Effects of the Improper Modeling of Viscous Damping on the First‐mode and Higher‐mode Dominated Responses of Base‐isolated Buildings

December 2, 2019
Publication: Earthquake Engineering and Structural Dynamics
Author(s): Ricardo Medina Hamidreza Anajafi Erin Santini‐Bell

In many finite element platforms, a classical global damping matrix based on the elastic stiffness of the system (including isolators) is usually developed as part of the solution to the equations of motion of base‐isolated buildings. The conducted analytical and numerical investigations illustrate that this approach can lead to the introduction of unintended damping to the first and higher vibration modes and the spurious suppression of the respective structural responses. A similar shortcoming might be observed even when a nonclassical damping model (ie, an assembly of the superstructure and isolation system damping sub‐matrices) is used. For example, the use of Rayleigh damping approach to develop the superstructure damping sub‐matrix can lead to the undesired addition of damping to the isolated mode arising from the mass‐proportional component of the superstructure damping. On the other hand, the improper use of nonclassical stiffness‐proportional damping (eg, determining the proportional damping coefficient, βk, based on the first mode) can result in assigning significant damping to the higher‐modes and the unintended mitigation of the higher‐mode responses. Results show that a nonclassical stiffness‐proportional model in which βk is determined based on the second modal period of a base‐isolated building can reasonably specify the intended damping to the higher modes without imparting undesirable damping to the first mode. The nonclassical stiffness‐proportional damping can be introduced to the numerical model through explicit viscous damper elements attached between adjacent floors. In structural analysis software such as SAP2000®, the desired nonclassical damping can be also modeled through specifying damping solely to the superstructure material.

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