Parametric instabilities in variable angle tow composite panels

Advancement in the automation of composite manufacturing techniques like automated fiber place- ment, embroidery fiber placement, and continuous tow shearing enables the three-dimensional elastic tailoring and the concept of tow placement. This technology allows the tows to be steered in prin- cipal load direction paths in composite structures. These composites with curvilinear fibers exhibit spatially varying stiffness, and are termed as variable angle tow (VAT) composite laminates. Elas- tic tailoring has been successfully performed to improve the modal, buckling, and post-buckling performance of the VAT structures. Aircraft structures like fuselage and wings are often subjected to dynamic loads in addition to the static loads. These structures, under periodic in-plane loads, exhibit parametric resonance for certain combinations of the excitation frequencies and loads. Therefore, the present thesis work focuses on investigating the dynamic stability behavior of VAT composite panels under in-plane periodic compression load. Since the fiber orientation in the VAT panel changes with the position, the stiffness properties vary continuously across the lamina. As a result, unlike straight-fiber composites, in VAT panels, the in-plane stress distributions over the laminate are non-uniform even under uniform compression load. Therefore, pre-buckling analysis has to be carried out first to determine the non- uniform in-plane stress distributions due to the applied load along the edges. Then the evaluated stress distributions are used to investigate the dynamic stability characteristics of the VAT panel. A flat VAT panel, a delaminated VAT panel with a cutout, and a curved VAT panel are tailored for enhancing the dynamic performance under periodic axial compression load. A linear fiber-angle variation with symmetric VAT layup has been considered, and the effect of fiber-angle variation on the dynamic stability behavior of the VAT composites is studied. The performance of the VAT panel is then compared with the straight-fiber laminates. In addition, the effect of various other parameters like boundary conditions, orthotropy ratio, aspect ratio, span-thickness ratio, delamination area, and radius of curvature on the dynamic stability behavior of the VAT panel is studied. Further, new evidence on the benefits of tow-steering over the straight-fiber composites in tailoring the dynamic stability and stiffness properties of the VAT panel simultaneously is reported. Subsequently, an implicit Floquet analysis is used to determine the dynamic stability character- istics of the VAT panel. In the literature dealing with the stability of structures with time-periodic loads, Bolotin’s method is widely used for determining the instability regions. However, Bolotin’s approach is an approximate method, and the evaluated instability regions are accurate only up to certain limit. To avoid this, Floquet theory can be used to determine the accurate dynamic stability characteristics of the systems. In Floquet theory, a Floquet transition matrix (FTM) is computed, and the dominant eigenvalue of the FTM determine the stability of the system. However, for large degree of freedom systems like finite element models of VAT panels, calculation of FTM becomes computationally expensive. Whereas, an implicit Floquet analysis can significantly reduce the com- putational load. In this technique, the dominant eigenvalue of the FTM is computed without the explicit computation of the full FTM matrix. Also, unlike Bolotin’s method, Floquet analysis pro- vides information about the effective damping present at different locations in the parametric space and the nature of bifurcation through which the stability is lost