###### Abstract  
This paper investigates the planar vibration characteristic of heavy load radial tires with a large flat ratio. A proposed tire model with a flexible ring on an elastic continuous foundation is investigated utilizing kinematic modeling and experimental modal analysis. Planar coupling deformation of the radial and tangential direction is considered to enrich the kinematic characteristic of the flexible belt and the continuous sidewall; a flexible ring on an elastic continuous foundation tire model is proposed to investigate the coupling vibration characteristic between the flexible belt and the continuous sidewall. In-extensibility assumption is utilized to simplify the proposed tire model and the planar vibration modal features of the heavy load radial tire are discussed. The variation of the inflation pressure on the radial and tangential stiffness of the sidewall spring model is enriched into the flexible ring on an elastic continuous foundation tire model to extend the modal prediction of the tires with a different inflation pressure. Taking the relative error between the experimental and analytical modal resonance frequency of the tested tire with a different inflation pressure as the object value, structural parameters of the proposed tire model are identified by a backward genetic algorithm. Experimental and theoretical results show that: the planar coupling vibration characteristic of the heavy load radial tire can be predicted precisely with the flexible ring on an elastic continuous foundation  
interaction [6] have always been of interest. Different tire models with the different model complexity levels have been developed and researched for different applications. Simplified tire models with an analytical expression or purely empirically/semi-empirical formulae, such as the magic model [7], brush model [8], and LuGre model [9], etc., are used to investigate the longitudinal and lateral dynamics of the tire-road interactions with the computationally effective feature, while the structural elasticity and the flexible deformation of the tire belt and tire sidewall are ignored, leading to the existing deviation under certain manoeuvres. At the other extreme, taking the advantage the powerful computation and the composite characteristic [10], detailed tire models, such as the finite element tire model [6], absolute nodal coordinate formulation (ANCF) finite element tire model [11], and spectral element tire model [12], present the detail material feature and geometrical feature at the expense of much computation resource. Additionally, the detailed tire/road contacting feature can be investigated with the detailed tire and road model, while the large computation resource, the extensive finite element analysis (FEA)-oriented pre-processing, and the difficultly-obtained material parameters limit the extended application for vehicle dynamics. With less computation resources required than the detailed tire model, and a higher precision than the simplified tire model, the mechanical structure-based tire model [13] is proposed and much research has been devoted to focus on the kinematic modeling and numerical solving. Being the typical tire model respective of the mechanical structure-based tire model, the flexible belt tire model simplifies the tire as the flexible belt on an elastic foundation (referred to as the tire sidewall) and can range from one dimension to three dimensions. The circumference vibration of the flexible belts can be featured as the one-dimensional tire model [14] (referred to as the radial deformation in the polar coordinate system), or the two-dimensional tire model [15] (referred to as the radial and tangential deformation in the polar coordinate system), while the cross-section vibration of the belts [16] is added to form the three-dimensional tire model (referred to as the radial, tangential, and lateral deformation [17] in polar coordinates).