# Natural frequencies of rectangular membranes

In summary, an engineering student at Purdue University is conducting research on ribbon transducers. These transducers consist of a rectangular metal foil suspended in a magnetic gap and clamped at its ends. The foil bends in response to the interaction between the applied current and magnetic field. The student is interested in calculating the natural frequencies of the membrane, but is finding it difficult. They have access to Timoshenko's "Vibration problems in Engineering" but it assumes uniform stretching, which does not apply to their specific problem. They are looking for alternative resources and wondering if the provided equations can account for materials properties. Additionally, they are trying to determine the minimum tension that will prevent sagging in the membrane.
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,

Approximate it as a string ...

## 1. What are natural frequencies of rectangular membranes?

Natural frequencies of rectangular membranes refer to the specific frequencies at which the membrane will vibrate when excited by an external force. These frequencies are determined by the physical properties of the membrane, such as its size, shape, and material composition.

## 2. How are natural frequencies of rectangular membranes calculated?

Natural frequencies of rectangular membranes can be calculated using mathematical equations that take into account the dimensions and physical properties of the membrane. These equations are based on the principles of vibration and mechanics.

## 3. Why are natural frequencies of rectangular membranes important?

The natural frequencies of rectangular membranes are important because they determine how the membrane will respond to external forces. This is crucial in applications such as musical instruments or engineering structures, where the desired frequency of vibration needs to be achieved.

## 4. Can the natural frequencies of rectangular membranes be altered?

Yes, the natural frequencies of rectangular membranes can be altered by changing the physical properties of the membrane, such as its size or material. This can be achieved through design changes or by applying external forces.

## 5. How are natural frequencies of rectangular membranes used in real-world applications?

Natural frequencies of rectangular membranes have many practical applications, including in the design of musical instruments, such as drums and string instruments, and in engineering structures, such as bridges and buildings. They are also important in the field of acoustics, where they help determine the sound quality of a space.

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