Free Vibration of Axially Loaded Composite Beams using a Quasi-3D Theory

This paper deals with free vibration behaviour of axially loaded composite beams with arbitrary lay-ups by using a quasi-3D theory, which accounts for shear and normal deformation effects as well as coupling effects arising from the material anisotropy. The axial and transverse displacement variations are assumed to be cubic and quadratic functions of the depth, respectively. Using an assumed displacement field, the governing differential equations of motion are derived by applying Hamilton's principle. A two-node C1 finite element with six degree-of-freedom at each node is developed to solve the free vibration problem. Numerical results are obtained for representative composite beams and the effects of fiber orientation on the natural frequencies and mode shapes are demonstrated. An elastic buckling analysis is also carried out as a degenerate case of free vibration analysis at zero frequency. In order to achieve this, a compressive axial load in the beam is gradually increased so that the natural frequencies decrease and in doing so, there comes a stage when for a particular high value of compressive load, the beam becomes unstable and buckling occurs as a degenerate case of free vibration at zero frequency. The load-frequency curves and the corresponding mode shapes are illustrated. The results are discussed and the paper concludes with some important remarks.