replace the original damped structure by an equivalent undamped structure.
• We get an approximate analytical solution for optimal tuning ratio of TMD for two models, excitation force and ground motion.

Design of tuned mass damper (TMD) for damped linear structures has attracted considerable attention in recent years. Some approximate expressions of optimal tuning ratio of a TMD attached to a damped linear structure have been proposed. In the paper, another closed-form expression for the optimum tuning ratio is presented for two models, excitation force and ground motion. This approximate analytical solution is obtained by using improved equivalent linearization method according to dual criterion. The values of optimum tuning ratio derived from the expression proposed in the present study have been compared with those obtained numerically and from results investigated by other authors. The comparisons have verified the accuracy of the suggested expression for both small and large structural damping.