Application of the Reissner method to derive the coupled bending-torsion equations of dynamic motion of rotating pretwisted cantilever blading with allowance for shear deflection, rotary inertia, warping and thermal effects

Abstract

The dynamic Reissner functional in conjunction with variational calculus has been employed to derive the equations of motion of pretwisted cantilever blades of asymmetric aerofoil cross section. Shear deflection, rotary inertia, warping, thermal and rotational effects are considered, with the blade assumed to be mounted on a rotating disc at a stagger angle. It is observed that the thermal bending and twisting moments form an implicit set of additional terms in the respective conventional equations and further that these equations appear to be unwieldy when pretwist is present. A direct solution by using the dynamic Reissner functional appears to be far easier than the solution of the coupled equations in complex vibration problems.