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In a monotube magnetorheological fluid damper (MRFD), there usually exists a compensation chamber with designated initial gas pressure. This enclosed compensation chamber works as an air spring to some degree to provide force to the working piston. In this work, in order to extend the external damping force range and improve the controlling efficiency, a structure of MRFD with three additional accumulators is proposed. These additional accumulators are connected to the atmosphere through an air pump and the compensation chamber with a barometric valve. The external damping force range thus can be rapidly adjusted through mode shifting with this configuration. A mathematical model of this damper with coupled effects between the air and the magnetorheological fluid (MRF) is developed. Comparing the bench tests results with some simulation outcomes, the simulation model of this MRFD is validated.