Linear Analysis and Non-linear Analysis with Co-Rotational Formulation for a Cantilevered Beam under Static/Dynamic Tip Loads

In this paper, the behaviour of a cantilevered beam was predicted to examine the difference between linear and non-linear static, dynamic analysis for a structure by using CR nonlinear formulation. Then, external transverse static and dynamic loads were applied at the free tip of the beam. Classical theories were used for the present linear analysis and co-rotational dynamic FEM program was used for the present nonlinear analysis. In the static analysis, effects of the load for the beam deflection were observed in both linear and nonlinear analysis. Then, normalized displacement at the tip of the beam was predicted for different frequency ratio and a significant difference was obtained in the vicinity of the resonant frequency. In addition, effects of frequency and time for the beam deflection were investigated to find the frequency delay. Keywords :linear analysis, nonlinear analysis, two-dimensional beam, natural frequency, harmonic excitation, co-rotational dynamic FEM, static analysis, frequency delay