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Free vibration analysis of variable stiffness laminated composite beams

Abstract In this paper, the free vibration analysis of composite laminated beams reinforced with parabolic fibers are studied on the basis of the equivalent single layer theory (ESLT) using the isogeomtric analysis method. In the composite material with variable stiffness (VSCL), each layer is reinforced by curvilinear fiber, while in the traditional composite materials with constant stiffness (CSCL) each layer is reinforced by straight fiber. The Equivalent Single Layer Theory (ESLT) given by the Continuum-based Timoshenko beam theory (CTBT) is combined with the isogeometric analysis, in which twisting and stretching effects are considered. The differential equations of motion governing the dynamics of stretching, shearing, bending and twisting composite beam are derived using the Hamilton principle. A new isogeometric composite beam element with six degrees of freedom per control point is developed and used to find natural frequencies of variable stiffness composites beams with parabolic fibers. In this new model, the effects of transverse shear deformation, rotary inertia, and the coupling effect due to the lamination of composite layers are included. Results are obtained for a number constant stiffness composite beam. The results confirm that the solutions converge as the number of elements or the degrees of basic functions are increased. Highly accurate values are obtained with the use of a very few degrees of freedoms, in which h-, p- and k-refinement are used in the convergence analysis. New numerical results of comparison study between the variable stiffness composite beams and constant stiffness composite beams are investigated. Next, parametric study is presented to investigate the impact of orientation angle of parabolic fiber, the stacking sequences, number of layers, boundary conditions, modulus ratio and length to mean diameter ratios on the natural frequencies of the variable stiffness composite beams. The solutions of variable stiffness composite beams are provided as benchmark for future studies.