Abstract
By comparing the phase velocity predictions of various higher order beam theories with the second order approximations to the exact frequency equations for circular and thin rectangular section beams it is concluded that equivalence requires the inclusion of rotatory inertia, shear deflection, lateral contraction inertia and transverse direct stress corrections to the Euler-Bernoulli beam theory. In addition it is shown that Cowper's expression for the shear coefficient in the constitutive equation for shear is in fact identical to the original Timoshenko definition, the apparent difference arising through employing averaged rather than centre-line displacement quantities.
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