Free vibration analysis of elastically restrained cantilever timoshenko beam with attachments

Abstract

This paper investigates the lateral vibration of a cantilever Timoshenko beam with attachments. It is assumed that the beam carries a mass attached to the free end with a linear spring and there exists a rotational spring at the left end. Depending upon these assumptions, mode shapes and natural frequencies are obtained in terms of non -dimensional parameters which describe the effects of additional mass, linear spring and rotational spring. The results are tabulated, and the comparison of Timoshenko and Euler-Bernoulli beam approaches are carried out for some parameters. Results reveal that natural frequencies decrease while the values of end mass increase. Large values of the rotational spring constant cause high natural frequencies.