Reconstruction of vibro-acoustic response of a plate using Helmholtz equation least-squares method

• Published in: The Journal of the Acoustical Society of America Vol. 120; no. 5_Supplement; p. 3344
• Main Authors: Lu, Huancai, Wu, Sean F.
• Format: Journal Article
• Language: English
• Published: 01.11.2006
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/1.4781367

A numerical investigation of reconstructing the vibro-acoustic responses of an arbitrary structure subject to vibration excitations based on the Helmholtz equation least-squares (HELS) method is presented. It is emphasized that in many engineering applications, the exact solution to a general vibrating structure does not exist, and the HELS method is one way of getting approximate solutions in a cost-effective manner. In this study, the test object is a simply supported, unbaffled thin plate. The reason for selecting this simply supported plate is that the analytic solutions to the plate vibrations are readily available. The field acoustic pressures generated by the Rayleigh integral are taken as input to HELS algorithms to reconstruct the normal velocity and normal acoustic intensity on the plate surface using Tikhonov regularization associated with generalized cross-validation methods. The reconstructed normal surface velocities are compared with the benchmark values, and the out-of-plane vibration patterns at the first five natural frequencies are compared with natural modes of the simply supported plate. The effects of measurement aperture, stand-off distance, and location of the origin of the coordinate system on the resultant accuracy of reconstruction are examined. [Work supported by NSF.]