# Cantilever Beam First Mode of Vibration

• Oscar6330
In summary, the conversation is about identifying the first mode of vibration of a cantilever beam. The speaker developed a COMSOL model and calculated the first 6 modes, and later watched a video on YouTube which showed the first mode. They discuss differentiating between normal vibrating beam and first mode, and the speaker mentions that one way to identify normal modes is by measuring amplitude versus frequency. They also mention that visually, one can tell when the beam is near its normal mode due to increased amplitude.

#### Oscar6330

I developed a COMSOL model and calculated the first 6 modes of vibration of cantilever beam. Later out of curiosity, I looked up some videos on youtube to see actual cantilever. I found this video which shows the first mode.

How do you know that its first mode of vibration? More specifically, how do you differentiate between normal vibrating beam and first mode (they look quite the same)?

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any help please!

Oscar6330 said:
How do you know that its first mode of vibration? More specifically, how do you differentiate between normal vibrating beam and first mode (they look quite the same)?

What do you mean by "normal vibrating beam"?

nasu said:
What do you mean by "normal vibrating beam"?

From Normal vibrating beam/ cantilever, I mean a beam which is vibrating at a freq other than its mode freg. For e.g if first mode a beam is at 100 hz and its vibrating at 40Hz.

Now I understand. One way to go is the following:
If you vibrate the cantilever and change the excitation frequency continuously, you can tell the normal modes by an increased amplitude. For low damping this may be very sharp.
If you measure amplitude versus frequency, you will see some peaks corresponding to the normal modes (or resonant frequencies).
For the setup in the clip I guess you can tell visually when it is near the normal mode, from the increased amplitude.

## What is a cantilever beam?

A cantilever beam is a type of structural element that is supported at one end and free to move at the other end. It is commonly used in bridges, buildings, and other structures to support loads and resist bending.

## What is the first mode of vibration of a cantilever beam?

The first mode of vibration of a cantilever beam refers to the lowest frequency at which the beam can vibrate, with the largest amplitude of deflection. This mode is also known as the fundamental mode or the natural frequency of the beam.

## What factors affect the first mode of vibration of a cantilever beam?

The first mode of vibration of a cantilever beam is affected by several factors, including the material properties of the beam (such as stiffness and density), the length and cross-sectional shape of the beam, and the boundary conditions at the fixed end.

## How is the first mode of vibration of a cantilever beam calculated?

The first mode of vibration of a cantilever beam can be calculated using the Euler-Bernoulli beam theory, which takes into account the material properties, geometry, and boundary conditions of the beam. This calculation typically involves solving a differential equation and determining the natural frequency of the beam.

## Why is the first mode of vibration of a cantilever beam important?

The first mode of vibration of a cantilever beam is important because it determines the maximum deflection and stress that the beam can experience under a given load. Understanding the first mode of vibration can help engineers design more efficient and safe structures.