Assessment of rod behaviour theories used in spectral finite element modelling

In this work different theories of rods have been discussed and compared. The investigated theories are widely used in spectral finite element modelling of rod behaviour associated with propagation of symmetric longitudinal waves. These are various single, two-mode and three-mode theories including the elementary, classical Love and Mindlin–Herrmann approaches as well as new two, three and four-mode theories proposed by the authors. Dispersion curves associated with each theory, obtained by the use of Hamiltonʹs principle, have been presented and discussed in the paper. The investigation programme carried out by the authors aimed to show major differences and similarities between the rod theories and to discuss certain numerical aspects of their application. Great attention has been paid on properties, limitations as well as difficulties associated with the use of the theories. The results obtained from a wide program on numerical tests allowed the authors to draw certain general conclusions that are valid not only in the field of the spectral finite element method but also in the field of dynamics of engineering rod structures.