Low-frequency bandgap mechanism of nonlinear stiffness-elastic metamaterial plates

Abstract To address the challenges of narrow bandgaps and low load-bearing capacity in traditional locally resonant structures for low-frequency vibration control, this study proposes a design method for elastic metamaterial plates based on a nonlinear stiffness mechanism. By introducing a hinge-type nonlinear stiffness system and combining theoretical modeling with finite element analysis, the regulatory effects of structural parameters (stiffness ratio <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>δ</mml:mi> </mml:math> , geometric dimension D, and angle <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>θ</mml:mi> </mml:math> ) on the lower boundary and bandwidth of bandgaps are revealed. Theoretical results indicate that adjusting hinge parameters reduces the normalized effective modulus zero-point frequency ( ω *) from 0.8 ω 0 to 0.6 ω 0 , expanding the bandgap width by more than twofold. Simultaneously, the parallel design of positive and negative stiffness achieves reduced dynamic stiffness while enhancing load capacity, resolving the contradiction between high-load deformation and low stiffness. Finite element simulations verify that three types of nonlinear stiffness models form broadband bandgaps up to 175 Hz within the 50–270 Hz frequency range. Modal analysis further demonstrates that nonlinear stiffness suppresses energy propagation through torsional coupling of resonators with bending waves, forming low-frequency bandgaps. This research provides theoretical support for metamaterials in low-frequency vibration suppression and establishes a parameterized design framework for engineering vibration isolation systems, paving a new path for high-performance and compact solutions.