Dynamic Analysis of Heavily Damped Structures with Supplemental Energy Dissipation Devices

A structure supplemented with dampers may be over-critical damped as a result of more deformations in higher modes. Over-critical modal damping can significantly decrease structural displacements but also increase absolute accelerations and consequently the seismic forces. In dynamic analyses, undamped and complex mode superposition approaches are always employed due to their efficiency. However, the critical and over-critical damping issues are normally ignored because of more complexities introduced in the calculation of mode vectors. Particularly, the critical damping can result in the defectiveness of non-classically damped systems such that the analysis methods aforementioned become invalid. In this paper, a generalized complex mode superposition method is developed without the limit of modal damping. Orthogonality conditions among under-critical, critical, and over-critical damped modes are firstly constructed based on the linear algebra theory and the generalized complex mode superposition method is derived in time domain. Then, this approach is further extended to frequency domain and associating with the response spectra. The implementation and effectiveness of the proposed methods are presented in numerical examples. The results show that the over-critical damped modes have a remarkable effect on the structural response, particularly for the low stories.