# Effective Mass of Cantilever beam (getting .36m instead of .23m)

• Mike415
In summary, the conversation is about finding the equivalent mass of a beam for a hanging point mass problem. The person is struggling with their calculations and is getting a different result than expected. After checking the expansion of a term in their calculation, they realize they need a refresher on completing the square.
Mike415

## Homework Statement

Im trying to find the equivalent mass of a beam so it can be modeled as a hanging point mass problem.

Given the v = y_dot equation, y equation, and T

Somewhere I am messing up with my math I believe as I am getting .36m instead of what I believe should be .23m.

## The Attempt at a Solution

http://i.imgur.com/NQc9V.png

Check the expansion of the []^2 term in the sixth line of your calculation.

SteamKing said:
Check the expansion of the []^2 term in the sixth line of your calculation.

Ha, thanks. Didn't think Id need a refresher on completing the square!

## 1. What is the effective mass of a cantilever beam?

The effective mass of a cantilever beam is a measure of its mass distribution and how it affects its dynamic behavior. It is often used in structural engineering and mechanical design to calculate the response of a beam to external forces.

## 2. How is the effective mass of a cantilever beam calculated?

The effective mass of a cantilever beam can be calculated using the Euler-Bernoulli beam theory, which takes into account the beam's length, cross-sectional area, and material properties. It also considers the beam's boundary conditions, such as being fixed at one end and free at the other.

## 3. Why am I getting a different effective mass value than expected?

There could be several reasons for this discrepancy. It could be due to errors in measurement or input data, assumptions made in the calculation method, or variations in the physical properties of the beam. It is important to carefully check all steps of the calculation and consider potential sources of error.

## 4. How does the effective mass of a cantilever beam affect its design?

The effective mass of a cantilever beam can significantly impact its dynamic response, such as its natural frequency and vibration amplitudes. Engineers must consider this when designing structures to ensure they can withstand external forces and maintain structural integrity.

## 5. Can the effective mass of a cantilever beam be reduced?

Yes, the effective mass of a cantilever beam can be reduced by altering its physical properties, such as its length or cross-sectional area, or by changing its boundary conditions. However, these changes may also affect the beam's structural integrity and must be carefully evaluated in the design process.

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