Nonlinear vibrations in homogeneous nonprismatic timoshenko cantilevers

摘要: Deep cantilever beams, modeled using Timoshenko beam kinematics, have numerous applications in engineering. This study deals with the nonlinear dynamic response in a nonprismatic Timoshenko beam characterized by considering the deformed configuration of the axis. The mathematical model is derived using the extended Hamilton’s principle under the condition of finite deflections and angles of rotation. The discrete model of the beam motion is constructed based on the finite difference method (FDM), whose validity is examined by comparing the results for a special case with the corresponding data obtained by commercial finite element (FE) software abaqus 2019. The natural frequencies and vibration modes of the beam are computed. These results demonstrate decreasing eigenfrequency in the beam with increasing amplitudes of nonlinear oscillations. The numerical analyses of forced vibrations …