On Vibration of Multi-span Continuous Beam in View of Rotational Inertia

Abstract

The paper deals with oscillation of a multi-span continuous beam in view of the rotational inertia forces. A mathematical model for kinematically excited harmonic vibrations are discussed. The amplitude as a function of displacements for steady-state oscillations are determined on the ground of three basic equations. The calculations are performed using a graphical representation of the increasing frequency of disturbances. The calculation results obtained excluding the rotational inertia of concentrated masses are also encompassed in the study. A comparison of the samples shows noticeable decrease in amplitudes with an increase in the frequency perturbations. Next, we consider the effect of the disturbances’ phase shift on beam oscillations. It was revealed that these vibrations most dangerously affect the strength of the beam. When analyzing oscillation of the beam kinematically excited by random disturbances, we found that the root-mean-square deviations significantly depend on the degree of correlation of the components of the random vector.