Perturbation treatment for the vibrations of a circular membrane subject to a restorative force

الملخص EN

We have investigated the motion of a stretched elastic circular membrane which is subjected to a restorative force proportional to the velocity.

The wave equation which describes the vibrations in this case is written in polar form.

The perturbation method is applied together with the usual method of separation of variables.

The oscillations are then given at any instant of time t and point on the membrane depending on the given boundary and initial conditions.

The roles of the restorative force and the initial displacement are discussed.

The numerical solutions are then given by using the program Mathematica