Dynamic response of structural beams undergoing moving loads and thermal strains using finite elements–Part 1

Many structures undergo forced vibration to moving loads: bridges, railway and subway tracks, aircraft carrier decks, etc. Many of these structures are also subjected to various types of thermal loading in addition to mechanical loads. Currently, there are very limited or no analytical or experimental methods for analyzing the combined effects of the mechanically induced vibrations and thermal loads on complicated structures such as curved beams and plates with moving loads. In lieu of these considerations, it is preferable to analyze such problems by numerically discretizing the spatial portion of the equations of motion using Finite Elements and the temporal portion with numerical time stepping algorithms. The preferred time discretization method presented here is the well-known GSSSS framework of algorithms in conjunction with the Finite Element method. Our primary objectives are simply to provide representative results for simple applications so as to be able to duplicate the results for comparison purposes, and to serve subsequent use as benchmark solutions to verify newer and other related developments and applications and not upon a wide variety of investigative studies, comparisons and/or parametric studies. In Part 1 of this paper the focus is upon (1) Developing a straightforward and simple procedure for solving the dynamic response of structures undergoing forced vibration due to moving mechanical loads, and (2) Applying this procedure to straight/curved beam structures with moving loads and thermal effects. In Part 2, we focus attention upon analyzing the effects of the moving loads and thermal effects, but this time upon the combined dynamic response of applications involving flat plates. These overall developments provide baseline benchmarks for verifying future research in the areas of combined transient thermo-mechanical problems of structure under moving load and thermal considerations using the novel GSSSS family of algorithms.