An improved variant of Hencky bar-chain model for buckling and bending vibration of beams with end masses and springs

This paper presents a new lumped parameter method for buckling and bending vibration analysis of a uniform beam subject to an axial compressive load with attached springs and lumped masses at the beam ends. The method represents modification of the classical Hencky bar-chain model. Three types of beams are considered: Euller-Bernoulli, Rayleigh, and Timoshenko beams. The method proposed consists in replacing the elastic beam by a system consisting of massless rigid beams carrying lumped masses. The massless beams are connected through frictionless two-degrees of freedom joints with appropriate lateral and rotational springs in them. The validity and accuracy of the method are proven through the comparison with the classical Hencky bar-chain model, methods which using rigid finite segments as well as the analytical methods for vibration analysis. Also, the influence of the springs and masses at the beam ends on the natural frequencies and mode shapes of the beam is examined.