Reduced-Order Models for Nonlinear Flutter of Composite Laminates with Curvilinear Fibers

Abstract

Approximation errors due to using reduced-order, instead of full-order, models in the nonlinear flutter problem of variable-stiffness composite laminates (VSCLs) are qualitatively and quantitatively discussed. These VSCLs are made of composite laminates with curvilinear fibers. A third-order shear deformation theory (TSDT) and a -version finite element are used to model the laminate and discretize its displacements and rotations. The VSCLs are subjected to a supersonic airflow and the aerodynamic pressure is approximated using the linear piston theory. The equations of motion of the self-excited vibrational system are formed using the principle of virtual work. In this study, static condensation and/or a modal summation method are used to reduce the number of degrees of freedom of the full-order model. The equations of motion are solved using a method to calculate the amplitudes of limit-cycle oscillations (LCOs), and to study the dynamic responses, stresses, and damage indexes based on a failure criterion. Approximations are calculated for LCO amplitudes of VSCL plates with various boundary conditions, laminate thickness, and initial deflection (geometric imperfection). Viscous damping can have a major importance in this problem, and the approximation errors are discussed when viscous damping is included or excluded from the equations of motion.