Abstract
Abstract
Developing metamaterial structures that simultaneously possess low frequency broadband vibration isolation capability and programmable tunability is of great significance for high-precision engineering applications. In this work, a pre-folded negative stiffness mechanical metamaterial (NSMM) is proposed, and a systematic investigation is carried out on its nonlinear compression behavior, bandgap formation mechanism, programmable tuning characteristics, and the forward prediction and inverse design of band structures based on the proposed residual-trunk POD-DeepONet. The results show that the proposed structure can stably exhibit a typical NS response under quasi-static compression. The geometric parameters significantly affect the peak load, the NS regime, and the stiffness recovery behavior, while 2 l andq enable a continuous transition of the equivalent stiffness from positive stiffness (PS) to quasizero stiffness (QZS) and then to NS. Multiple distinct bandgaps are formed within the frequency range of 0-2500Hz, and vibration response experiments verify its effective vibration attenuation capability. Group velocity and phase velocity analyses reveal pronounced anisotropic dispersion and direction dependent wave propagation behavior. Further results show that the positions, widths, and low frequency evolution of the bandgaps can all be effectively regulated by geometric parameters and programmable compression paths. Meanwhile, the residual-trunk POD-DeepONet framework achieves accurate forward prediction and multi-candidate inverse design of band structures, providing an efficient data-driven route for bandgap-oriented structural design. This work provides a new design strategy for the application of NSMM in low frequency vibration isolation, reconfigurable bandgap tuning, and adaptive wave propagation control.