On numerical solution methods for flexural waves in stepped beams

Abstract A detailed literature survey is presented on various numerical solution methods for flexural wave propagation problems. The numerical methods considered are transform methods, finite element methods, finite difference methods and the method of characteristics (MOC). Some numerical solution have been obtained for stepped beams using the MOC and taking into account the effect of wave reflections. Several factors have been found to affect the level of stresses and the associated peak values, the main ones being the diameter ratio and the position of discontinuity. This work demonstrated that the use of the MOC should be encouraged in finding solutions for complicated flexural wave problems, where no other numerical solution method can deliver satisfactory results.

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