# What is the Eigenfrequency mean in vibration?

• HunterYeoh
In summary, the Eigenfrequency refers to the "characteristic" frequency of a system, in this case the rotational frequency at which a camshaft experiences the most vibration. In order to analyze this vibration frequency, a modal and buckling analysis can be done using a model from the comsol library. However, creating a model of four rotating camshafts with a plate on top may be challenging due to the difficulty in modeling the contact between the cams and the plate. One approach is to use periodic boundary conditions and solve the problem as an eigenvalue problem. Another method is to use the Rayleigh method to calculate the natural frequencies of a clamped plate. The results can then be compared to the desired frequency for optimal design.
HunterYeoh
Hi,

I have a simple question to ask: What is the Eigenfrequency mean in vibration? I am confused and can anyone here explain to me or provide me some useful link?

I am trying to use comsol to analyse the vibration frequency from a plate, which was mount on top of 4 camshafts. These camshafts will rotate and hence the plate sitting on top will vibrate. If anyone is familiar with comsol, Pls help me by teaching me which mode i should use.

Many Thanks.

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In a modal and buckling analysis, you have a problem that looks something like:

$$[K]\left\lbrace\phi_i\right\rbrace = \lambda_i [M]\left\lbrace\phi_i\right\rbrace$$

Where [M] is the structural mass matrix, [K] is the stiffness matrix. For i modes, the eigenvalues represent the the ith mode, and the eigenvector represents the "shape" of that mode.

The eigenfrequency that you're referring to is probably the ith mode.

Eigenfrequency basically means the "characteristic" frequency. "Eigen" comes from German and means "own", so i guess "own-frequency" is more literal but sounds dumb. As for the Eigenfrequency of a camshaft in the context of vibration, i think this would refer to the rotational frequency at which you would have the largest amount of vibration, which could also be called the resonant frequency. In the design of the camshaft, this is something you want to avoid during operation. So you design it to make this frequency higher than the max speed required.
I have used comsol quite a bit, but not so much for structural mechanics. However, i do know there is a model in the library which simulates the vibrational modes of a crankshaft. This would be a good place to start. As for making a model of four rotating camshafts with a plate on top, i think this will be very challenging, if not impossible. The biggest problem is modeling the contact between the cams and the plate, which you haven't really explained in your post. As a start, i would try and make up functions to describe the forces imposed on the plate by the camshaft and then impose them as periodic boundary conditions onto the plate. Then you should be able to solve it as an eigenvalue problem. This is one of the solver options that you can select.

Good luck!

As coryeh says, the eigenfrequency is the "characteristic" frequency in the sense of the frequency that characterizes the system, the frequency that is natural or characteristic of the system.

You dont' really need to do a full transient test with contact elements. Basically, just do a modal analysis of the plate. That gives you the numbers. Then multiply that by how many times the cam lobes "hit" the plate per revolution. For example, if the four lobes are all 90° out of phase, then multiply by four. This gives you essentialyl "exitations per revolution". From here you can convert to frequency to make it easier to compare to the results.

Anyways, the modal analysis will give you the natural frequencies, neglecting any type of damping. You then just dont' want to be there, you don't need any other type of analysis unless your design forces you to run close.

coreyh said:
Eigenfrequency basically means the "characteristic" frequency. "Eigen" comes from German and means "own", so i guess "own-frequency" is more literal but sounds dumb. As for the Eigenfrequency of a camshaft in the context of vibration, i think this would refer to the rotational frequency at which you would have the largest amount of vibration, which could also be called the resonant frequency. In the design of the camshaft, this is something you want to avoid during operation. So you design it to make this frequency higher than the max speed required.
I have used comsol quite a bit, but not so much for structural mechanics. However, i do know there is a model in the library which simulates the vibrational modes of a crankshaft. This would be a good place to start. As for making a model of four rotating camshafts with a plate on top, i think this will be very challenging, if not impossible. The biggest problem is modeling the contact between the cams and the plate, which you haven't really explained in your post. As a start, i would try and make up functions to describe the forces imposed on the plate by the camshaft and then impose them as periodic boundary conditions onto the plate. Then you should be able to solve it as an eigenvalue problem. This is one of the solver options that you can select.

Good luck!

Hi, Thanks for the reply. Can I ask you how can I do the rotation? I am new to comsol. I try to apply the rotational force on the shaft so it can turn and i will analyses the frequency. But fail to do it. and Is there possible to see the rotation animation just like in Cosmos or Ansys? Thank you

minger said:
You dont' really need to do a full transient test with contact elements. Basically, just do a modal analysis of the plate. That gives you the numbers. Then multiply that by how many times the cam lobes "hit" the plate per revolution. For example, if the four lobes are all 90° out of phase, then multiply by four. This gives you essentialyl "exitations per revolution". From here you can convert to frequency to make it easier to compare to the results.

Anyways, the modal analysis will give you the natural frequencies, neglecting any type of damping. You then just dont' want to be there, you don't need any other type of analysis unless your design forces you to run close.

Thanks for the reply. I have difficulty in applying the rotational force to the shaft. Can you tell me how to do it? thank you.

FredGarvin said:
You essentially have a rectangular plate that is clamped on all sides. There are methods for calculating the natural frequencies of this scenario, like the Rayleigh method. I would start there. Check out this link. It is to a book that lists a sample calculation including some varying boundary conditions.

please helpe me!I'm new in comsol I want to simulate a RF filter that includes 2 IDT and some electrodes in comsol but I can't get accurate response:(i want to analyse at frequency domain with some condition boundaries but osculate with a error but at eigenfrequency analyse not be problem so I have some question:1)at eigenfrequency analyse at comsol how many responses can we get?and about frequncy domain?2)we want to get resonant frequncies of my model can I get the curve of it or admittance matrix at comsol?

## 1. What is the definition of eigenfrequency in vibration?

Eigenfrequency, also known as natural frequency, is the frequency at which an object or system naturally vibrates without any external forces acting on it. It is determined by the physical properties and geometry of the object or system.

## 2. How does eigenfrequency affect vibration?

The eigenfrequency of an object or system determines its vibration characteristics, such as its amplitude and frequency of oscillation. If an external force is applied at the eigenfrequency, it can cause resonance, which can lead to excessive vibration and potential damage to the object or system.

## 3. How is eigenfrequency calculated?

Eigenfrequency is calculated by taking the square root of the stiffness of the object or system divided by its mass. This is known as the natural frequency equation: f = √(k/m), where f is the eigenfrequency, k is the stiffness, and m is the mass.

## 4. What factors can affect the eigenfrequency of an object or system?

The eigenfrequency of an object or system can be affected by its stiffness, mass, and geometry. Changes in any of these factors can alter the natural frequency and vibration characteristics of the object or system.

## 5. How is eigenfrequency used in practical applications?

Eigenfrequency is important in engineering and design, as it helps determine the natural vibration modes of structures and machines. This information is crucial in ensuring the safe and efficient operation of various systems, such as bridges, buildings, and aircraft.

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