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# Vibro-acoustic behaviour of a non-uniform beam traversed by a moving point load

Date Issued

01-01-2014

Author(s)

Sudheesh Kumar, C. P.

Sujatha, C.

Shankar, K.

Abstract

Vibro-acoustic behaviour of a non-uniform beam of sinusoidally varying height, traversed by a single point load, is investigated in this paper. A method to reduce the vibration responses and sound power radiation by a uniform beam by modifying it into a non-uniform one having the fundamental mode shape of a uniform beam, without adding or removing any mass, is presented for the first time. The significance of this type of non-uniform beam is that, it has the same shape as the first mode of a simply supported uniform beam which contributes predominantly to the vibration response due to moving load excitation. Since a closed form solution is not possible in this case, finite element method is used to formulate the equations of motion of the beam in matrix form. The forced response of the beam is calculated numerically using central difference method with appropriate time steps. The vibration responses are compared with that of a uniform beam having the same mass and material properties. The sound power radiated by the beam is calculated using Rayleigh integral with the assumption that it is vibrating in an infinite baffle. Velocity responses obtained from finite element method are used to determine the sound power radiated by the beam. Radiated sound power, for different speeds of the moving load, is calculated and compared with that of a uniform beam. The paper aims at predicting the influence of geometry on the vibration and sound radiation characteristics of a simply supported beam subjected to a single moving concentrated load. The results show that by changing the shape of a uniform beam to a sinusoidal one, the vibration response and sound power radiation can be considerably reduced. This, being a numerical method, can predict the vibro-acoustic response of any non-uniform beam to moving load excitation. The present analysis, though limited to a single moving load, can be extended to a series of loads and thus the vibration and acoustic responses of a bridge due to passage of trains can be predicted.