Approximate equations of motion are derived by use of Hamilton’s variational principle. The warping function, which is part of the solution, depends on wavelength. Numerical results on dispersion for rectangular cross sections have been obtained by the finite-element method. A comparison with the experimentally verified Barr theory is given. The paper is a contribution to the low-order approximate theories of torsional waves. It shows how good the Saint Venant warping function assumption in the low-order theory is at long relative wavelengths and it provides a modification of the theory for use at shorter wavelengths.

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