Wave - based Finite Element

The Wave-based Finite Element Method or WFEM is applied to in-vacuo cylindrical shells to studystructure-borne wave interaction with bulkhead and keel-type plate attachments. The frequency rangeconsidered is from one to ten times the shell "ring" frequency. The goal is to better understand theshell-plate interaction, which plays an important role in the acoustic scattering and radiation processesfrom submarine hulls.Two formulations of a WFEM stiffness matrix for in-vacuo cylindrical shell are derived. I referto them as the axial wave formulation and the circumferential wave formulation. Both are based onthe Herrmann-Mirsky theory for thick 2D shells, which supports five wave types: compressional, shear,flexural, evanescent, and through-thickness shear. The WFEM method is shown to be exact to withinthe underlying assumptions of the governing equation. The method is numerically efficient by effectivelyeliminating an integration over wavenumber in the direction of the propagating wave. I show that anordered formulation of the stiffness matrix allows one to decompose the solution in post-processing bywave-type without wavenumber processing. The wave-sorting is also exact, numerically efficient, andcan be done in the near-field of structural discontinuites and in the presence of heavy material damping.In addition, I apply the WFEM method to a 3D solid cylinder that is infinitely extended in theaxial direction. The stiffness matrix relates displacements at the inner and outer radii to correspondingsurface stresses. Wavenumber integration is used in the other two directions to find the total solution.The 3D model may also be used for cylindrical shells with multiple layers. The global stiffness matrix forthe WFEM formulation is less than one sixth the size of a global matrix as derived by Ricks using theDirect Global Matrix method (DGM) [10] due to symmetry about the main diagonal and fewer degreesof freedom. I use the 3D WFEM model to establish the limits of the Herrmann-Mirsky theory versusfrequency and shell thickness.The 2D WFEM shell model is hybridized with a conventional FEM model of the shell-plate T-junctionto provide an accurate model of the junction from middle to high frequencies. I also use it to evaluatethe typical boundary matching condition when a FEM T-junction model is not used. This evaluationis carried out by comparing wave power scattering coefficients. I show that the hybrid model is neededat all frequencies when the shell thickness is relatively thick (10% of the shell radius). I show thatT-junction details are even important for relatively thin shells (2%-4%) especially when the bulkhead isthicker than the shell. In any case, the hybrid model may be used without sacrificing the good numericalefficiency of the WFEM method because the number of required conventional FEM elements is minimal.To demonstrate the use of the 2D shell model, I compare the predicted response of a cylindrical shelldue to an array of piezoelectric volume sources embedded in the shell wall with available experimentaldata collected by Lin [24]. I show that the agreement between the experimental data and the modelis very good down to the ring frequency of the shell. I provide a detailed analysis of the source-shellinteraction.P__1