Dynamic instability of a slender flexible aerospace vehicle

In this thesis, the dynamics and instability behavior of a slender flexible aerospace vehicle are carried out. Two different beam theories are used to model aerospace vehicles, which are defined as rocket, missile, and launch vehicle; firstly Euler-Bernoulli and secondly thin-walled composite beam. For these analyses, a rocket is subjected to a thrust force and considering has various characteristic features and flight conditions. For the both cases, geometrical formulation is established to predict of the beam behavior rigorously undergoing deformations. Contribution of this thesis to the literature is to determine the problem, which was solved previously with different beam theories, the dynamic stability of slender flexible aerospace vehicle regarding thin-walled composite beam theory. First of all, dynamic stability analysis of a free flight aerospace vehicle is investigated by using the Euler-Bernoulli beam theory. At first, rocket body is modeled as a classic uniform beam that subjected to constant thrust. The structural model is accepted one-dimensional and free-free beam under follower force. The equations of motion is obtained applying extended Hamilton's principle for non-conservative systems. Natural vibration characteristics of the rocket are determined using finite element method. The static and dynamic instability of rocket are examined with the increasing value of the thrust force. So, the value of critical thrust is obtained. Finally, numerical results are demonstrated and compared with the previous papers. Regarding these results, it can be said that stability characteristics can change according to the variations in physical conditions or design of the rocket. When the thrust, mass or rigidity of the rocket changes, the stability of the system changes. The results for the model obviously indicate that, when thrust increases natural frequencies of the rocket reduce. Moreover, as the natural frequency becomes zero, the divergence instability occurs. The critical thrust value where the flutter occurs is stated and the system is defined as instable. Moreover, in the context of the thesis, natural vibrations characteristics and aeroelastic stability behavior of two realistic launch vehicles are examined. Initially, a discrete mass system is developed for obtaining the equations of motions of free-free unsymmetrical beams. Total deflection and slope values of non-uniform beam are investigated by considering influence coefficients. Also, the effect of joints is regarded in order to compute total deflection and slope influence coefficients. For the numerical results representation, two different generic launch vehicle models are used. Firstly, natural frequencies, mode shapes and mode slopes, also bending moments are obtained for three-staged launch vehicle. Secondly, aeroelastic behavior of a non-uniform launch vehicle is represented. The dynamic divergence pressure and generalized static margin are considered to figure out the stability criteria of a launch vehicle under aerodynamic forces. For both dynamic and aeroelastic analysis, two realistic launch vehicles that given in NASA research at early space flight investigations are used for numerical results. In this context, numerical results indicate that second launch vehicle is in stable region when considering two stability criteria. Secondly, the theory of the thin-walled composite beam model is dealt with comprehensively to establish our rocket model. This model is used for two cases according to the rocket properties and loading conditions. First dynamic stability analysis of a flexible spinning launch vehicle subjected to thrust is modeled by using thin-walled composite beams. Second, a flexible spinning launch vehicle carrying a concentrated mass and subjected to thrust is modeled as a thin-walled composite beams to overcome the dynamic stability analysis. Within this context, the results of the dynamic stability analysis of a flexible spinning launch vehicle subjected to thrust modeled as a thin-walled composite beam with circular cross-section is presented. Due to the presence of gyroscopic forces, we mainly aimed to find divergence and/or flutter instabilities and establish the stability boundaries of the spinning beam. For this purpose, we implemented a Circumferentially Uniform Stiffness lay-up configuration (CUS) to exhibit the coupled motion of bending-bending-shear. The solution of the eigenvalue problem is handled by the extended Galerkin method (EGM) and we computed the results addressing the effects of various parameters such as spin speed, axial load, ply-angle, aspect ratio and transverse shear on the dynamic stability of the beam. Insights revealed by this study contribute to the design of advanced aerospace structures modeled as thin-walled composite beams reflecting the potential influence of transverse shear and aspect ratio on dynamic stability characteristics. A notable contribution is that we show that divergence/flutter instabilities can be delayed or even avoided using the directionality property of composite materials. In the presence of axial load and for nonzero spin speeds, the stability regions of both flutter and divergence instabilities expand with the increase of ply-angle. The impact of aspect ratio on the critical axial loads and the critical spin speeds are investigated and found that both critical loads and spin speeds tend to decrease as the aspect ratio increases. Also, the transverse shear has been found to have a profound effect on divergence and flutter instabilities and has to be addressed carefully in order to accurately determine the dynamical instabilities of the beams. Furthermore, the dynamic stability analysis of a flexible spinning launch vehicle with a concentrated mass subjected to thrust force modeled as a thin-walled composite beam with circular cross-section is presented. Considering thrust and gyroscopic forces, we first seek divergence and/or flutter instabilities and set up the stability boundaries of the spinning beam. Again, CUS configuration lay-up is constituted for displaying the coupled motion of bending-bending-shear. The extended Galerkin method is used for the solution of the eigenvalue problem. The effects of various parameters such as spin speed, axial load, and ply-angle on the dynamic stability of the beam are investigated in a comprehensive manner. Otherwise, according to the value and the location of the concentrated mass, dynamic stability boundaries are discussed for spinning beam. Bearing this situation in mind, numerical results of dynamic stability analysis for different mass values and different mass locations along the beam are demonstrated for all configurations. Natural frequencies of the beam decrease while the value of the concentrated mass increases. Similarly, asthe location of the concentrated mass moves from root to tip, natural frequencies of the beam decrease. Divergence instability of the beam is depend the axial force and spin rate, not change with or without the concentrated mass. As the value of mass becomes smaller, the critical flutter load Pflutter decreases. In addition, as the location of mass alters, the critical flutter load Pf lutter decreases.