Abstract
This chapter deals with the generalization of the wave equation to describe wave propagation on two-dimensional surfaces and sound waves in a three-dimensional space. Again linearity is postulated, which is only justified if amplitudes are sufficiently small. It will be shown how wave equations can be derived for rectangular and circular membranes , plates and disks and how analytic results can be obtained for a three-dimensional case with relatively simple boundary conditions. This chapter will also review techniques for the calculation of resonance frequencies and for the prediction of associated modal shapes.
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Abbreviations
- FEM:
-
finite element method
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Kausel, W. (2018). Waves in Two and Three Dimensions. In: Bader, R. (eds) Springer Handbook of Systematic Musicology. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55004-5_3
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DOI: https://doi.org/10.1007/978-3-662-55004-5_3
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