Variational analysis for the steady state flexural behaviour of rotating orthotropic sandwich beams

Abstract

Governing equations for predicting the steady state flexural behaviour of rotating sandwich cantilever beams with two orthotropic facings and an isotropic inner core are formulated by using the variational principle. Those for describing the steady state deformation and displacements of an orthotropic beam are also formulated by using the same method. The effect of the curing temperature of the orthotropic material upon steady state stress distributions is also included in this analysis. Exact solutions of these differential equations are obtained to calculate displacements and stress distributions in both symmetric and non-symmetric sandwich beams subjected to uniformly distributed loads. Steady state stress values for an orthotropic beam loaded with a flatwise tip force are calculated so that they can be compared to dynamic measurements for the type of beam reported in the literature. The present analysis also predicts both the lateral and the transverse inertio-elastic instabilities due to the rotational action of the beam.