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Chapter 4

CHAPTER 4

BOUNDARY CONDITIONS

Overview

The selection of boundary conditions and the axes to be constrained was based on the procedures used by Rossing [9] during testing of the Martin D-28 guitar. The guitar was buried in tightly packed sand enclosure during testing to determine the resonance frequencies of the top and back plate. Rossing also covered the soundhole to eliminate coupling of the air modes with the modes of the top and back plates. Since air is not included in this iteration of the finite element model, this coupling effect did not exist.

BC1: Top Plate Free, Ribs, Back Plate, and Neck Constrained

This set of boundary conditions was used during all analysis of the top plate. The back plate nodes were constrained in the Z axis and free in the X and Y axes. As stated above, the intent was to simulate the constraint that the sand enclosure would place on the guitar. Similarly, the ribs were constrained in the X and Y axes and not in the Z axis.

In order to eliminate the weight of the neck from contributing in any way to the modal effective weight observed during that portion of the analysis, all of the neck nodes were constrained in the X, Y, and Z axes. A complete step by step account of BC1 assignment is listed in Appendix B. The picture of BC1 as applied to the model is shown below in Figure 23.

FIGURE 23. Boundary condition 1 (BC1).

BC2: Back Plate Free, Ribs, Top Plate, Neck Constrained

This set of boundary conditions was used during all analysis of the back plate. The top plate nodes were constrained in the Z axis and free in the X and Y axes. As stated in the overview, the intent was to simulate the constraint that the sand enclosure would place on the guitar. Similarly, the ribs were constrained in the X and Y axes and not in the Z axis. In order to eliminate the weight of the neck from contributing in any way to the modal effective weight observed during that portion of the analysis, all of the neck nodes were constrained in the X, Y, and Z axes. A complete step by step account of BC2 assignment is listed in Appendix B. The picture of BC2 as applied to the model is shown below in Figure 24.

FIGURE 24. Boundary condition 2 (BC2).

BC3: Top Plate Free, Contour Constrained

This set of boundary conditions was used during the linear static analysis where a pressure load was applied to the top plate and the nodal displacements were extracted for top plate arching. The contour nodes were constrained in X, Y, and Z axes. The nodes used both by the neckblock and tailblock tet elements and the top plate tri and quad elements were constrained in the X, Y, and Z axes. A complete step by step account of BC3 assignment is listed in Appendix B. The picture of BC3 as applied to the model is shown below in Figure 25.

FIGURE 25. Boundary condition 3 (BC3).

BC4: Back Plate Free, Contour Constrained

This set of boundary conditions was used during the linear static analysis where a pressure load was applied to the back plate and the nodal displacements were extracted for back plate arching. The contour nodes were constrained in X, Y, and Z axes. The nodes used both by the neckblock and tailblock tet elements and the back plate tri and quad elements were constrained in the X, Y, and Z axes. A complete step by step account of BC4 assignment is listed in Appendix B. The picture of BC4 as applied to the model is shown below in Figure 26.