Free Vibration of Beam Elastically Restrained Against Translation and Rotation at Ends


An approximate solution of the vibration of elastically restrained , uniformed and non-uniformed beams with translational and rotational springs is obtained using Rayleigh-Ritz approach. The frequencies are presented for wide range of restrained parameters and some of these have been compared with those available in the published literature illustrating the accuracy and versatility of the approach. It is believed that the results present in this paper will be of use in design of beams , shaft, and piping under dynamics consideration.