Transverse vibrations of a flexible beam sliding through a prismatic joint

Abstract In this paper, the vibrations of an axially moving flexible beam sliding through an arbitrarily driven prismatic joint, restricted to move on a horizontal plane, are investigated. Upon considering the assumption of an Euler–Bernoulli beam in addition to the effects of rotary inertia, end-mass and axial force in association with axial foreshortening, the equations of motion and the associated boundary conditions of the dynamic system are derived by using the extended Hamilton's principle, forming a complex boundary value problem. Due to difficulties in finding an analytical solution, the assumed modes method is utilized to obtain an approximate solution to the problem . Simulation results are presented for some typical kinematical inputs of the prismatic joint of the model.