Document Type

Thesis - University Access Only

Award Date


Degree Name

Master of Science (MS)

Department / School

Mathematics and Statistics

First Advisor

Kurt Cogswell


A partial differential equation is developed to model the displacement of a drumhead with consideration given to where and how the drumhead is struck. Timpani are struck near the edge of the drumhead, instead of in the center like most drums, so a new coordinate system was constructed where the center of the new coordinate system is where the drumhead was struck. This was done to make the boundary condition locations of the partial differential equation more natural. To make the model complete, boundary conditions are presented for three different strokes: the dead stroke, the assisted-rebound stroke, and the free-rebound stroke. The del-squared operator for our new coordinate system was developed using a curvilinear coordinate approach. To provide the framework for understanding the approach, the del-squared operator was developed in polar coordinates.

Library of Congress Subject Headings

Cylinders -- Vibration.
Differential equations, Partial.
Music -- Mathematical models.


South Dakota State University



Rights Statement

In Copyright