稀疏测点条件下的结构法向速度重建

Normal velocity reconstruction with sparse measurement points

为了实现稀疏测点条件下结构表面法向速度的准确重建,利用声辐射模态包含结构表面几何形状信息的性质,以声辐射模态作为基函数提出了一种稀疏测点条件下的结构法向振速重建方法。首先对结构表面的声辐射模态进行计算,并建立结构表面法向振动速度与声辐射模态之间的关系;在此基础上,由实际布置情况形成测点位置处的振速与其声辐射模态值的关系,并通过最小二乘法求得展开系数;最后由展开系数重建出结构表面的全部法向振速。利用两端封闭的双层钢质圆柱壳体在消声水池中进行了试验验证,分别开启激振器和转子台进行激励,两个试验的结果均表明,当测点数目较少时,所测的结果不能准确地表示结构的实际振动情况,在波数域内就表现为与振动相关的波数成份的丢失;利用所提出的方法,可以较为准确地重建和恢复结构的表面法向速度及其波数成份,由此验证了所提出方法的有效性。

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 ve- locity and corresponding wavenumber components can be restored accurately according to the presented method, which demonstrates obvious effectiveness of the presented method.