This paper is concerned with the dynamic stability and response of an inclined Euler–
Bernoulli beam under a moving mass and a moving follower force. The extended Hamil-
ton’s principle is used to derive the governing equation of motion and the boundary
conditions for this general moving load/force problem. Considering a simply supported
beam, one can solve the problem analytically by approximating the spatial part of the
deflection with a Fourier sine series. Based on the formulation and method of solution,
sample dynamic responses are determined for a beam that is inclined at 30◦ with respect
to the horizontal. It is shown that the dynamic response of the beam under a moving
mass is rather different from an equivalent moving follower force. Also investigated herein
are the dynamic stability of inclined beams under moving load/follower force which are
described by four key variables, viz. the speed of the moving mass/follower force, con-
centrated mass to the beam distributed mass, vibration frequency and the magnitude of
the moving mass/follower force. The critical axial load and the critical follower force are
different when they are located at different positions in the beam; except for the special
case when they are at the end of the beam.
關聯:
International Journal of Structural Stability and Dynamics 20(14), 2043004
