Modal Mass of Floors Supported by Beams

Long-span, light weight floors may show considerable vibration, which might disturb the occupants. The floor is often supported by beams, the stiffness of which may significantly reduce the natural frequency. For the simplified vibration analysis of floors, where the vibration is due to human activity, the natural frequency, the modal mass and the damping ratio must be known. The stiffness of the supporting beams will affect both the frequency and the modal mass. Well-known expressions are available for the calculation of the natural frequency, based on Föppl's (Dunkerley's) approximation. In this paper Föppl's approximation is extended for the calculation of the modal mass and then it is applied to the vibration of floors supported by beams. The results are verified numerically, and its usage is demonstrated by a numerical example.