This work gives exact vibration frequencies of columns, loaded by compressive axial force, two bending moments, and torsional moment, for several combinations boundary conditions. The proposed solution is based on a new method that enables to get the dynamic stiffness matrix for the member including the effects of the axial loading. The frequencies are found as the values that make the determinant of the stiffness matrix equal zero. Several examples are given and compared to published results to demonstrate the accuracy and flexibility of the method. New exact results are given for several other cases.
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