Abstract Summary
Curvilinear reinforcement fibres allow tailoring the elastic properties of composite laminates in space, leading to Variable Stiffness Composite Laminates (VSCL). This work intends to analyse if variable stiffness composites can be used to increase the critical aerodynamic pressure, under which aeroelastic instabilities develop on circular cylindrical composite shells. The airflow is considered to be supersonic and along the shell’s axial direction. A linear mathematical model for thin circular cylindrical VSCL shells is developed for that purpose. The representation of the aerodynamic pressure caused by the supersonic airflow is derived recurring to a linearised piston theory, with a correction term to account for the shell’s curvature. The p-version of the finite element method is used, resulting in a set of second order ordinary differential equations of motion. These equations are transformed into a set of first order differential equations of motion in state space coordinates. Writing the solution to these equations as the product of a vector of coefficients by an exponential function of L*t, where L is a complex parameter and t represents time, a generalised eigenvalue problem is defined. If the real part of any eigenvalue L is positive, then the shell will not return to its undeformed configuration after a perturbation: an aeroelastic instability occurred. In the numerical tests, convergence and verification analyses are performed. The values of the present approach are compared with the ones computed by other authors in conventional, constant stiffness, composite laminate shells. The required number of degrees of freedom of the present p-version FEM model is relatively low. However, the large number of circumferential waves in some modes of interest leads to an increase in this number, if one wishes that the model is able to represent not only the modes involved in instabilities but also all modes until those. Four types of curvilinear fibre paths are explored. The geometry of the shell and most airflow parameters are fixed, in the numerical tests; the shell ends are either considered to be both clamped or both simply supported. An iterative procedure – using the free stream pressure as parameter - is applied to find fibre path parameters that result in an increase of critical flutter pressure for each type of fibre path. Limitations in the fibre path turning radius, due to manufacturing restraints and fibre buckling, are considered. The values of the critical aerodynamic pressure are found to be very sensitive to changes in the fibre path and it is shown that substantial increases can be achieved by using curvilinear fibres. Hence, variable stiffness composite laminates present a great capacity to postpone aeroelastic instabilities in the supersonic regime.
