Abstract:

This paper attempts to quantify in a general way the spatial scales that occur on fluid-loaded plates and shells for the purpose of assessing various modeling techniques. Modelers using the SARA finite-element code typically follow a ``quarter-wavelength rule,'' which states that the size of a quadratic element should be less than a quarter of the minimum wavelength in the problem. The minimum wavelength for fluid-loaded plates and shells is often the flexural wavelength. Questions naturally arise regarding the accuracy of this rule near discontinuities. In this paper, a straightforward theoretical justification for the quarter-wavelength rule is presented in terms of a Taylor series expansion of the wave field. This justification is extended to the local evanescent fields generated near discontinuities. The complex wave numbers describing these fields, as well as SARA finite-element data for some canonical problems, are examined to determine the expected accuracy of a given discretized model. The fundamental conclusion is that modeling rules based on the propagating wave fields also give convergent answers for the evanescent fields generated near discontinuities.