Seismic control of multidegree‐of‐freedom structures using a concentratedly arranged tuned viscous mass damper

Abstract

AbstractConnecting a flexible supporting element to an inerter arranged in parallel with a viscous element yields a tuned‐mass damper‐like system, designated as a tuned viscous mass damper (TVMD). The advantage of a TVMD is that it exploits the flexibility of the supporting member, which is usually considered to compromise the energy‐dissipating performance, and the inerter and soft spring form a supplemental oscillator to enhance the damping performance with resonance to the primary structure. The fixed‐point method for the optimal design of a single‐degree‐of‐freedom structure containing a TVMD is further expanded to a multidegree‐of‐freedom structure, in which a TVMD is arranged concentratedly. Furthermore, approximated closed‐form formulae for a concentratedly arranged TVMD are derived under the assumption that the primary structure is undamped, remains in an elastic range, and the target mode dominates the response of the structure. An analytical example illustrates that installing a TVMD spanning three stories in a concentrated manner based on the proposed design methods ensures the efficiency of the damping system, which demonstrates a damping effect similar to that of stiffness‐proportionally distributed TVMDs with less demand for inertance and total control force, thus resulting in a lower cost.