Representative experimental and computational analysis of the initial resonant frequency of largely deformed cantilevered beams

Abstract

This paper presents an investigation of the initial resonant vibration frequency of largely deformed cantilevered beams. This study is important because the vibration of beams with this level of deformation occurs from a position that differs significantly from the undistorted configuration. As the deformation of the beam increases, the lateral force component acting tangentially to the beam's newly curved shape also increases, changing its stiffness and influencing the resonant frequency of the system. The experimental component of this study shows that as the deformation of the beam increased, the difference between the resonant frequencies of the straight and deformed beams increased with the length of the beam. However, this difference decreases and the frequency rises slightly, precisely indicating the moment in which the aforementioned lateral force component starts to influence the stiffness of the bending piece. A computer model was then prepared to obtain the resonant frequency of the beam using the finite element method to confirm the experimental results for two scenarios: considering the beam in its horizontal configuration, and considering the beam in its deformed configuration using nonlinear static analysis processing, which has been previously applied in other theoretical investigations of large displacements. The results of the second method demonstrated a favorable approximation of the experimental values. An analytical evaluation was also performed.