6. Conclusions
The present study can be summarized as follows:
• A new approach for seismic response control of structures with the elasto-plastic TMD (P-TMD), which consists of a mass and an elastoplastic spring without the need for a viscous damper, has been presented in this paper.
• A simple yet effective method to estimate the design parameters of the device was developed and applied to the structural systems subjected to the seismic excitations. The proposed procedure has resulted in the explicit formulas to compute the tuning and acceleration ratios of the device for a given set of mass and damping ratios of the main system so that the inelastic behavior of the P-TMD can be equivalent to the visco-elastic behavior of a given optimum TMD.
• For the purpose of comparative analysis, the suggested optimum TMD by Sadek et al. [12] was then considered as a reference TMD. Comparison of the energy responses of a structural system equipped with P-TMD and optimum TMD shows that hysteretic behavior of PTMD dissipates nearly the same energy as that dissipated by the viscous damper of TMD.