Isogeometric Analysis of transverse vibration of continuous systems under harmonic loads

Isogeometric analysis of forced vibration of continuous systems was investigated in this paper. The basis of this method is the use of NURBS functions, which provide an integrated mathematical basis to display the analytical models. The most important advantage of this method compared to conventional methods such as finite element is the accurate geometric modeling and almost no approximation with a new and easy method. The NURBS and B-Spline functions can have a higher continuity of derivatives in comparison with Lagrangian functions used in the finite element method. The forced vibration of Euler-Bernoulli and Timoshenko beams was studied in this paper. Using the Galerkin method and the principle of virtual work, the stiffness and mass matrix of these continuous systems were obtained considering the effects of shear deformation and rotational moment. Also, displacement functions were determined based on NURBS functions. Numerical examples of forced vibration of continuous systems are provided to prove the validity and efficiency of the proposed method. The natural frequencies of the members were obtained using MATLAB software and applying specific boundary conditions. furthermore, the results of the isogeometric analysis were compared with the exact solution of the Dynamic Stiffness Method. The results showed that the isogeometric method provides more accurate results due to the use of NURBS functions instead of approximate selective functions of the element.