Exact modal analysis of an idealised whole aircraft using symbolic computation

Abstract

AbstractExact expressions for the frequency equations and mode shapes of an idealised whole aircraft are derived using the symbolic computation package REDUCE. The aircraft is idealised as a bending-torsion coupled beam for the wing with the associated mass and inertia of the fuselage, tail-plane, fin and rudder assembly being concentrated at the root. The governing differential equation of motion of the aircraft is then solved in its most general form. The analysis is split into symmetric and anti-symmetric cases to formulate the equations from which the natural frequencies and the corresponding mode shapes of the unrestrained aircraft are derived. The analytical approach used here is of great significance, particularly from an aeroelastic optimization point of view, for which repetitive calculations of natural frequencies and mode shapes are often required. The application of the theory is demonstrated by numerical results. These results have been compared with those obtained from the dynamic stiffness and finite element methods.