Vibration characteristics of a beam with generalised end supports

Abstract

The boundary conditions of basic load support structures formed by beam elements are neither purely simply supported nor clamped that can be termed as conventional. It has certain finite rotational and translational stiffness representing an intermediate state (a welded end/riveted structures to name a few). The conventional methods of separation of variables for beam vibration analysis have not found substantial applications for boundary conditions which are not conventional. The paper attempts to bring out the effect of variation of the end supports, in terms of variation in translational and rotational stiffness, on the vibration characteristics of a beam element in terms of frequency and mode shapes. Fourier sine series approximation has been used for theoretical evaluation. Numerical assessment has been undertaken on an I-beam. Variable stiffness has been accounted for by using variable elastic end conditions and results on frequencies and mode shapes of the I-beam have been presented.