nurbs functions

This research mainly presents the in-plane and out-of-plane vibration analysis of laminated composite beams with arbitrary lay-ups using isogeometric approach. In this study, the first-order shear deformation theory and NURBS basis functions are used to obtain the free vibration response of the structure. The material couplings, i.e., bending-stretching, bending-twisting, and stretching-twisting couplings, and the effects of shear deformation, rotary inertia and poisson’s effect are considered. The obtained results using the isogeometric approach show excellent agreement with the results which are available in the open literature. The convergence study has been done using three different refinement schemes such as h-, p-, and k-refinement. It is observed that p-refinement has a faster convergence than h-refinement, and k-refinement is more suitable than p-refinement due to the lower number of degrees of freedom. It can also be concluded that using isogeometric analysis, the frequencies converged rapidly compared to the finite element method. Finally, the effects of slenderness ratio, material anisotropy, and width to thickness ratios on the in-plane, out-of-plane, axial, and torsional vibration modes in different boundary conditions are studied.