Dynamic Response of a Beam Subjected to Moving Load and Moving Mass Supported by Pasternak Foundation

Abstract

This paper presents the dynamic response of an Euler-Bernoulli beam supported on two-parameter Pasternak foundation subjected to moving load as well as moving mass. Modal analysis along with Fourier transform technique is employed to find the analytical solution of the governing partial differential equation. Shape functions are assumed to convert the partial differential equation into a series of ordinary differential equations. The dynamic responses of the beam in terms of normalized deflection and bending moment have been investigated for different velocity ratios under moving load and moving mass conditions. The effect of moving load velocity on dynamic deflection and bending moment responses of the beam have been investigated. The effect of foundation parameters such as, stiffness and shear modulus on dynamic deflection and bending moment responses have also been investigated for both moving load and moving mass at constant speeds. Numerical results obtained from the study are presented and discussed.

The role of statistics in data-centric engineering

“…Simplified models (e.g. Uzzal et al, 2012;Thambiratnam and Zhuge, 1996;Iwnicki, 2006, Chapter 6), usually based on an Euler-Bernoulli beam equation, can be used to approximate a single span girder bridge. As an illustration, the differential equation introduced in Iwnicki (2006, Chapter 6), models the deflection w(x, t) at location x ∈ R at time t as…”

Effects of foundation mass on dynamic responses of beams subjected to moving oscillators

“…Hence, several following foundation models proposed to overcome the deficiency of the Winkler model by introducing some kind of interaction between the independent springs by visualizing various types of interconnections such as an additional thin elastic membrane stretched by a constant tension (Filonenko [2]); plate with flexural rigidity (Hetenyi [3]); an incompressible layer that resists only transverse shear deformation (Pasterna [4], Reissener [5], Kerr [6]), or accounts for the effect of the neglected shear strain energy in the soil and shear forces that come from surrounding soil (Vlasov and Leont'ev [7]). These foundation models were also used widely for solving almost all discontinuity problems by analyzing the response of the structure on the foundation due to dynamic loads, moving random loads, moving oscillator as per various methods [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. It can be seen that above foundation models attracted the attention of many researchers during many past decades for solving the almost all problems of structures-foundation interaction applied in many practice problems such as road-foundation-vehicle, airplane-runway-foundation, track-train-foundation.…”

A Nonlinear Dynamic Foundation Model for Dynamic Response of Track-Train Interaction

“…However, the most important deficiency of the above foundation model is that it does not have displacement continuity on the foundation surface and it does not have any discontinuity between the loaded and the unloaded part in reality. So, it was developed into the many-parameter foundation models to overcome the above deficiencies as done by Filonenko-Borodich [12], Hetényi [13], Pasternak [14], Reissner [15], and Kerr [16], and these models have been also applied in many problems for analyzing a response of the structure-foundation interactions [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”