Dynamic modeling of curved fish bone active camber morphing concept using shallow shell theory and negative-stiffness artificial springs

Existing models for the morphing concept of fish bone active camber (FishBAC) rely on several simplifying assumptions, hindering the accurate evaluation of its static and dynamic response. This study proposes a general framework according to which the theory of shallow shells and the Rayleigh–Ritz method are combined with artificial springs to present a basis for the dynamic evaluation of FishBAC, focusing on the free-vibration behavior as a first step for such objectives. A comprehensive code, which considers any desired boundary conditions, is written in Wolfram Mathematica to obtain the frequency parameter. After establishing the validity of the formulation through a set of comparisons with other articles and methods, a few FishBACs based on NACA 4412 are examined. Partitioning the structure and using the dimensions of these sections as the input yield accurate results compared to the finite element findings in COMSOL Multiphysics in an eigenfrequency analysis. The findings also show the notable error of neglecting the existence of curvature in the mean camber line of the trailing edges of airfoils or the span of wings based on FishBAC.