Small-Amplitude free vibrations of straight beams subjected to large displacements and rotation

In this study, a systematic approach to study small-amplitude vibrations of large deflected straight beams is presented. The differential equation system of small-amplitude free vibrations about the deflected configuration is presented considering the effects of axial extension, shear deformation, and rotatory inertia. It is shown that in the absence of axial, and shear forces, the differential equation system of small-amplitude vibrations of the deflected beam becomes identical to that of an initially curved beam. To solve the differential equation system of the large deflection problem, Variational Iterational Method is used. Free vibration analysis around the deflected configuration is performed by using Differential Quadrature Method. Several numerical examples are solved to show the versatility of the presented approach.