Insertion loss analysis of slender beams with periodic curvatures using quaternion-based parametrization, FE method and wave propagation approach

Abstract

The use of repeating cells in general wave theory is a well-known method for obtaining filter-like characteristics. This work targets the effects of periodic structures and their filtering behaviour on the waves propagating through structural paths. To this intent, a finite element (FE) procedure was developed specially to use the wave propagation approach, called NuSim, which uses semi-infinite elements as boundary conditions and calculates power flow coefficients through displacement responses. This particular combination of actions turns this algorithm suitable for analyzing the changes in insertion loss of slender structures. Furthermore, this FE approach is also appropriate for exploring various spatial configurations, without the difficulties encountered with analytical solution methods. A curvature parametrization based on avionics is introduced with the concepts of pitching and rolling angles, implemented with the aid of quaternions to avoid the rotation locking. Hence, the FE algorithm is applied in several different geometry configurations and the results are discussed. The configurations of spiral-eight and flat-bent springs found in the work of Søe-Knudsen are compared with the results obtained herein, for determining the accuracy of NuSim to represent stop-band frequencies. Finally, we show how to apply the same methodology on a full spring model, which considers its inactive coils, to show how easily NuSim can be employed to applications where an analytical response could be demanding.