On the basis of the nearfield acoustic holography (NAH) based on the distributed source boundary point method (DSBPM), a novel NAH based on the equivalent source method (ESM) is proposed. The theoretical model of the proposed method is established at first. And then, the error sensitivity and the reconstruction problems of a multi-source acoustic field and a semi-free acoustic field are analyzed, and the corresponding treatment methods are proposed. Subsequently, an experiment on a speaker is investigated to validate the feasibility and correctness of the method. In the method, no discretization is needed on the boundary of the vibrating body. The acoustic field is predicted directly by a set of weighted equivalent sources located inside the vibrating body. Therefore, the variable interpolation, the treatments of singular integrals and non-uniqueness of solutions in the characteristic wave number are avoided. Additionally, the method is adapted to arbitrary-shaped source, so it is really a meshless method. Furthermore, there are such merits as the simple principle, the high calculation efficiency and precision. It is valuabe for the NAH to be applied in the practical engineering field.
In a multi-source acoustic field, the actual measured pressure is a scalar sum of pressures from all the sources. The pressure belonging to every source cannot be separated out with the existing techniques. Consequently, routine formulas cannot be used to reconstruct the acoustic source and predict the acoustic field directly. In this paper, a novel theoretical model of reconstruction and prediction of multi-source acoustic field in the distributed source boundary point method (DSBPM) based nearfield acoustic holography (NAH) is established. Three different methods, namely combination method with single surface measurement, combination method with multi-surface measurement and elimination method with multi-surface measurement, are proposed to realize the holographic reconstruction of sources. With these methods, the problem of reconstruction and prediction of acoustic field existing multiple coherent sources synchronously is solved effectively. Using the particular solutions constructed by the DSBPM to establish the vibro-acoustic transfer matrix, the calculation time, calculation precision and calculation stability are improved. These methods are valuable in localizing acoustic source and predicting acoustic field in engineering field.
A robust technique has been proposed for reconstructing sound field for all wave-numbers, which is suitable for the radiation analysis on an arbitrarily-shaped body. According to the wave superposition formulation, the spatial sound field of an actual radiator can be represented equivalently by superposing the fields generated by some fictitious sources interior to the actual radiator. Meanwhile, the strength density on the fictitious sources can be obtained by matching the sound pressures of a finite number of field points. Once the strength density is calculated, the acoustic information at any field point can be obtained subsequently. Finally, some typical numerical examples are given to validate the theoretical analysis, and some investigations are made to analyze the influence of sound frequency and the fictitious source position on the reconstruction precision, which are helpful to the application of the proposed technique to real industrial measurements.
