Reduced Formulae for Vibration of Continuous Beams with Application on Moving Loads

Abstract

The present paper concludes via an analytical method to reduced formulae for determining the eigenfrequencies and eigenmodes of multi-span continuous beams with spans of different lengths and bending rigidities in a very easy and efficient way. The rigorous determination of eigenfrequencies and eigenmodes allows us to focus on the derivation of the time function for the forced vibrating beam subjected to the action of moving loads. The dynamic response of such beams subjected to a load moving with constant velocity is thoroughly studied. The analysis is carried out by the modal superpo- sition method. Numerical examples are presented to verify the applicability of the presented formulae.