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Sean F. Wu
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Proceedings Papers
Proc. ASME. IMECE2009, Volume 15: Sound, Vibration and Design, 505-511, November 13–19, 2009
Paper No: IMECE2009-13201
Abstract
Vibro-acoustic responses of a vibrating rectangular plate were reconstructed using Helmholtz Equation Least Squares (HELS) method. The experiments were conducted on baffled rectangular plates of different aspect ratios with free as well as clamped boundary conditions under point force excitations via random and chirp sine signals. The radiated acoustic pressures were measured using a planar array of microphones at a very close distance to the plate surface, and taken as input to the HELS codes. The normal surface velocity distributions were reconstructed using HELS and compared against the benchmark data obtained using a laser vibrometer. Good agreements were obtained for both free and clamped boundary conditions. Finally, theoretical structural modes of the plate were compared against those obtained by HELS reconstruction and experimental modal analysis (EMA) for establishing their effectiveness in identifying closely coupled modes.
Proceedings Papers
Proc. ASME. NCAD2008, ASME 2008 Noise Control and Acoustics Division Conference, 397-413, July 28–30, 2008
Paper No: NCAD2008-73089
Abstract
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.
Proceedings Papers
Proc. ASME. IMECE2002, Noise Control and Acoustics, 43-49, November 17–22, 2002
Paper No: IMECE2002-32734
Abstract
The validity of the HELS method (Wu, 2000) for reconstructing the acoustic pressure field inside the minimum circle that encloses an arbitrary object is examined. Results show that the HELS solutions are approximate and the corresponding matrix equation is ill conditioned in general for back propagation of the acoustic field. Accordingly, the further the reconstruction point moves inside the minimum circle, the worse the reconstruction accuracy becomes. To overcome this difficulty new strategy for sensor placement is proposed. This strategy together with a constrained minimization are shown to yield satisfactory reconstruction inside the minimum circle. The same procedures can be extended to three-dimensional problems.