Spectral Finite Element Analysis for Laminated Composite Periodic Frame Structures

The current work investigates wave propagation in composite periodic frame structures by combining Bloch’s theorem with the spectral finite element (SFE) approach. SFE is a semi-analytical methodology for solving governing differential wave equations in the transformed frequency domain. It properly represents dynamic behavior while reducing the number of elements necessary. Bloch’s theorem takes advantage of the elemental property of unit cell elements, which decreases the computing cost of the problem even more. Each beam element in the periodic structures (PS) is represented as a three-degree of freedom Timoshenko beam element. The bandgaps in the PS are explored using the wave propagation constant from a polynomial eigenvalue problem equation produced from the matrix reduction method of the elemental dynamic stiffness matrix in conjunction with Bloch’s relation and shown as a dispersion curve. The impact of PS geometric and material features on bandgaps is considerable. It is further demonstrated that by altering the structural factors, the required frequency band may be achieved.