On wave interaction and diffraction from the junction of two curved plates under unilateral fluid loading

• Published in: Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 356; no. 1741; pp. 1421 - 1467
• Main Authors: Norris, A. N., Rebinsky, D. A., G. R., Wickham
• Format: Journal Article
• Language: English
• Published: The Royal Society 15.06.1998
• Subjects: Acoustic Diffraction; Approximation; Coefficients; Curvature; Elastic Shells; Flat plates; Flexural Wave; License plates; Longitudinal waves; Polynomials; Reflectance; Structural Acoustics; Wave diffraction; Wave reflection; Wiener-Hopf Technique
• ISSN: 1364-503X; 1471-2962
• DOI: 10.1098/rsta.1998.0228

A general solution is developed which describes the acoustic and dynamic structural response generated at the junction of two curved plates subject to unilateral fluid loading. The plates are modelled by two-dimensional thin-shell theory, and the solution is found by applying the Wiener-ndash;Hopf technique to the dual integral equations for the unknown pressure on the plates. A simple method is presented for evaluating the Wiener-ndash;Hopf split functions in semi-analytic form. The general solution is found by expressing the pressure transform in terms of a polynomial function whose coefficients are determined by the conditions at the joint. Here we consider welded and clamped junctions, either of which requires four unknown coefficients to be determined. Several limiting cases are examined including the practically important ones where either one or both plates are flat. Various diffraction coefficients associated with the fluid-ndash;structure interaction are studied and numerical predictions are presented for the magnitudes of the diffracted acoustic and structural waves. Energy partition among the various wave types is also investigated. It is found that even the small curvature effects considered here can lead to significant coupling between flexural and longitudinal structural waves.