Free transverse and lateral vibration of beams with torsional coupling

The free vibration of beams whose flexural motions in both principal planes are coupled with torsion is investigated by using the dynamic stiffness method. First, the governing differential equations of motion in free vibration are derived using Hamilton's principle. The dynamic stiffness matrix is then developed from the solution of these differential equations when the oscillatory motion of the beam is harmonic. Finally, the resulting dynamic stiffness matrix is applied with particular reference to the Wittrick-Williams algorithm to carry out the free vibration analysis of a few illustrative examples. The numerical results are discussed and this is followed by some concluding remarks.