Is there a way to improve the calculation efficiency in this case?

[sfan]

Hi, everyone,

I am trying to use Duhamel Integral to calculate a continuous bar axial vibration response,

Below is my process:

I only used the eta1(t) part and the first phi*eta1(t) (add from i=0 to 0)

But it takes 5mins for Mathcad to finish the calculation of this simple case. 

Is there a way to improve the calculation efficiency?

Before this, I also tried to create a matrix with 100 points for u1, and plot the matrix,

but the time for the final calculation is also very long.

Given this is only a simple case, adding from 0 to 0, I am afraid that it takes forever to finish the accumulation of more phi*eta.

I propose that the problem of this low efficiency is with the Duhamel integral,

Is there a way to improve it?

Thank you very much!

Best Regard

Shawn

[sfan]

I also tried this way, but it is also very slow.

[sfan]

Hi, guys,

I tried this way, similar to Matlab, and it improved the efficiency a lot.

I just save the expression of Duhamel integral as a function, and substitute n, omega, t as variables to find eta.

With the expression saved beforehand, the later calculation is much more faster.

Hope this could help if anyone needs.

And if you have better ways, please leave a comment.

Thank you

Success!

Shawn