Designing Vibration Absorber: Questions Answered

[renta]

I'm trying to design a vibration absorber that will reduce the vibration of a machine by about 60%. I found the equations of motion of the machine without the absorber to be..
m1+x2"+ k1*x1+k2(x1-x2)+C2(x1'-x2')=Fo*sin(wt)
and the absorber alone to be..
m1+x2"+k2(x1-x2)+C2(x2'-x1')=0

How do I do a two degree of freedom system (the machine and absorber together)? I have to calculate the natural frequencies and write the equations of motion in matirx form, and find the K and M matrices, form M^(-1)*K, and for designed k2 and c2, find the eigenvalues of M^(-1)*K. I really don't have much experience with this area, can someone please help me?

 

[Greg Bernhardt]

It sounds like you have a good understanding of what needs to be done, but might be having trouble putting it all together. You're right that you need to calculate the natural frequencies and write the equations of motion in matrix form. To do this, you'll need to combine the two equations of motion into one. This can be done by subtracting one equation from the other. Once you have the combined equation, use the method of assumed modes to solve for the natural frequencies and write out the equations in matrix form. After that, you can find the K and M matrices and M^(-1)*K. Finally, you can find the eigenvalues of M^(-1)*K for the designed k2 and c2.

If you're still having trouble, I'd recommend looking for tutorials online that explain how to do a two degree of freedom system. There are lots of resources available and some of them might be better suited for your specific needs. Good luck!

 

[GSXR750]

Designing a vibration absorber can be a complex task, but there are steps you can take to simplify the process. Here are some suggestions to help you design your absorber and achieve a 60% reduction in vibration.

1. Determine the natural frequencies of the system: The first step in designing a vibration absorber is to determine the natural frequencies of the machine without the absorber. This can be done by solving the equation of motion for the machine alone. Once you have the natural frequencies, you can design the absorber to have a natural frequency close to one of these frequencies.

2. Design the absorber: The absorber should have a mass, stiffness, and damping that are tuned to the natural frequency of the machine. The goal is to have the absorber vibrate in an opposite direction to the machine, effectively canceling out the vibration.

3. Calculate the K and M matrices: To create a two degree of freedom system, you will need to calculate the K and M matrices for both the machine and the absorber. These matrices represent the stiffness and mass of each component in the system.

4. Form the M^-1*K matrix: Once you have the K and M matrices, you can form the M^-1*K matrix, which represents the dynamic characteristics of the entire system.

5. Find the eigenvalues: The eigenvalues of the M^-1*K matrix represent the natural frequencies of the entire system. By choosing the stiffness and damping of the absorber, you can adjust these eigenvalues to match the natural frequency of the machine.

6. Verify the reduction in vibration: Once you have designed your absorber, you can test it on the machine to verify that it reduces vibration by 60%. You can use sensors to measure the vibration before and after the absorber is installed to confirm the reduction.

Overall, the key to designing a successful vibration absorber is to carefully tune its characteristics to match those of the machine. It may take some trial and error, but by following these steps, you should be able to achieve your goal of a 60% reduction in vibration.