Abstract
Conventional analysis methods for building structures with added viscoelastic dampers, such as direct integration, complex mode superposition, and modal strain energy method, were compared, and a procedure based on rigid diaphragm assumption and matrix condensation technique was proposed for application in the preliminary analysis and design stages. The results from the various analysis methods with and without the matrix condensation were compared, in view of both accuracy and efficiency. According to the eigenvalue analysis the major vibration modes were mostly preserved after the matrix condensation. It was also found that the matrix condensation technique applied to dynamic analysis of a structure with added viscoelastic dampers provided quite accurate results in significantly reduced time, regardless of the plan shape and the location of the viscoelastic dampers.
1. Introduction
For years viscoelastic dampers have been widely used not only to improve residential comfort in strong winds but also to enhance structural safety against large earthquake ground motion. There are many examples, such as World Trade Center in New York and Columbia Center in Seattle, USA, where viscoelastic dampers were applied successfully to enhance the structural performance against dynamic loads [1,2].
Generally, in practice, the behavior of viscoelastic dampers is represented by a spring and a dashpot connected in parallel [3,4]. Although more rigorous methods of analytical modeling exist taking into account the nonlinear behavior of the viscoelastic material, such as based on Boltzmann’s superposition principle [5] or on fractional derivative constitutive relationship [6], they may not be applicable for the analysis of large scale structures because of their huge computational demands. With this can be constructed by superimposing the contribution from the dampers onto the system matrices of the structure.
5. Conclusions
In this study an efficient analytical procedure, based on matrix condensation technique, was proposed for the seismic analysis of structures with added viscoelastic dampers. Special attention has been paid to the condensation of the stiffness and damping matrices contributed from the added dampers. The results from the modal strain energy method, direct integration and the complex mode superposition method without matrix condensation were compared with the results from the proposed method to check the reliability and efficiency of the proposed method.
