Vibration of Beam with Elastically Restrained Ends and Rotational Spring-Lumped Rotary Inertia System at Mid-Span

Abstract

This technical note addresses the free vibration problem of an elastically restrained Euler–<br><br>Bernoulli beam with rotational spring-lumped rotary inertia system at its mid-span hinge. The<br><br>governing differential equations and the boundary conditions of the beam are presented. Special<br><br>attention is directed toward the conditions of the intermediate spring-mass system which plays<br><br>a key role in the solution. Sample frequency parameters of the beam system are solved and<br><br>tabulated. Mode shapes of the beam are also plotted for some spring stiffnesses.