Abstract: Abstract: Viscoelastic suspension is a newly applicable suspension for a large power and heavy crawler vehicle. The viscoelastic suspension can support a heavy load efficiently when walking and working on the off road, raise the adhesion property of a vehicle, and decrease the impact vibration level of the vehicle. The suspension consists of a metal part and viscoelastic material which are spaced and arranged to notably control vibration by transforming vibration energy into thermal energy to dissipate it into the air due to the hysteretic characteristic of viscoelastic materials. To predict and accurately study the dynamic behavior of viscoelastic suspension and evaluate its vibration damping capability, fractional calculus was introduced because of the facts that the fractional calculus exhibits global correlation and data-fitting well when describing rheological phenomenon. In this context, a fractional order Kelvin-Voigt model considering the geometric factors i.e. A radius-thickness ratio incorporated into a dynamic model of viscoelastic suspension for crawler vehicle was established. In this model, the viscoelastic part was represented by a parallel-combination of a spring whose stress is in direct proportion to the strain and a spring pot whose stress is in direct proportion to the fractional derivative of the strain differentiating from the conventional damping pot with stress being proportional to the first derivative of the strain. A numerical solution was obtained by adoption of a Grumwald-Letnikov fractional derivative definition and a matrix function theory and its calculating codes were programming in Matlab. A history correlation coefficient was achieved to embody the afore-history influence of the viscoelastic suspension on its dynamic behavior. Parameters of a fractional model was acquired by fitting data using a least-square method based on a viscoelastic material tensile test carried out on a Testometric M350-10kN according to GB/T 528-1998 and GB/T 9865.1. For a pragmatic study case, a heavy crawler tractor installed with 8 viscoelastic suspensions was considered to analyze its vibration control effect by establishing its fractional model. Also the parameter influence on the vibration control effect, including exciting frequency, fractional order, and ratio of radius to thickness, was examined. The results showed that, compared with rigid suspension, the viscoelastic suspension exhibited remarkable vibration control capability, especially at the resonant frequency of about 4.5 Hz by reducing the response magnitude of the vehicle body by 64.10% in max value and 66.40% in RMS, thus satisfying the supporting and stable demands of the crawler tractor walking and working on the off road. Radius-thickness has a negative influence on the response magnitude of viscoelastic suspension, that is to say there is an effective way to reduce the vibration by introducing a geometry-modified viscoelastic suspension with higher thickness and lower action aero. Fractional order, however, exhibits a positive correlation to the behavior of the response magnitude, which inspires another valid method of altering the viscoelastic material parameter to perfect the vibration of the crawler tractor. The history-dependent factor gives evidence of the long range correlation of the fractional model, i.e., the system response at current time relates to the whole history whose influence increases with time closer to the current time. This research provides an essential theoretical basis for multi-objective optimization and dynamic design of a viscoelastic suspension for a higher power and heavy load crawler vehicle. Experiment study is an essential procedure as a further study. So our future work will stress the indoor test of a dynamic mechanical analysis (DMA) of viscoelasitc materials, deriving a fractional constitutive model considering the temperature-frequency effect of viscoelastic material, and carrying out an in-situ test of a real crawler vehicle establishing a different-parameter viscoelastic suspension to investigate stable/dynamic stiffness, fatigue features, and vibration control capability under working conditions of cutting, pulling, digging, and crossing over an obstacle.