Nonlinear vibration solution of an inclined Timoshenko beam under the action of a moving force with constant/non-constant velocity - Mamandi, A.; Kargarnovin, M.H.; Farsi, S. (Нелінійні коливання, 2013)
This study focuses on the nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions subjected to a moving force under the influence of three types of motions, including accelerating, decelerating and constant velocity types of motion, respectively. The beam’s nonlinear governing coupled partial differential equations (PDEs) of motion for the bending rotation of warped cross-section, longitudinal and transverse displacements are derived using Hamilton’s principle. To obtain the dynamic response of the beam under the action of a moving force, the derived nonlinear coupled PDEs of motion are solved by applying Galerkin’s method. Then the beam’s dynamic response is obtained using mode summation technique. Furthermore, the calculated results are verified with those obtained by finite element method (F.E.M.) analysis. In the next step a parametric study on the response of the beam is conducted by changing the magnitude of the traveling concentrated force, its velocity and beam’s boundary conditions and likewise their sensitivity on the beam’s dynamic response are studied, respectively. It is observed that the existence of quadratic-cubic nonlinearity in the governing coupled PDEs of motion renders hardening/softening behavior on the dynamic response of the beam. Moreover, it is noticed that any restriction on the beam mid-plane stretching will introduce nonlinear behavior in the beam’s PDEs of motion.