Damping term in Euler Bernoulli equation

[umarkhan]

hello,
I have made an FEM simulation of a cantilever beam in Matlab. I have included the damping using damping matrix C= alpha x M + beta x K. Problem is that I want to compare my result with this paper

http://flyingv.ucsd.edu/rvazquez/Journal/nano.pdf (See eq.1)

where the author has put the damping in the Euler Bernoulli equation directly as follows,

EIz_xxxx(x,t) + czdot(x,t) + mzddot(x,t) = -u(t)


Question is how do I convert alpha and beta to c which is used for damping in the Euler Bernoulli eq?

Umar.

 

[Navin A S]

Unfortunately, there is no straightforward answer to this question. As you have probably noticed, the damping coefficient c in the Euler-Bernoulli equation is different from the damping matrix C in FEM simulations. The damping coefficient c represents a linear model of structural damping, while the damping matrix C incorporates nonlinear effects. Therefore, it is not possible to directly convert one into the other. In order to compare your results with those of the paper you referenced, you will need to use an equivalent linear damping model in both cases. This can be done by fitting the damping matrix C to a linear damping model, such as Rayleigh damping or an equivalent viscous damping model. Once you have obtained an equivalent linear damping model, you can then use this to determine the value of the damping coefficient c for the Euler-Bernoulli equation.