Abstract: Nonlinear vibration isolators intended for engineering applications must simultaneously achieve precise tailoring of dynamic characteristics and parsimonious yet accurate model construction. Balancing these two requirements remains a critical challenge in the design and analysis of nonlinear isolation systems. To address the first requirement, this paper proposes a curved-track vibration isolator. By hierarchically designing the surface parameters, the restoring-force coefficients of different orders can be independently and progressively decoupled, enabling the flexible and targeted tailoring of nonlinear dynamic characteristics. This design strategy provides a systematic way to match the nonlinear characteristics of the isolator with those of the primary system. To address the second requirement, a frequency-domain data-driven modeling approach is developed. The measured steady-state response is first expanded into a Fourier series, based on which a library of candidate frequency-domain signal models is constructed. The modeling problem of the curved-track isolator is then reformulated as a sparse least-squares regression problem over this model library. To avoid the overfitting issue caused by the full-retention property of conventional Least-Squares Estimation, the OFR (Orthogonal Forward Regression) method is employed to identify the dominant terms of the model, thereby ensuring both model sparsity and accuracy. The numerical simulations are conducted to investigate the influence of training data with different excitation frequencies and amplitudes on the identified dominant terms. The results indicate that training data covering a broader frequency bandwidth facilitate the identification of more accurate models. In addition, since the Fourier series provides an effective decomposition of white noise, the proposed frequency-domain approach exhibits superior noise robustness compared to conventional time-domain methods. Finally, experiments are carried out to validate the feasibility of the proposed methods. The results demonstrate that both the parameter-decoupled design strategy for the curved-track vibration isolator and the frequency-domain data-driven modeling method are effective, and they show strong potential for practical engineering applications.