Tuned Mass and Parametric Pendulum Dampers Under Seismic Vibrations

Abstract

In the last hundred years, the height of the tallest buildings (skyscrapers) went up from 283 m (Woolworth Building, New York City, 1913) to 830 m (Burj Khalifa, Dubai, 2013). Building such structures presents various architectural and engineering challenges, including the development of plumbing and air conditioning systems, fast elevators, etc. Nevertheless, the main effort is always directed toward safety and reliability of buildings and occupants. These concerns are not immanent to tall buildings only but important as well for any structures, whether it is a bridge or nuclear plant. Earthquake and wind load are the major reasons for worries when designing structures or buildings, especially tall ones, since these loads are hard to predict. Tuned mass damper (TMD) is a concept (Den Hartog 2013; Hunt 1979), which has appeared in the beginning of the twentieth century. The concept seemed to be so attractive that it was properly developed and one of the first TMDs were installed in CN Tower, Toronto, and John Hancock Building, Boston, in 1976. Since then the number of different types of implemented TMDs has been rapidly increasing, approaching one hundred (Soto and Adeli 2013), including those which are used to mitigate the motion of tall buildings (Kareem et al. 1999), bridges, pumps, structures, etc. The basic idea behind a TMD is that an oscillatory two-degree-of-freedom (TDOF) system may have such a response that one of the masses (primary mass) will be motionless. Thus, if the response of the primary mass itself was high due to resonance, adding a second mass will significantly reduce the primary mass response amplitude. However, the response attenuation does not happen by default, so the properties of the added mass-springdamper system have to be tuned to deliver the best outcome; therefore, the name tuned mass damper is used to reflect this feature. A concern may be related to the fact that adding another degree of freedom to the system will result in two peaks of the response amplitude curve rather than one, characteristic for a single-degree-of-freedom (SDOF) system, but this issue can be handled by proper tuning as well. It has also been shown that the tuning of a stochastic system (a system subjected to a random excitation) is different from that for a deterministic system. There are different types of devices, which serve as passive TMDs: conventional TMD, liquid TMD (TLD) (DiMatteo et al. 2014 and references therein), and parametric pendulum TMD (PPD). An excellent review paper by Ibrahim (Ibrahim 2008) provides a full description of various passive vibration isolators. It has been argued that the passive TMDs are effective means of mitigating buildings’ vibrations due to seismic loading. It became a motivation for the development of a theory of active and hybrid TMDs