Abstract
An analytical method for determining natural frequencies and mode shapes of the torsional vibration of continuous beams with thin-walled cross-section is developed by using a general solution of the differential equation of motion based on Vlasov's beam theory. This method takes into account the effect of warping stiffness; it leads to an exact solution and is called the continuous mass method. Also, the approximate method based on the finite discrete element approach is presented. The mathematical relationship between the exact and the approximate methods is discussed, and the accuracy of the natural frequencies obtained by these analytical methods is investigated. Some typical continuous beams are analyzed to illustrate the applicability of the lumped, consistent, and continuous mass methods, and the computed results are given in tabular form.
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