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UNDAMPED MODAL ANALYSIS
COMPLEX MODAL ANALYSIS
ORTHOGONALITY OF ROTOR DAMPED NATURAL FREQUENCIES AND
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Amplitude Phase Angle amplitudes of motion bearing damping Charlottesville complex eigenvalues complex mode shapes computed critical speed modes CROSS COUPLED DAMPING damped mode shape damped natural frequencies damping coefficients damping matrix damping ratio determination displacement vector equation 2.l0 equations of motion EXAMPLE ROTOR finite element analysis Finite Element Program fourth mode FREQUENCIES AND MODE gyroscopics jth mode lb-sec/in left handed eigenvector LundL mass stations modal amplification factor modal analysis modal damping modal method number of mass number of undamped numerical difficulties operating speed orthogonality conditions peak response speed peak unbalance response predicted rad/sec RLES rotor amplification factor rotor bearing systems rotor critical speeds rotor motion rotor system rotor unbalance response second critical second resonance speed set of equations solved speed and amplification speed range speeds and mode stiffness third mode transient analysis transpose unbalance response speeds uncoupled undamped critical speeds undamped modes University of Virginia values vector