Direction-Specific Nonlinear Hysteresis Modeling and Parameter Identification of a Composite Metal Rubber Vibration Isolator

Metal rubber (MR) exhibits excellent environmental adaptability and nonlinear damping characteristics, making it a promising material for multi-directional vibration isolation in aerospace and marine applications. However, the hysteresis behavior of MR-based isolators strongly depends on loading direction due to different structural layouts and load paths. This paper proposes a direction-specific modeling strategy for a composite MR-spring vibration isolator that shows pronounced hysteresis asymmetry under vertical loading and nearly symmetric hysteresis under lateral loading. An asymmetric model (including quadratic and cubic stiffness plus linear and quadratic velocity damping) is established for the vertical direction, and a symmetric model (cubic stiffness and power-law damping) for the lateral direction. Model parameters are identified from dynamic tests (2–4 Hz, amplitude ranges: vertical 0.6–1.0 mm, lateral 0.2–0.6 mm) using hysteresis loop decomposition and nonlinear least-squares fitting. The identified stiffness parameters are expressed as polynomial functions of excitation amplitude, and damping parameters as bivariate quadratic functions of amplitude and frequency. Model validation demonstrates that the proposed models achieve goodness-of-fit (GFI) values above 0.97, with normalized root-mean-square errors (NRMSE) and relative dissipated-energy errors (εΔW) below 5.3% and 3.4%, respectively, under the investigated interpolation and extrapolation conditions. Compared with the classical Bouc–Wen model, the proposed models exhibit higher overall predictive accuracy in reproducing the vertical and lateral hysteresis responses, highlighting the effectiveness of the direction-specific modeling approach. The model parameters are further interpreted in relation to the structural characteristics of the central spring, tubular MR, and annular MR. The direction-specific modeling approach provides a practical framework for characterizing the nonlinear hysteresis behavior of the investigated composite isolator.