Natural frequencies and open-loop responses of an elastic beam fixed on a moving cart and carrying an intermediate lumped mass

In this paper, the motion of a Bernoulli-Euler cantilever beam clamped on a moving cart and carrying an intermediate lumped mass is considered. The eq uations of motion of the beam-mass-cart system are analyzed through unconst rained modal analysis, and a unified characteristic equation for calculatin g the natural frequencies of the system is established. The changes of natu ral frequencies and the corresponding mode shapes with respect to the chang es in the ratios between the beam mass, the lumped mass and the cart mass a nd to the concentrated position of the lumped mass are investigated with th e frequency equation, which can be generally applied to this kind of system . The exact and assumed-mode solutions including the dynamics of the base c art are obtained, and the open-loop responses of the system by arbitrarily designed forcing functions are given by numerical simulations. The results match well with physical phenomena even in the extreme cases where the mass is attached to the bottom and to the top of the beam. (C) 2000 Academic Pr ess.