Analysis of Tapered Timoshenko and Euler–Bernoulli Beams on an Elastic Foundation with Moving Loads

This research studies the vibration analysis of Euler–Bernoulli and Timoshenko beams utilizing the differential quadrature method (DQM) which has wide applications in the field of basic vibration of different components, for example, pillars, plates, round and hollow shells, and tanks. The free vibration of uniform and nonuniform beams laying on elastic Pasternak foundation will be studied under three sets of boundary conditions, that is, mixing between being simply upheld and fixed while utilizing the DQM. The natural frequencies and deflection values were produced through the examination of both beam types. Results show great concurrence with solutions from previous research studies. The impact of the nonuniform cross-section area on the vibration was contemplated. A comparison between the results from both beams is obtained. The focus of this work is on studying the deflection difference between both beam theories at different beam dimensions as well as showing the shape of rotation of the cross section while applying a nodal point load equation to simulate the moving load. The results were discussed and a general contemplation about the theories was developed.