۱- Introduction

۲- Vibration and sound calculation

۳- Results and discussion for plates

۴- Results and discussion for plate strips

۵- Conclusions

References

Abstract

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.

Introduction

Plates with different sizes and aspect ratios are widely used as important structural components in vehicles, airplanes, industrial machinery, buildings and bridges. They are also important components in the radiation of noise when the structures are subjected to dynamic loading. For the purpose of predicting and mitigating noise from complex structures, it is helpful to understand the sound radiation from vibrating plates; particularly common are those with rectangular shape. Two important factors that influence the radiated sound power of a vibrating plate are the spatiallyaveraged vibration velocity and the radiation efficiency of the plate. In addition, the sound directivity also plays an important role in determining the distribution of sound pressure for external radiation problems. The radiation efficiency of a rectangular plate has been extensively studied, both for individual modes of vibration and for broadband excitation. Wallace [1] derived the modal radiation efficiency of simply-supported rectangular plates set in an infinite rigid baffle, based on the far-field acoustic intensity on a hemisphere of large radius. Gomperts [2,3] studied the modal radiation efficiency of rectangular plates with different boundary conditions.