Experimental research about the first natural frequency of largely deformed beams

Alexandre de Macêdo Wahrhaftig¹; Reyolando M. L. R. F. Brasil²

¹ Federal University of Bahia (UFBa); ² Federal University of ABC (UFABC)

doi:10.20906/CPS/COB-2015-0086

Resumo

This paper presents a study about the first vibration mode 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 to a great extent from the undistorted configuration. Thus, a component of the generalized force starts to appear that changes the stiffness of the system as a function of the deflection assumed by the piece. As the deformation of the rod increases, the component of the lateral force that acts tangentially to the curved shape that the beam assumes is also increased, changing its stiffness and influencing the natural frequency of the system. This experimental study shows that as the deflection of the beam increases, the difference between the results of the frequency considering the straight shaft and those computed from the deformed position increases with the length of the piece. However, the downward trend is interrupted and the frequency rises slightly, precisely indicating the moment in which the said component starts to influence the stiffness of the bending piece. A computer model to obtain the natural frequency of the beam was then prepared using the Finite Element Method in order to follow the experimental results in two ways. The first considered the beam in its horizontal configuration. The second was based on nonlinear static analysis processing that was previously performed with the large displacement theory; the second method results show a good approximation with the experimental values.

Palavras-chave: Experimental Research; Beams; Geometric Stiffness; Fundamental Frequency; Large Deformed