Nonlinear dynamic modeling of bistable variable stiffness composite laminates

The room-temperature equilibrium stable states of cured unsymmetric composite laminates have been the focus of recent research, with a particular emphasis on shape morphing applications. It has been shown that changing the fiber orientation of unsymmetrical laminates using curvilinear fiber path description can results in a plethora of bistable configurations with an enriched design space. In bistable structures, snap-through involves transition from one stable shape to another, which is a non-linear phenomenon exhibiting rich dynamics during the shape transition. Past works involving such dynamic characteristics show encouraging potential in designing efficient morphing strategies. In this work, a novel semi-analytical model using Föppl von Kármán kinematics has been formulated to predict the non-linear dynamic characteristic of bistable variable stiffness (VS) laminates. An efficient energy formulation is adopted where the membrane and bending energies are decoupled using the semi-inverse constitutive equation. The in-plane stress resultants and the energy components are expressed in terms of curvatures using the in-plane equilibrium equations and compatibility conditions. Using Hamilton’s principle in conjunction with the Rayleigh–Ritz approach, a set of non-linear equations are generated, which is solved to obtain the dynamics of the snap-through process. The accuracy of the predicted non-linear vibration results of bistable plates from the semi-analytical model is verified using a fully non-linear finite element framework and validated exemplarily by tests on a straight fiber laminate configuration. Finally, a parametric study is performed by tailoring the VS parameters to identify the effect of different curvilinear fiber alignments on the dynamic characteristics of bistable VS laminates.