The fractional model considering geometric factor of viscoelastic damping systems is proposed by adopting fractional viscoelastic oscillator. To obtain dynamic responses of the fractional model, a numerical method is derived based on matrix function theory and Grumwald-Letnikov discrete form of fractional derivative. As a special engineering application example, the vibration response of the viscoelastic suspension installed in heavy crawler-type vehicles is studied through the proposed model. Furthermore, the parameter influence on the vibration control capability of the viscoelastic suspension is researched. The results indicate that the fractional viscoelastic oscillator is a favorable choice to characterize the dynamic behavior of viscoelastic damping structures. Additionally, the parameters in fractional viscoelastic oscillator namely geometric factor and fractional order exert considerable impact on the dynamic response of viscoelastic damping structures.
Due to various applications of bamboo as a loading structure, it is necessary to have a deep understanding of the relationship between its morphology and mechanics, including how its structure adapts to taking the applied load. In this paper, diaphragms are considered concave or convex rather than flat plates. Two kinds of cavities (concave and convex) comprising internodal tubes and diaphragms were studied. One loaded bamboo model was established to deduce the formulas for the deformation amount of cavity volume (concave and convex cavities). Variations of their volume and inner radius, internode length, the curve surface depth, and the shortening rate were analysed. The deformation of one loaded bamboo with actual shortening rate (0-0.3) was simulated by software. The result revealed that bamboo culms showed wavy deformation as the two cavities alternately appeared. The concave cavity shrinkage restrained further deformation, while the convex cavity expansion gave rise to further deformation. Both cavities interacted to improve the bending strength of bamboo culms and prevented large deformation or fractures. This study could provide new ideas and methods for the design of structures with desired bending performance.
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