On the Vibration of a Circular Membrane with Added Mass

The characteristic frequencies of a circular membrane carrying a rigidly attached concentric circular mass of finite area and vibrating symmetrically are studied. The main problem is that of determining the ranges of the parameters for which the frequencies will always be above or always be below those of the unloaded case. One of the chief tools is the minimum principle appropriate to the problem. The first term in the asymptotic expansion of the higher frequencies is obtained.