Abstract
A problem arises from combining flexible rotorcraft blades with stiffer mechanical links, which form a parallel kinematic chain. This paper introduces a method for solving index-3 differential algebraic equations for coupled stiff and elastic body systems with closed-loop kinematics. Rigid body dynamics and elastic body mechanics are independently described according to convenient mathematical measures. Holonomic constraint equations couple both the parallel chain kinematics and describe the coupling between the rigid and continuum bodies. Lagrange multipliers enforce the kinetic conditions for both sets of constraints. Additionally, to prevent numerical inaccuracy from inverting stiff mechanical matrices, a scaling factor normalises the dynamic tangential stiffness matrix. Finally, example tests show the verification of the algorithm with respect to existing computational tests and the accuracy of the model for cases relevant to the problem definition.
Highlights
Solving high-stiffness rigid bodies coupled with flexible elastic bodies is an important, but difficult, problem within computational dynamics
Within the smart hybrid active rotor control system (SHARCS) program, an adaptive pitch link (APL) controls the vibrations transmitted from the rotor blades to the fuselage via a system of linkages that control the aerodynamics of the rotor
The results shown for verification purposes have preset hinges for the aerodynamic chain, the swashplate tilt and collective, and the pitch link and its actuator
Summary
Solving high-stiffness rigid bodies coupled with flexible elastic bodies is an important, but difficult, problem within computational dynamics. The thrust in this work is to quickly and inexpensively solve index-3 DAEs arising from the constrained (parallel) kinematics of the rigid body system with the numerical stability and controllable dissipation of the generalised-α scheme for flexible body mechanics. This includes the second-order accurate constrained mechanics work from Arnold and Brüls [3] and the second-order accurate (when elastic dissipation is zero) generalised-α energymomentum method outlined in [23], into a constrained generalised-α method, or abbreviated as CGα
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