LONGITUDINAL, TORSIONAL AND FLEXURAL DYNAMICS OF 1-D PERIODIC STRUCTURES

In this work longitudinal, torsional and flexural vibrations of 1-D periodic structures were investigated. For that purpose the Time-Domain Spectral Finite Element Method (TD-SFEM) was applied by the authors. It is well known that the TD-SFEM is very effective when used to solve high frequency structural dynamic responses of various mechanical structures regardless their geometrical complexity. However, its application for the investigation of structural responses of periodic structures is not widely reported in the available literature. In this work the authors demonstrated that the TD-SFEM is superior over other numerical techniques traditionally used for that purpose. It additionally provides numerical results in an excellent agreement with known analytical solutions, if only such solutions are available. In the current case the dynamic responses of 1-D periodic structures were studied as natural and forced vibrations as well as wave propagation patterns. In order to study the longitudinal and torsional vibrations the elementary theories were used, while for the flexural vibrations the Timoshenko beam theory was applied. The influence of structural periodicity understood as the material discontinuity (jumps in the velocity of propagating mechanical waves) or the geometrical discontinuity (presence of drill-holes, jumps in the cross-section) were all investigated on the presence and the width of frequency band gaps and their characteristics. In this work an effective methodology was applied by the authors for modelling the drill-hole type of geometrical discontinuities in periodic structures. The methodology proposed was positively evaluated by its result comparison to those obtained from the classical Finite Element Method (FEM) in the low frequency regime.