Position-Dependent Vibration Response and Inverse Design of X-Type Nonlinear Supports for a Cargo–Vehicle–Road Coupled System

Cargo items at different longitudinal positions experience different local base excitations because of vehicle-body bounce and pitch, creating position-dependent demands on vibration isolation and support stroke. This study presents a response-guided equivalent-design framework that links critical-position identification to the selection of nonlinear support characteristics represented by an equivalent force model for X-type cargo supports. A coupled model comprising prescribed stochastic road inputs, linear tire stiffness and damping, a four-degree-of-freedom half-car subsystem, and five vertically supported cargo masses of 2000 kg each is established. Cargo acceleration, relative support displacement, interaction force, and energy-related indicators are evaluated. Under the nominal condition used for design-target extraction, P5 is identified as the critical position, with a dominant local-base frequency of 2.3994 Hz and an RMS-equivalent displacement amplitude of 15.339 mm. These response characteristics, together with prescribed design constraints, guide the selection of equivalent support properties. The support force law includes basic stiffness, delayed hardening, a displacement-activated limiting term, displacement-dependent damping, and regularized friction. In the nominal system-level comparison, the low-frequency-compliant X-type scheme reduced the maximum P5 stroke from 35.68 mm to 31.81 mm relative to the feasible low-frequency linear reference, accompanied by small increases in acceleration and interaction-force RMS. Under the investigated perturbed conditions, the grouped X-type configuration reduced the largest P5 stroke from 56.05 mm to 47.83 mm relative to the linear reference; however, it still exceeded the prescribed 40 mm limit. Further parameter optimization, independent benchmark comparison, and experimental validation are required before engineering feasibility can be established.