Reconstruction of Normal Surface Velocities of a Simply-Supported Baffled Plate Using Helmholtz Equation Least Square Method

The normal surface velocities of highly a non-spherical object are reconstructed based on the measurement of field acoustic pressures using Helmholtz equation least-squares (HELS) method. The objectives of this study are to numerically examine the feasibility and accuracy of reconstruction and the impacts of various parameters involved in reconstruction of vibro-acoustic responses using HELS. The vibrating object is a simply-supported and baffled thin plate. The reasons for selecting this object are that plate is the most challenging source geometry for HELS method, and it represents a class of structures that cannot be exactly described by the spherical Hankel functions and spherical harmonics, which are primarily embedded in the HELS formulation, yet the analytic solutions to vibro-acoustic responses of a baffled plate are readily available so the accuracy of reconstruction can be checked in detail. The Rayleigh integral is used to generate the input field acoustic pressures for reconstruction. The Euler’s equation is employed to establish the system model of reconstruction of vector velocities. Regularization associated with the truncated singular value decomposition is utilized to compromise the resultant accuracy and stability of the vector velocity reconstruction. The reconstructed normal surface velocities are validated against the benchmark values, and the out-of-plane vibration patterns at several natural frequencies are compared with the natural modes of a simply-supported plate. The impacts of various parameters such as the measurement points, measurement distance, the location of origin of coordinate system, microphone spacing, and ratio of measurement aperture size to the area of source surface of reconstruction on the resultant accuracy of reconstruction are examined.