- #1

- 25

- 0

The beam is made out of

**aluminum**that's L in length with a rectangular cross-section b and h. The relative magnitudes of L, b, and h pretty much make the system look like a diving board. Now if I displace the very end of my diving board some δy how long will it take to effectively die out.

I'm interested in displacements on the order of microns or less. So far I've modeled my system as a damped harmonic oscillator with L = 500 mm, b = 100 mm, h = 50 mm.

[itex]Y(t) = A e^{-\alpha t} cos(\omega t)[/itex]

where

[itex]\omega = \sqrt{k/\omega - \alpha^2}[/itex]

[itex]\alpha = \frac{C}{2I}[/itex]

and C is some damping coefficient in [itex]\frac{Nm \cdot sec}{rad}[/itex], I is the moment of inertia in [itex]kgm^2[/itex], and k is the spring constant in [itex]\frac{Nm}{rad}[/itex]

Any ideas on how to estimate k and C for this rectangular beam made of aluminum? There's no physical damper, and my best guesses as to how the energy is dissipated would be through friction (like bending paper clip back and forth). Am I even modeling this correctly?