A three-dimensional periodic beam for vibroacoustic isolation purposes. (1st September 2019) - Żak, A.; Krawczuk, M.; Redlarski, G.; Doliński, Ł.; Koziel, S.
Highlights: In the work dynamics of a 3-D periodic beam is investigated. The beam is modelled by 6-node SFEs of smooth geometry optimised to predefined dynamic properties. This results in the emergence of one common frequency band gap in the beam spectrum. The common frequency band gap allows to use the beam a sound isolator or filter. Numerical and optimisation results by TD-SFEM/FEM agree well with experimental ones by 1D-SLDV. Abstract: This paper presents results of investigations on a three-dimensional (3-D) isotropic periodic beam. The beam can represent a vibroacoustic isolator of optimised dynamic characteristics in the case of its longitudinal, flexural and torsional behaviour. The optimisation process concerned both the widths as well as the positions of particular frequency band gaps that are present in the frequency spectrum of the beam. Since the dynamic behaviour of the beam is directly related to its geometry, through an optimisation process of the beam geometry, desired dynamic characteristics of the beam were successfully obtained. For the purpose of the optimisation process a new numerical model of the beam, based on the spectral finite element method in the time domain (TD-SFEM), was developed by the authors. This model enabled the authors to investigate the beam behaviour not only in a wide frequency spectrum, but also ensured a high accuracy of the model predictions. The accuracy of this modelling approach was checked against well-known analytical formulas. However, in the case of the optimised geometry of the beam for the verification of the correctness of the modelling approach a commercial finite element method (FEM) package was used. Finally, based on the results of numerical predictions and optimised geometry of the beam a sample for experimental verification was prepared. Experimental measurements were carried out by the authors by the application of one-dimensional (1-D) laser Doppler scanning vibrometry (LDSV). The results of experimental measurements obtained by the authors confirmed the correctness of the numerical predictions, showing a high degree of correspondence.