Vibration band gap analysis of a new periodic beam model using GDQR method

- Introducing a periodic beam model having wide band gaps at low frequency ranges.
- Applying GDQR method to vibration band gap analysis.
- Investigating the effects of mass, mass moment of inertia and taper ratio on the band gaps.

In this study, a new periodic beam model is introduced. This beam consists of the concentrated rigid masses and tapered beam elements with linearly variable width. The theoretical equations are derived by employing the Euler-Bernoulli beam and the Bloch-Floquet theorem and then solved using the generalized differential quadrature rule method to calculate the first two band gaps. The effects of the mass, mass moment of inertia and taper ratio on the widths and central frequencies of the first two band gaps are investigated. Results show that the wide band gaps at low frequency ranges can be obtained by changing the geometrical parameters. This is of interest for different applications of the band gap phenomenon such as broadband piezoelectric energy harvesting. Finally, the finite element simulation (ANSYS software) is used to validate the analytical method and good agreement is found.