ULTRASONIC MEASUREMENT OF THE THICKNESS, PHASE-VELOCITY, DENSITY OR ATTENUATION OF A THIN-VISCOELASTIC PLATE .2. THE INVERSE PROBLEM
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Part II of this two-part paper is concerned with the inverse problem: given the measured transfer function, deduce any one of the four acoustical properties of a thin, linear-viscoelastic plate (thickness, wave-speed, density or attenuation) given the remaining three, through a comparison with the theoretically predicted transfer function. A systematic and detailed analysis of the sensitivity of the through-transmission transfer function to the four acoustical parameters is presented. An inverse algorithm, which utilizes the well-known secant method in conjunction with the method of least squares, is used to deduce the acoustical parameters. The technique is fully automated and computer controlled and can be easily adapted for in situ NDE applications. The technique is used to measure the acoustical properties of plates made up of aluminium (thickness = 100 m to 2 mm), steel (25 m-500 m), brass (1.625 mm), glass (1 mm), Plexiglas (500 m-2 mm) and bulk epoxy (1.54mm), using commercially available, low frequency transducers (0.5-10 MHz). The errors are frequency dependent and become progressively worse as frequency decreases. In the case of thickness, where the sensitivity is relatively large, excellent results were obtained down to ( h gl) = O(10-2), where h is the layer thickness and is the wavelength. 1995.
