Abstract
In this study, a new periodic lattice model with special vibration-absorbing properties is introduced. This periodic structure consists of the connected beam elements with circular cross-sections. Four models with different sets of cross-sectional radii are considered for this periodic lattice. The theoretical equations of longitudinal, torsional, and transverse vibrations of beams are solved using the combination of generalized differential quadrature and generalized differential quadrature rule methods to calculate the first three complete bandgaps. Investigating the effects of geometrical parameters on the bandgaps shows that all bands are close to each other for specific values of the cross-sectional radii. Having close bandgaps means that this periodic structure has a relatively wide bandgap in total. Furthermore, this wide band can move to low-frequency ranges by changing the lattice thickness. Absorbing both in-plane and out-of-plane vibrations over a wide bandgap at low-frequency ranges makes this periodic lattice a good vibration absorber. Verification of the analytical method using ANSYS software shows that the combination of generalized differential quadrature and generalized differential quadrature rule methods can be used for vibration analysis of two- or three-dimensional structures such as frames and trusses with high accuracy.
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