| Author | Nicolaas J. Theron |
|---|---|
| Title | Multi-Body Dynamic Analysis of Helicopter Rotors |
| Year | 1994 |
| School | Mechanical Engineering |
| Institution | RPI |
| Abstract | A helicopter rotor is a prime example of a non-linear multi-body dynamic system, in which various elastic bodies are interconnected with joints imposing kinematic constraints. The finite element method is chosen to model the rotor in non-linear multi-body dynamic analyses. The most important elastic element in this case is the beam element, to model the blade. The three dimensional Saint-Venant beam theory is implemented to calculate the sectional properties of naturally curved and twisted composite beam sections of complex shape. This theory is expanded to allow the analysis of differential warping and a non-linear strain effect common to rotor blades. Various examples illustrate the use of both methods, and show their powerful capabilities. The kinematic constraints are implemented through a Lagrange multiplier technique. This results in stiff, non-linear differential-algebraic equations, the numerical solution of which is plagued by spurious high frequency oscillations, unless a method with high frequency numerical dissipation is used. Conventional time integration schemes with high frequency numerical dissipation that were developed for linear systems, are regularly applied also to non-linear systems, however without any proof of unconditional stability. The energy preserving and energy decaying integration schemes are introduced. With these schemes, the equations of motion of the elastic bodies are discretized in such a way that the total energy of each body is preserved exactly, in the energy preserving scheme, or decays, in the energy decaying scheme. The forces of constraint associated with the kinematic constraints are discretized in such a way that they perform no work. The combination of these two features establishes the preservation or decay of the total energy of the system, thus implying unconditional stability in non-linear analysis. The energy preserving scheme does not present any numerical dissipation. It is shown that this often leads to high frequency oscillations that bury the useful information, cause convergence problems and render strict energy preservation impossible. The energy decaying scheme, even though more expensive, is shown to present numerical dissipation with asymptotic annihilation. This scheme is shown to be ideally suited for the integration of constrained multi-body dynamic systems. |
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