A measurement analysis on pretwist non-unform beams

The governing characteristic differential equations for the bending vibrations of pretwisted beams are two coupled differential equations with variable coefficients. In the past, the exact solutions of the system have never been found and the problems were mainly studied by approximated methods. In this paper, the explicit relations between the two flexural displacements are derived. With these explicit relations, the two coupled governing characteristic differential equations can be decoupled and reduced to a sixth-order ordinary differential equation with variable coefficients in one flexural displacement. The derived explicit relations can also be used to reduce the difficulty in experimental measurement.