Vibration band gap analysis of the non-uniform periodic beams using GDQR

Effects of the geometry on the vibration band gaps of non-unifrom periodic beams are investigated. Three different non-uniform unit cell models are considered for the periodic beam and a new geometrical parameter is defined for these models. The theoretical equations are derived by employing the Euler-Bernoulli beam and the Bloch–Floquet theorem. These equations are solved using the generalized differential quadrature rule method to calculate the first two band gaps. Results show that the widths and central frequencies of the first two band gaps can be changed considerably by changing this geometrical parameter and these changes are different for each model.

Keywords:

Non-uniform periodic beam , Vibration band gap , Generalized differential quadrature rule , Finite element simulation