10. Probabilistic Analysis of Modal Properties for Floor Systems with Uncertain Support Conditions

Traffic and construction work as well as internal sources may cause vibration of floors in buildings. Potentially, this leads to annoyance for people living or working in the buildings—especially when resonance occurs as a result of excitation frequencies coinciding with eigenfrequencies of the floors. Hence, proper design of floors requires insight into the dynamic properties of the system in order to avoid resonance. In this context, the boundary conditions for the floor—or the connections to the main structure—play an important role. A floor clamped along the entire edge reacts differently than a floor which is simply supported. However, whereas the floor system may well be described in terms of material and geometry, an assessment of the supports can be difficult. Often, calculated eigenmodes and eigenfrequencies do not match those identified for a real floor system and this is, to a great extent, due to uncertain and poorly described supports. Hence, the paper suggests a probabilistic approach focussing on the dynamic properties of the floor given uncertain support conditions. Especially, a rectangular concrete floor, representative of a floor in an office or residential building, is assessed regarding its eigenfrequencies. A stochastic model is introduced for the rotational stiffness of the supports, and a numerical analysis is performed in order to quantify how uncertainty related to the supports for the floor system transfers into uncertainty of its eigenfrequencies.