Results of truncating higher frequency modes associated with a modal representation of an aeroelastic high-speed civil transport

The objective of this study is to determine to what extent higher frequency modes may be truncated while retaining accuracy of the solution of the modal representation employed. Finite element equations of motion representing the flexible fuselage dynamics of a large aircraft with n links connected by torsional springs are derived using Lagrangian techniques. Aerodynamic forces are idealized as linearly varying with angle of attack and as being concentrated wing lift at the mid point of the middle link and tail lift at the free end of the last link. Implementation of these equations is done using Matlab. Simulink is used to simulate the system and an m-file is written for animation.;A one second period (initially downward) doublet force of 88,964.4 N (20,000 lbs) is applied at the tail of the aircraft and its effects propagated through the fuselage to the nose of the aircraft. Graphical and animation results were generated for 5, 7, 11 and 21 link models. Consistently, deflections of the nose experienced a time delay of about 0.2 seconds, then an initial smooth downward nonminimum phase motion of about 6.35 mm (0.25 in) which is followed by a period of upward motion. It is expected that the nose would initially move upward rather than down. There seems to be a tendency toward convergence to a common solution (presumably to the exact solution) with a higher number of links.;For both full and truncated models, a time response occurs in the pilot station due to a step input of tail lift. However, when the full and truncated models contain most of the low frequency modes, the behavior at the pilots station remains consistent.