Analytical Study on Torsional Vibration of Thin-Walled Straight Beams

Three different mass matrix methods for determining natural frequencies of thin-walled continuous beams are presented. One method is the exact method based on a general solution of the differential equation of motion for torsional vibration, and it is called the continuous mass method. The other two matrix methods are the lumped and consistent mass methods based on the approximate finite element approach. The mathematical relationship between the exact and approximate methods is discussed. The numerical results computed by the lumped, consistent, and continuous mass methods are given in tabular form, and the accuracy of natural frequencies obtained by these mass matrix methods is investigated.