Abstract
In this paper, free transverse vibration of single-stepped Timoshenko and Euler-Bernoulli beams consisting of two uniform homogeneous segment with attached springs and lumped masses at the beam ends is analysed by using the modified Hencky bar-chain model. The effects of the springs and masses at the beam ends on the natural frequencies and mode shapes of the stepped beam is examined. Theoretical considerations are accompanied by numerical examples to illustrate the accuracy of the modified Hencky bar-chain model. The paper extends the application range of the modified Hencky bar-chain model in the field of vibration analysis of mechanical systems.
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