DYNAMIC STIFFNESS MATRIX FOR FLEXURAL-TORSIONAL, LATERAL BUCKLING AND FREE VIBRATION ANALYSES OF MONO-SYMMETRIC THIN-WALLED COMPOSITE BEAMS

Abstract

This paper presents the elastic strain energy, the potential energy with the second order terms of finite rotations, and the kinetic energy with rotary inertia effect for thin-walled composite beams of mono-symmetric cross-section. The equations of motion and force-displacement relationships are derived from the energy principle and explicit expressions for displacement parameters are given based on power series expansions of displacement components. The exact dynamic stiffness matrix is determined using the force-displacement relationships. In addition, the finite element model based on Hermitian interpolation polynomial is developed. In order to verify the accuracy and validity of the formulation, numerical examples are solved and the solutions are compared with results from ABAQUS's shell elements, analytical solutions from previous researchers and the finite element solutions using the Hermitian beam elements. The influence of constant and linearly variable axial forces, fiber orientation, and boundary conditions on the vibration behavior of composite beam are also investigated.