Normal velocity reconstruction with sparse measurement points

To achieve normal velocity reconstruction of vibrating surface with sparse measurement points, a recon- struction method is presented by exploiting of acoustic radiation modes as expansion functions, which are capable of describing geometric shape of vibrating surface. Firstly, acoustic radiation modes of vibrating surface are calculated and the relationship between normal velocity and acoustic radiation modes is built. Then the expressions of normal velocity on actual measurement points by corresponding acoustic radiation mode values are deduced and the expansion coefficients are calculated. Subsequently, all normal velocity values can be reconstructed by the obtained expansion coefficients. Experiment validations have been performed by a double-layer steel cylindrical shell with enclosed ends in an anechoic water tank. Two cases were designed with a vibration shaker and a rotor device respectively. Both two experiment results show that actual vibration distribution cannot be revealed exactly with sparse measurement points, which corresponds to severe loss of vibration related wavenumber components. On the other hand, normal velocity and corresponding wavenumber components can be restored accurately according to the presented method, which demonstrates obvious effectiveness of the presented method.