Natural frequencies of rectangular membranes

[thadman]

Hello physicsforums members,

I am an engineering student at Purdue University and am currently conducting research with regards to ribbon transducers.

A ribbon transducer consists of a rectangular element of metal foil suspended within a magnetic gap (ie free at the sides) and clamped at its ends (ie a clamped-clamped membrane). Current is applied to the foil, which produces an electromagnetic field that interacts with the magnetic field generated by the permanent magnets. The foil bends in response to this force.

I am interested in calculating the natural frequencies of the aforementioned membrane. However, I am finding it to be non-trivial.

I have acquired access to Timoshenkos "Vibration problems in Engineering" through my Universities online library. On page 411 "Vibration of membranes", membranes are discussed as per the title.

-Timoshenko assumes that the membrane is uniformly stretched in all directions, however this does not apply to my particular problem. Is there anyway to get around this assumption? If not, are there any other texts anyone could recommend?

-The provided equations do not include a materials property element, only weight/area and tension. Would this not suggest that two materials with equal density, but dissimilar material properties, have the same natural frequencies?

How can I determine the minimum tension applied to the membrane which does not result in sagging?

Best Regards,
Thadman

 

[neurosport]

Approximate it as a string ...