Approximations By Reduced-Order Models for Nonlinear Flutter of Variable Stiffness Composite Plates

Abstract

In this investigation, we analyze errors due to using reduced-order models instead of full-order models in the examination of nonlinear flutter of variable stiffness composite laminates (VSCLs). These plates can be made, e.g., by Automated Tow Placement Machines, using composite laminates with curvilinear fibers; in our particular case, the orientation angle of the reference curvilinear fiber path changes linearly from T0 at the left edge to T1 at the right edge of the plate. A Third-order Shear Deformation Theory (TSDT) is used to model the laminate and a p-version finite element is applied to discretize the displacements and rotations. The plates are subjected to a supersonic airflow of which the aerodynamic pressure is approximated using linear Piston theory. The equations of motion of the full-order model of the self-excited vibrational system are formed using the principle of virtual displacements. In order to reduce the number of degrees-of-freedom of the full-order model, static condensation and/or a modal summation method are used. The equations of motion of the reduced-order and full-order models are solved using Newmark method to study the dynamic responses, focusing on limit cycle oscillations (LCOs). Approximation errors are discussed for LCO amplitudes of VSCL plates with various curvilinear fiber paths.