journal homepage: www.elsevier.com/locate/acme Available online at www.sciencedirect.com Original Research Article Kinematically excited parametric vibration of a tall building model with a TMD—Part 1: Numerical analyses K. Majcher n , Z. Wo ´ jcicki Wroclaw University of Technology, 27 Wybrzeże Wyspiańskiego St, 50-370 Wroclaw, Poland article info Article history: Received 15 July 2013 Accepted 8 September 2013 Available online 12 September 2013 Keywords: Parametric vibration Tall building Kinematical excitation Pendulum tuned mass damper Finite element method abstract This paper undertakes to analyze the research problem of vibration of a tall building with a Pendulum Tuned Mass Damper (PTMD). The vibration of the building-damper system is due to kinematic excitation representing seismic load. It was assumed that during an earthquake the ground can move horizontally and vertically. An analysis of various earthquakes reveals that, sometimes, the vibration has comparable amplitudes in both these directions. It is usually the horizontal vibration that is catastrophic to structures. Vertical vibration is therefore often omitted. As this paper will show, in cases where the TMD model is a pendulum, the vertical ground motion can be transmitted through the building structure to the pendulum suspension point. In such cases, parametric resonance may occur in the system, which is especially dangerous as it amplifies vibration despite the presence of damping. Taking this phenomenon into consideration will make it possible to better secure the structure against earthquakes. As the teams carrying out theoretical and experimental analyses differed, the paper was purposely divided into two parts. In the first part, the idea was formulated and the MES model of the building-TMD system was created. The second part contains an experimental verification of the theoretical analyses. & 2013 Politechnika Wroc"awska. Published by Elsevier Urban & Partner Sp. z o.o. All rights reserved. 1. Introduction One of the most important issues in tall building dynamics is safeguarding the structure from vibration caused by earth- quakes. There are different ways to secure a building against earthquakes. One of the most basic ways to reduce the influence of seismic vibration is to design a building structure that is flexible enough that it will absorb part of the seismic excitation's energy, but at the same time is stiff enough to support the building's own weight and the loads on it. During the dynamic analysis of such a structure, a few variants of its vibration damping hypotheses are considered. However, it is often impossible or impractical to carry out vibration reduc- tion using only the choice of materials and the designed shape of the structure. Such a solution is not effective when the load exciting the vibration oscillates with a frequency 1644-9665/$ - see front matter & 2013 Politechnika Wroc"awska. Published by Elsevier Urban & Partner Sp. z o.o. All rights reserved. http://dx.doi.org/10.1016/j.acme.2013.09.004 n Corresponding author. Tel.: þ48 713202934. E-mail address: krzysztof.majcher@pwr.wroc.pl (K. Majcher). archives of civiland mechanical engineering 14 (2014)204–217