Structural stability of slender aerospace vehicles: Part II: Numerical simulations

The methodology presented in Part I of this paper is used to obtain the numerical results for different cases. First, the predictions on stability regimes for a vehicle subjected to end thrust are validated by comparing results from published literature. Finite element simulation results involving aeroelastic effects are compared with the published literature. For numerical simulations, the analysis is carried out for assumed state of translational velocities. Also, the vehicle is assumed to be moving at zero angle of attack and the angular velocity is assumed to be small and it is neglected. Numerical simulations are carried out for a representative vehicle to determine the instability regimes with vehicle speed and thrust as the parameters, neglecting the aerodynamic forces. Simulations are carried out for a typical nose-cone launch vehicle configuration to analyze the aeroelastic stability at two different Mach numbers. Phenomenon of static instability (divergence) and dynamic instability (flutter) are observed. Vibrational mode shapes of the vehicle for different thrust and speed are analyzed. In the end, axial responses (displacements and velocities) of a typical vehicle subjected to axial thrust are determined using direct integration of the equations of motion. The axial displacements along the length of the vehicle due to two different thrust histories are compared. The coupling of rigid body motion with the elastic displacements is illustrated.