Directivity of sound radiated from baffled rectangular plates and plate strips

Rectangular plates are important components in structures such as vehicles and bridges. The noise radiated by vibrating plates is mainly determined by three factors: the mean-square vibration, the radiation efficiency of the plates and the directivity of the sound. Although the first two factors have been widely investigated, much less attention has been paid to the directivity. The aim of this study is to investigate the directivity indices for rectangular plates subjected to either a single point force or multiple incoherent forces. Particular attention is given to plates with a large aspect ratio, referred to as plate strips. New definitions of directivity index are introduced that are more appropriate to such plate strips. The vibration of the plates is calculated from a modal superposition method based on approximate modal solutions of the plates with various boundary conditions. The Rayleigh integral method is used to obtain the sound pressure radiated from the vibrating plates, assuming that they are set in an ideal infinite baffle. Directivity indices of sound are firstly determined for plates with a small aspect ratio, and then for plate strips with a larger aspect ratio. Examples are given to illustrate the effects of the structural boundary conditions, and the effect of the baffle. For distributed incoherent excitation, as often found in practice, it is shown that the sound directivity pattern in the far field corresponding to the width direction varies insignificantly along the length of the strips; this is different from a single point force excitation. It is also found that the noise radiation from different concrete plates is approximately omnidirectional in the plane perpendicular to the longitudinal direction. Plates and plate strips are much less directional at high frequencies than the corresponding rigid piston. Nevertheless, the maximum value of directivity increases at high frequency as the number of modes in a one-third octave band increases. The dominant directions of sound radiation from plates are mainly controlled by the acoustical wavelength and vibrational wavelength, while the structural boundary conditions and the presence of the baffle have only a minor influence on them. Finally it is shown that, for the prediction of sound directivity of plate strips under distributed incoherent excitation, a two-dimensional vibro-acoustic model can be used in place of the three-dimensional one.