Vibration band gap properties of a periodic beam-like structure using the combination of GDQ and GDQR methods

Abstract

In this study, a periodic beam-like structure consisting of the horizontal and inclined beam elements is proposed. Three models with three different angles of inclination are considered. The generalized differential quadrature (GDQ) and generalized differential quadrature rule (GDQR) methods are used to solve the differential equations of longitudinal and transverse vibrations, respectively. The effects of two geometrical parameters on the first three band gaps of each model are investigated, comprehensively. Results show that this periodic structure has wide band gaps at low frequency ranges. Furthermore, the band gaps can get close to each other by changing the geometrical parameters. Another important advantage of this periodic structure is that it can absorb both longitudinal and transverse vibrations over its wide band gaps. Finally, the analytical method is validated by the finite element simulation via ANSYS software and good agreement is found.