A New Solution to Free Transverse Vibration of Straight Beam with Elastical Supports of Arbitrary Spans

This paper presents a new analytical solution to free transverse vibration fo straight beam with elastical supports (including rotational elastic supports)of arbitrary spans. The analytical solution of the dynamic response of the forced transverse vibration of the beam is obtained through regarding the reaction forces (including the reaction moments) of the elastical supports on the beam as the unknown external forces acted on the beam and the undecided integral constants are given by the boundary condition of the beam. The frequency equation is described by a determinant which is derived by the linear relationship between the reaction forces (including the reaction moments) of the elastical supports on the beam and the displacements (including the rotational angles) of the beam at the supports and its order is equal to the number of the elastical supports. The mode shape function is described by a unified analytical representation. The rigid supports are the special cases of the elastical supports in this paper. The frequency equations at several common boundary conditions are performed and finally a numerical example is given.