Effect of geometry on the vibro-acoustic responses of beams under moving point loads

Vibration and acoustic responses of simply supported beams under the excitation of moving point forces are predicted in this paper. Four types of geometries, which include a uniform beam, a parabolic beam, a beam with sinusoidally varying height and a beam with height varying linearly (tapered) from ends to mid-span are considered in the study. Vibration responses under a single and a series of moving loads are estimated. The sound pressure radiated by the vibrating beam in an infinite baffle is obtained by evaluating Rayleigh surface integral. The accelerations of all elements on the beam surface due to the moving loads are treated as acoustic monopoles radiating sound, the contributions of which are added with appropriate time delays. Surface irregularities of the beam are not considered in the analysis and thus the sound radiated falls mainly in the range of low frequency, inaudible, infrasound. The present work assumes significance as most of the acoustic studies in moving load problems are on the high frequency noise, excited mainly by the surface irregularities. This study also helps to identify a particular geometry for which the vibro-acoustic responses are the minimum. Among the given beams, the tapered beam is found to have minimum displacement response while its acoustic response is estimated to be maximum. A beam with sinusoidally varying height is observed to have minimum acoustic response for most of the operating speed range when excited by a single moving load. This analysis has applications in the vibro-acoustic responses of bridges subjected to railway car load excitation.