Orthogonal polynomials for energy methods in rotary wing structural dynamics

Rotary-wing structural dynamics leads to the analysis of elastic bending and torsion of a rotating blade. In solutions by the energy method, Duncan polynomials can be used as basis functions for elastic bending and torsion. However, these are not orthogonal and may lead to poor numerical conditioning. Here, a complete set of orthogonal polynomials is developed through modification of the Duncan trinomials and binomials. The new polynomials for hingeless and articulated rotors are orthogonal and satisfy both geometric and natural boundary conditions at the tip and root. Test problems are presented to study their behavior and to compare the mode shapes. The results show that these orthogonal polynomials are a viable choice for the Ritz-Galerkin method applied to rotary-wing aeroelasticity analysis.