Physics Based Finite Element Interpolation Functions for Rotating Beams

Abstract

Rotating beams are ubiquitous members of industrial structures such as wing turbine rotors, helicopter rotors, turbomachinery, robotic systems and aerial robots. Typically, finite element analysis is used to solve the vibration problem for these
structures. We show that it is possible to significantly enhance the efficiency of the finite element methods for rotating beams by creating basis functions which more closely satisfy the governing differential equation of the structure. Since the
rotating beam equation cannot be solved as an exact solution, different approximate strategies are explored to improve finite element convergence, especially at higher rotating speeds where the centrifugal stiffening terms become dominant.