Wave Propagation in Buildings as Periodic Structures: Timoshenko Beam with Rigid Floor Slabs Model

Abstract

Elastic wave propagation in high-rise buildings is studied using a Timoshenko beam model with rigid floor slabs, with the objective of gaining insight into the effects of their repeatable arrangement. The propagator of the composite beam was derived in the frequency domain and used to compute the state vector for input base translation and rocking. Further, the dispersion relation was derived for Bragg scattering from the slabs for an infinite, periodic beam. Results are shown for the dispersion and beam transfer functions and impulse response functions for properties typical for buildings. The results, extrapolated for illustrative purposes beyond the range of validity of simple beam models, reveal the banded nature of the dispersion and response with real phase velocity in the pass and imaginary in the stop bands. The latter act as mechanical filters of higher frequency waves and vibrations, and represent a possible attenuation mechanism in buildings. While real structures would have more complex banded spectra, the selective nature of the filtering could be exploited for passive higher frequency vibration control to protect sensitive equipment from vibrations created, e.g.,by high-speed trains, traffic, explosions, or smaller but near seismic events.