A study on quasi-zero stiffness metamaterial vibration isolators based on large deformation of curved beams governed by the nonlinear Euler–Bernoulli equation

Abstract The realization of quasi-zero stiffness (QZS) characteristics in single-beam structures primarily relies on large deformation effects. Currently, most related studies employ finite element method (FEM), while theoretical calculation approaches remain relatively scarce. To address this, the present study proposes a large deformation modeling method for rotating trigonometric curved beams based on the nonlinear Euler–Bernoulli beam theory. This method transforms the nonlinear governing equations into a boundary value problem of ordinary differential equations, which is solved using the collocation method local. The resulting theoretical model shows excellent agreement with finite element method (FEM) results under large deformation conditions, with a maximum error not exceeding 0.06%. Based on this, a metamaterial vibration isolator exhibiting QZS characteristics was designed, and its static and dynamic behavior was investigated. The results demonstrate that the isolator designed using the proposed nonlinear Euler–Bernoulli beam approach possesses QZS properties, validating the effectiveness of the method for designing large deformation QZS isolators. Moreover, the designed QZS metamaterial isolator exhibits excellent low-frequency vibration isolation performance.