Guided wave propagation in metallic and resin plates loaded with water on single surface

Our previous papers reported dispersion curves for leaky Lamb waves in a water-loaded plate and wave structures for several typical modes including quasi-Scholte waves [1,2]. The calculations were carried out with a semianalytical finite element (SAFE) method developed for leaky Lamb waves. This study presents SAFE calculations for transient guided waves including time-domain waveforms and animations of wave propagation in metallic and resin water-loaded plates. The results show that non-dispersive and non-attenuated waves propagating along the interface between the fluid and the plate are expected for effective non-destructive evaluation of such fluid-loaded plates as storage tanks and transportation pipes. We calculated transient waves in both steel and polyvinyl chloride (PVC) plates loaded with water on a single side and input dynamic loading from a point source on the other water-free surface as typical examples of metallic and resin plates. For a steel plate, there exists a non-dispersive and non-attenuated mode, called the quasi-Scholte wave, having an almost identical phase velocity to that of water. The quasi-Scholte wave has superior generation efficiency in the low frequency range due to its broad energy distribution across the plate, whereas it is localized near the plate–water interface at higher frequencies. This means that it has superior detectability of inner defects. For a PVC plate, plural non-attenuated modes exist. One of the non-attenuated modes similar to the A0 mode of the Lamb wave in the form of a group velocity dispersion curve is promising for the non-destructive evaluation of the PVC plate because it provides prominent characteristics of generation efficiency and low dispersion. INTRODUCTION Semi-analytical finite element (SAFE) calculations have been developed as an efficient calculation technique for guided waves propagating in elongated structures such as plates and pipes [3–9]. Most of the SAFE calculations were formulated for guided waves in an elastic waveguide with homogeneous geometry and material constants in the longitudinal direction under the traction-free boundary conditions. However, practical objects to be inspected such as pipes and tanks often come in contact with media like fluid and soil, causing ultrasonic energy to leak. Hence, attenuation caused by the leakage is an indispensable issue. Recently, SAFE calculations considering leaky media have become feasible by introducing absorbing layers and perfectly matched layers surrounding the leaky media or by expressing the outer open domain with the boundary element method [7–11]. SAFE calculations for leaky Lamb waves were formulated based on the characteristic that waves leaking into fluids propagate as plane harmonic waves with the sound speed of the fluids [1]. Moreover, SAFE calculations of transient responses for external dynamic loading were developed in Ref. [2]. Considering the inspection of pipes and tanks filled with water using guided waves, this study describes Lamb waves propagating in a plate loaded with water on a single surface. Dispersion curves, attenuation curves, wave structures, and transient responses for dynamic loading are calculated for steel and polyvinyl chloride plates as typical examples of metallic and resin plates. We discuss the detectability of inner defects in the walls of pipes or tanks. 42nd Annual Review of Progress in Quantitative Nondestructive Evaluation AIP Conf. Proc. 1706, 030003-1–030003-7; doi: 10.1063/1.4940475 © 2016 AIP Publishing LLC 978-0-7354-1353-5/$30.00 030003-1 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions IP: 130.54.110.31 On: Wed, 02 Nov 2016 04:56:05 TRANSIENT WAVE CALCULATION FOR LEAKY LAMB WAVES We consider a plate with a water-loaded lower surface and a traction-free upper surface on which the harmonic point force is loaded in the y direction at x = 0, with waves propagating in the plate and water. SAFE calculations for this condition were formulated based on the characteristic that a plane harmonic wave with the wavenumber of f ) ( f c is generated by the Lamb wave with the x-directional wavenumber of x , where is the angular frequency and f c is the wave speed of the fluid. Letting a nodal displacement vector at the cross-sectional nodes in frequency and wavenumber domains be x , U and the y component of the wavenumber in the fluid f be y , the following governing equation is obtained: