2.3 Vibrating Flat Membranes
21
Fig. 2.5 The title pages of the dissertations of Willem and Jacobus Cornelius Kapteyn
and concluded that theory and experiment were in agreement. He did not add
much new. Maybe that is why the judicium was ‘only’ cum laude.
Jacobus Kapteyn did his follow-up research with the special case of membranes instead of plates (Fig. 2.5). The thickness of membranes can be left out
of consideration (Willem had already limited himself to the planes halfway
inside the plates) and that made the research easier. One can also stretch membranes between a frame, while plates need to be supported. Many results of
experimental work were already available for square and rectangular, triangular
and circular and elliptical membranes. Kapteyn’s derivations for the shape and
positioning of the positions of nodes are described in a very clear manner,
although it is also clear that it is mainly a presentation of other people’s earlier
work. But there is probably more: what seems new here is that Kapteyn predicted that there are not only lines of nodes, but that point-like nodes must also
occur. In the experiments these are not visible, which he reasonably attributes
to irregularities in the thickness and elasticity of the membranes. I present the
research in a little more detail in Appendix A.1.
The research is interesting, but what is particularly striking are the propositions added to Kapteyn’s thesis. It is and was a feature of Dutch PhD theses, that
they are accompanied by a set of propositions that have to be defended too at
21
Fig. 2.5 The title pages of the dissertations of Willem and Jacobus Cornelius Kapteyn
and concluded that theory and experiment were in agreement. He did not add
much new. Maybe that is why the judicium was ‘only’ cum laude.
Jacobus Kapteyn did his follow-up research with the special case of membranes instead of plates (Fig. 2.5). The thickness of membranes can be left out
of consideration (Willem had already limited himself to the planes halfway
inside the plates) and that made the research easier. One can also stretch membranes between a frame, while plates need to be supported. Many results of
experimental work were already available for square and rectangular, triangular
and circular and elliptical membranes. Kapteyn’s derivations for the shape and
positioning of the positions of nodes are described in a very clear manner,
although it is also clear that it is mainly a presentation of other people’s earlier
work. But there is probably more: what seems new here is that Kapteyn predicted that there are not only lines of nodes, but that point-like nodes must also
occur. In the experiments these are not visible, which he reasonably attributes
to irregularities in the thickness and elasticity of the membranes. I present the
research in a little more detail in Appendix A.1.
The research is interesting, but what is particularly striking are the propositions added to Kapteyn’s thesis. It is and was a feature of Dutch PhD theses, that
they are accompanied by a set of propositions that have to be defended too at