Dynamics of interaction between an Euler-Bernoulli beam and a moving damped sprung mass: Effect of beam surface roughness

Abstract

This work presents analytical expressions that identify the dynamics of the interaction between a simply supported Euler-Bernoulli beam and a moving sprung damped mass on the beam when the roughness on the beam surface is taken into consideration. The roughness load can have significant effects on the dynamics of the beam and its loading capacity, especially when the beam has poor surface conditions. Using the concept of perturbation, the solutions of the beam and mass are presented and validated by comparing the results with the finite element model. Because the determination of the roughness load requires the solution of an ill-posed inverse problem, the Tikhonov regularization and generalized cross validation methods are used to identify the moving load caused by the beam surface roughness. The performances of different regularization matrices (L matrices) under four noise levels (1%, 5%, 10%, and 20%) and three road classes are investigated in terms of their effectiveness in reducing errors in the prediction of the roughness load and mass motion. The results demonstrate that there is no optimal selection of regularization matrices (L matrices) crossing all the beam surface roughness conditions under the noisy disturbance. Under the lower noise levels (1% and 5%), the L1 matrix provided less error in the solution. However, when the noise level increased to 10% and 20%, the L0 matrix, the lower order regularization matrix, provided an acceptable solution. The results also indicated that beam surface roughness has an important impact on the roughness load identification and mass motion prediction.