A CLOSED-FORM APPROXIMATE SOLUTION FOR COUPLED VIBRATIONS OF COMPOSITE THIN-WALLED BEAMS WITH MID-PLANE SYMMETRY
Original scientific paper The purpose of this paper is to develop and present an approximate analysis procedure to estimate the natural frequencies and mode shapes of thin-walled beams with arbitrary open cross-section, made of laminates with mid-plane symmetry. Theory of thin-walled composite beams is based on assumptions consistent with the Vlasov's beam theory and classical lamination theory. The equations of motion for coupled bending-torsional vibrations are derived from the principle of virtual displacements. In the case of simply supported thin-walled beam the frequency equation, given in determinant form, is expanded in an explicit analytical form, which gives the natural frequencies of free harmonic vibrations. For verification, the analytical study by other researchers and the FEM analysis using ANSYS are compared with the current results.
Free vibration of thin-walled composite beams with static initial stresses and deformations
The influence of the initial in-plane deformations, generated by the action of a static external loading, as well as the effect of shear flexibility on the dynamic behavior of bisymmetric thin-walled composite beams has been investigated in this paper. The analysis is based on a geometrically non-linear theory based on large displacements and rotations. The Ritz variational method is used in order to discretize the governing equation and an analytical method is used to obtain the natural frequencies. In the investigation open cross-section beams subjected to initial uniform moment, distributed load and concentrated load are considered. The numerical results show that when the ratio of the smaller axis flexural stiffness to the major axis flexural stiffness is large, classic analysis of vibration may lead to inaccurate predictions because of the effects of initial displacements. Besides, the effects of span length and height of the load point have also been investigated for different laminate stacking sequences.
Stiffness matrices for flexural–torsional/lateral buckling and vibration analysis of thin-walled beam☆
Abstract Based on the power series method, the static and dynamic stiffness matrices for the flexural–torsional buckling and free vibration analysis of thin-walled beam with non-symmetric cross-section subjected to linearly variable axial force are newly presented. Additionally, the static stiffness matrix for the lateral buckling analysis of non-symmetric beam is presented for the first time. For this, the elastic strain energy, the potential energy considering the second-order terms of finite rotations, and the kinetic energy for thin-walled beam with non-symmetric cross-section are introduced. Then equations of motion and force–deformation relations are derived from the energy principle. Explicit expressions for displacement parameters are derived based on power series expansions of displacement components. Finally, the static and dynamic element stiffness matrices are determined using force–deformation relationships. In order to verify the accuracy of this study, the numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and ABAQUS's shell elements.