Abstract
The influence of surface imperfections on the propagation of guided waves in an immersed elastic plate can be interpreted by means of a rheological model. The corrugated surface is modeled by a very thin interface, similar to a Jones spring model, which replaces the continuity boundary conditions at the liquid – corrugated solid-plate interface. As the surrounding liquid is considered to be perfect, only one complex stiffness is used for the model of Jones. The selection of the plate guided mode and the test frequency are motivated by the detectability and non-interference with other modes. The spring stiffness is obtained by a best fit procedure, between the analytical solution and the results obtained by the finite elements method (FEM). One way ensuring the agreement of the two approaches, rheological and FEM, is to consider angular resonances provided by the transmission coefficients. Small changes in the parameters of the roughness keep the positions of the angular resonances of the plate practically unchanged, while at the same time large variations of the half width of the transmission coefficient curve is observed. The effect of corrugation parameters on the guided modes in the plate can be predicted by using the rheological model with the deduced spring complex stiffness.
Highlights
Machined plane surfaces are prone to imperfections, which can be described as local deviations from the theoretical plane surface
Roughness is in general defined by statistical functions such as Rq [1], which is the root mean square (RMS) of the function hrðxÞ measuring deviations along a distance x 2 1⁄20; Lx, in which Lx is a characteristic length of the corrugation: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
The main objective is to represent the attenuation of the leaky Lamb waves by a rheological model, with normal spring stiffness depending on the corrugation geometry, which can provide much faster results than the finite elements method (FEM) approach for practical applications
Summary
Machined plane surfaces are prone to imperfections, which can be described as local deviations from the theoretical plane surface. Nagy and Adler [18,19] investigated the attenuation of reflected and transmitted waves by a rough aluminum plate immersed in water, but only at normal incidence. Drinkwater et al [21] have investigated the reflection coefficient for normal incidence waves at the interface between two rough aluminum blocks Their model integrates a spring model, for which the normal stiffness KL is deduced as function of frequency and reflection coefficient. Our justification of the use of Jones model is the following: the corrugation being periodic, one can assume for small heights of the asperities with respect to the wavelength that the interface is composed of a very thin layer, neither liquid nor solid, separating liquid from plate. The main objective is to represent the attenuation of the leaky Lamb waves by a rheological model, with normal spring stiffness depending on the corrugation geometry, which can provide much faster results than the FEM approach for practical applications
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