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M. Reiterer, F. Ziegler:
"Bi-axial seismic activation of civil engineering structures equipped with tuned liquid column dampers";
Journal of Seismology and Earthquake Engineering, 7 (2005), 45 - 60.

Tuned liquid column dampers (TLCD) considerably increase the effective damping of vibration prone civil engineering structures in horizontal motion. A single-degree-of-freedom (SDOF) basic system with a TLCD attached is analyzed under horizontal and vertical base excitations in order to prove its sensitivity with respect to the vertical parametrical forcing. The main result is cast in a sufficient condition for the linearized damping coefficient of the fluid motion to ensure its stability under the most critical, time harmonic forcing conditions. The output of computer simulations when varying the damping of the TLCD tuned with respect to frequency only, are verified experimentally by means of a novel model setup. The scaled Friuli 1976 earthquake is applied horizontally and vertically to an SDOF-shear frame with optimally tuned TLCD. A three-DOF-benchmark structure, equipped with two passive TLCD in parallel connection, optimally fine-tuned in state space, is analyzed by nonlinear computer modeling. Two different relevant earthquakes are alternatively applied in both, horizontal and vertical directions. In all cases it is verified, that sealed TLCD, (with the air-spring effect taken into account) are stable, since the optimal linear damping coefficient exceeds by far the required cut-off value of parametric resonance: the vertical component of the earthquake load remains ineffective. Hence, taking into account this sufficient condition with the maximum vertical ground (floor) acceleration assigned and the maximum amplitude of the fluid motion estimated, saves the consideration of the vertical seismic activation at all.