Nonlinear Stiffness Modulation for Adaptive Structural Dynamics

Nonlinear multi-stage stiffness structures with customizable deformative and dynamic responses can passively adapt and optimize their elastic properties to varying operational loads. A nonlinear multi-stage stiffness module, consisting of two oppositely curved thin flat beams, is designed and modelled. Static stress–strain analysis defines its nonlinear stiffness arises from beam bending, exhibiting two distinct stiffness stages before and after the topological contact between the beams that induces a stiffer stage upon a sufficient load. Elastic strain energy analysis has been performed to quantify the contribution of each individual deformation component in both stiffness stages, demonstrating that bending deformation still remains the dominant strain energy component over stretching and other components after the beams’ contact and even beyond the buckling limit. Vibration analysis presents frequency-amplitude dependency, with attenuation and asymptotic behavior of the frequency response under applied load as the module stiffens. Structural finite element simulations of modules integrated into an Euler–Bernoulli beam demonstrate that local stiffening near modal nodes yields the strongest global stiffening effect, validating the concept of stiffness compensation. The work presents a strategy for designing adaptive programmable structures with anisotropic stiffness distributions that evolve with operational load.