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(R-TCBs) based on the nonlinear Euler-Bernoulli beam theory. This method transforms the nonlinear governing equations into a boundary value problem(BVP) of ordinary differential equations, which is solved using the collocation method local(CML). The resulting theoretical model shows excellent agreement with 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.