Correlation between torsional vibration and translational vibration

This paper presents theoretical investigation on the cross correlation between torsional vibration (u(theta)) and translation vibration (u(x)) of asymmetrical structure under white noise excitation. The formula reveals that the cross correlation coefficient (p) is a function of uncoupled frequency ratio (Omega = omega(theta)/omega(x)), eccentricity, and damping ratio (xi). Simulations involving acceleration records from fifteen different earthquakes show correlation coefficients results similar to the theoretical correlation coefficients. The uncoupled frequency ratio is the dominating parameter to p; generally, p is positive for omega(theta)/omega(x) > 1.0, negative for omega(theta)/omega(x) < 1.0, and close to zero for omega(theta)/omega(x) = 1.0. When the eccentricity or damping ratio increases, p increases moderately for small Omega (< 1.0) only. The relation among u(x), u(theta) and corner displacement are best presented by p; a simple way to hand-calculate the theoretical dynamic corner displacements from u(x), u(theta) and p is proposed as an alternative to dynamic analysis.