Abstract
A classic problem in continuum mechanics is determining the normal modes of vibration of a thin elastic membrane with a circular geometry that is clamped at the edges. The analytical solution to the displacement field of such a problem are Bessel functions of the first kind. In this talk, I will describe the construction of a drumhead apparatus consisting of a latex sheet with a circular geometry in which the tension can be varied. Normal modes can be excited using a simple speaker and a strobe light can be used to slow the motion allowing close inspection of the displacement field. The various modes can then be compared to analytical solutions. The shift in natural frequencies of the system due to changing boundary conditions can be demonstrated by placing a hand close to the vibrating membrane.
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