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Earthquake Engineering Research - HKU Libraries - The University ...

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450<br />

Fig. 4.2: principle drawing of a semi-active tuned mass damper<br />

<strong>The</strong> output of the MR damper will be controlled by a special algorithm which aims at minimising the<br />

bridge displacements. Based on a set of continuously measured system state variables during a<br />

dynamic excitation, the algorithm evaluates an optimal force which will be approximated by varying<br />

the strength of the magnetic field. <strong>The</strong> maximum current supply for the MR device will be only a few<br />

amperes and therefore can be realized by a small battery and a solar panel.<br />

4.2.1 Numerical analysis and results<br />

<strong>The</strong> analysis of the footbridge was carried out using a simplified structural model (2 DOF system,<br />

representing the corresponding eigenform and the TMD) and the non-linear numerical model for the<br />

simulation of the MR damper. <strong>The</strong> investigations were performed implementing a passive and a semiactive<br />

TMD. <strong>The</strong> dynamic loading induced by a pedestrian was assumed by a stationary harmonic load<br />

(4.2.1)<br />

at maximum of the corresponding eigenform. <strong>The</strong> amplitudes A, represent dynamic components of a<br />

walking, running or jumping pedestrian (G = 1,0 kN) with corresponding phase angle 0 t . For running,<br />

the sum of these amplification factors can reach about 2.5 times the static load. As it is commonly<br />

known that pedestrians synchronize their movement due to the frequency of the bridge, the angular<br />

frequency (Ob is assumed to be the one of the corresponding bridge eigenform.<br />

In a first study the dynamic response of the footbridge in terms of its displacement (at maximum of the<br />

corresponding eigenform) without TMD, with a passive TMD in the optimal configuration and with a<br />

semi-active TMD with properties of the optimal passive one was investigated.<br />

As the dynamic behaviour of the footbridge with both types of TMD (optimal passive and semi-active)<br />

are more or less coincident, it can be concluded that no improvement (but also no deterioration) is<br />

obtained by implementing a semi-active damper - in case the TMD already exposes optimal properties

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