Open AccessTransfer matrix formulation for dynamic response of Timoshenko beams resting on two-parameter elastic foundation subjected to moving load
Author(s) -
Baran Bozyiğit
Publication year - 2021
Publication title -
journal of structural engineering and applied mechanics
Language(s) - English
Resource type - Journals
ISSN - 2630-5763
DOI - 10.31462/jseam.2021.04099110
Subject(s) - rotary inertia , vibration , timoshenko beam theory , finite element method , beam (structure) , structural engineering , foundation (evidence) , transfer matrix , normal mode , modal analysis , moving load , natural frequency , stiffness , displacement (psychology) , inertia , mechanics , mathematics , physics , engineering , classical mechanics , computer science , acoustics , psychology , archaeology , computer vision , history , psychotherapist
In this study, the dynamic response of beams resting on two-parameter elastic foundation subjected to moving load is investigated by using the transfer matrix method (TMM). The Timoshenko beam theory (TBT) which considers shear deformation and rotational inertia is used to model the beam. The two-parameter elastic foundation model is selected as Pasternak foundation that takes into account a shear layer at the end of linear springs of Winkler foundation. The TMM which uses the relation between analytically obtained state vectors of each end of the beam is applied to solve the free vibration problem. After performing the free vibration analysis, the mathematical model is simplified into an equivalent single degree of freedom (SDOF) system by using the exact mode shapes to obtain dynamic responses. The generalized displacement is calculated for each mode by using the Runge-Kutta algorithm. A numerical case study is presented for a simply-supported Timoshenko beam on the Pasternak foundation subjected to a concentrated load. The natural frequencies obtained from finite element method (FEM) results of SAP2000 are presented with the results of TMM for comparison purposes using the Winkler foundation. The effects of shear layer on the natural frequencies of the model are revealed. The mode shapes are plotted. The proposed approach for calculating dynamic responses is validated by using the results of FEM for Winkler foundation model. Then, the effects of Winkler springs and shear layer of the foundation model on the dynamic responses are presented in figures. The effects of modal damping are discussed. Finally, the critical velocities for the model are calculated for various elastic foundation scenarios and the effects of elastic foundation parameters on the dynamic response of beam model subjected to moving load with high velocity are observed.