Nonlinear Response Study Of Aeroelastic Shells

Based on the Piston Theory of supersonic aerodynamics and the theory of thin shell with geometric nonlinearity, the aeroelasticity flutter equations of the thin shell in axial supersonic airflow are established in order to analyze the nonlinear flutter responses of the aeroelastic system. The differential quadrature method (DQM) is introduced to discritize the governing differential equations of aeroelastic system. The higher-dimensions nonlinearity flutter equations can be reduced to the lower-dimensions one by the method of nature mode reduction of freedom degrees, the critical aerodynamic pressure of which is obtained with the method of eigenvalue analysis. The numerical integral method is used to calculate the nonlinear response of the aeroelasticity system. The major parts of this thesis can be specified as follows.(1) Thin shells have many kinds of forms in the skin stressed design of flight vehicle. It is difficult to investigate the aeroelastic flutter characteristics of all kinds of thin shell respectively. By means of choosing two types of basic model of thin shell, a shallow cylindrical shell model and a circular truncated conical shell model, as researching objects, the aeroelastic flutter problems of all kinds of thin shell can be reduced to the flutter analysis of these two basic models. The governing equations are established by the large-amplitude shell theory.(2) Differential quadrature method (DQM) is introduced to discretize the governing equations of the thin shell with geometric nonlinearity. The discret forms for the shallow cylindrical shells based on two-dimensional DQM and the discret forms for circular truncated conical shells based on one-dimensional DQM are found.(3) The aeroelastic flutter problems of a shallow cylindrical shell model, including linear analysis and nonlinear response analysis, are studied. In linear analysis part, the nature frequencies and linear critical flutter dynamic pressures are investigated by the eigenvalue method. The number of sampling points is discussed to get accurate results, and the effects of different curvatures, length-width ratios, initial stress, on the critical flutter aerodynamic pressure, are discussed. In the nonlinear analysis part, a nature mode reduction method is used to reduce the freedom degrees of the aeroelastic system, the nonlinear responses of which are compared with the ones of the primary system to get correct cut number of nature modes. It is found that the limite cycle oscillations (LCO), quasi-periodic responses and chaos are three typical nonlinear phenomena of the thin shell aeroelastic system with geometric nonlinearity. The curvature of the shell is emphasized to investigate the vibrating shape of LCO, and the effects of different curvatures and initial stress on the LCO amplitudes are discussed. When the circumferential angel is relatively small, a pitchfork bifurcation is found with different initial values of numerical integral at a certain aerodynamic domain. Taking initial stress as bifurcation parameter, the bifurcation process of the aeroelastic system and the routing to chaos are studied.(4) The aeroelastic flutter of a circular truncated conical shell model, including linear flutter and nonlinear flutter, is studied. In linear analysis part, the nature frequencies of the shell structure and 1-2 flutter critical aerodynamic pressures with different circumferential wave numbers are discussed with the eigenvalue analysis method. The effects of sampling point on calculating accuracy are discussed. Semi-cone angle, radius-thickness ratio, length-radius ratio, these parameters are emphasized on the influence to the minimal critical flutter aerodynamic pressures and the circurmferential wave. The angular velocity and initial stress parameters are also introduced to the nature frequency analysis and flutter analysis. In nonlinear analysis part, based on the assumption of standing-wave flutter and the nature modes reduction, the amplitude of LCO is investigated numerically. The effects of the geometric parameters, initial stress and angular velocity, on the LCO amplitude, are also studied.(5) The aeroelastic flutter of the circular cylindrical shell model and the circular conical shell model is studied. These two shell models can be taken as the special cases of a circular truncate conical shell model, the aeroelastic characteristics of which are similar to those of the circular truncate conical shell model. The research is focused on the influence of boundary conditions, inner pressure and axial press, on the critical flutter aerodynamic pressure and LCO amplitude of the circular cylindrical shell model. Because of the singularity of aeroelastic equations of the conical shell model at the vertex point of the conical shell, an approximate solution of LCO of standing-wave flutter is obtained by numerical approach.