The total energy relationships are given for a thin blade vibrating in combined bending-bending-torsion when allowance is made for bending of the longitudinal fibres occurring due to torsion. The Lagrangian function is, thus, obtained and, by use of variational methods, the equations of motion and the boundary conditions are derived. For the special case of a straight blade of uniform cross-section, symmetrical about both principal axes, an expression is deduced for the torsional frequencies which shows agreement with a similar expression obtained previously by a somewhat different approach
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