# Wind flutter; what is the reduced frequency, K?

1. Oct 15, 2009

### Krampus

Hi,

I'm trying to do a 2D-model of a bridge section subjected to wind, i.e. the bridge deck can have angular and vertical displacement due to the wind. I'm having some problem with understanding the theory.

The equations that I use to describe the aerodynamic lift and moment are (sorry for the messy equations...):
Lh = 1/2 * rho * U^2 * B * [K*(H1*)*h_prim/U + K*(H2*)*B*alpha_prim/U + K^2*(H3*)*alpha + K^2*(H4*)*h/B]

M_alpha = 1/2 * rho * U^2 * B * [K*(A1*)*h_prim/U + K*(A2*)*B*alpha_prim/U + K^2*(A3*)*alpha + K^2*(A4*)*h/B]

Where rho is the air density, U is the wind speed, B is the bridge deck width, K is the reduced frequency, Hi* and Ai* are the flutter coefficients, alpha and h are the angular and vertical displacements.

K=omega*B/U. Where U is the wind speed, B is the width of the bridge deck and omega is the circular frequency (omega=2*pi*n, n=frequency of oscillation).

My question is then; what is omega (or n)? Since it is a 2D-model of the bridge it can oscillate in either vertical direction or angular. Is omega connected to these oscillations? And if so, how? One idea that I thought of was to calculate 2 different K (one for h and one for alpha), this would solve my problem, but this approach has not been mentioned in any of the aeroelasticity books I've read...

If anyone can answer my question or have any thoughts around it I would very much appreciate it.

Thank you,
Maria