Wave reflections in a semi-infinitely long cylinder with an attached solid of revolution / by Nairui Yin.
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"A numerical procedure is presented for the study of end reflections in a semi-infinitely long isotropic circular cylinder with attached piezoelectric patch. The hybrid method which combines the finite element formulation in the piezoelectric patch with a wave function expansion representation in the isotropic cylinder is employed in the study. The global solution is obtained by imposing the continuity conditions on the displacements and tractions at the interface between the piezoelectric patch and the cylinder. To obtain the wave functions in the cylinder, the governing equations of the cylinder are discretized by a semi-analytical finite element formulation where the discretization occurs through the cylinder's thickness. Solutions in the cylinder are constructed with modal data from a spectral decomposition of the differential equations governing its natural vibrations. These modal data consist of all propagating modes and edge vibrations, constituting the basis for a wave function expansion of the reflection of waves arriving at the end of the cylinder. On the other hand, the piezoelectric patch is discretized by the axisymmetric finite element formulation. Both least-square and virtual work methods are used for evaluating the amplitudes of the reflected wave field.