Assessment of flexural beam behaviour theories used for dynamics and wave propagation problems

In this work, different theories of beam flexural behaviour have been discussed and compared. This analysis includes various one-, two- and three-dimensional beam behaviour theories comprising the classical one-dimensional Bernoulli, Bernoulli–Rayleigh, Timoshenko and Reddy theories, as well as various higher order and/or higher-mode theories of beam flexural behaviour developed by the authors. The dispersion curves obtained by the use of Hamiltonʹs principle and associated with each theory discussed in the paper have also been presented and analysed. The wide investigation programme carried out by the authors aimed at showing major differences and similarities between the beam theories and to discuss various numerical aspects of their application. Great attention has been paid on properties, limitations as well as difficulties associated with the use of particular theories of beam flexural behaviour. Based on a wide program on numerical calculations, the authors draw certain general conclusions that are valid not only in the field of wave propagation related problems, but also in the field of dynamics of engineering beam-like structures.