Abstract: A five-parameter fractional derivative model for characterizing the relations between excitation frequencies and dynamic properties of a hydraulic engine mount (HEM) is presented, and the five parameters in the model have definite physical meanings. A two-degrees-of-freedom vibration system containing two HEMs is considered, and the dynamic properties of the two HEMs are optimized with the aim of controlling the vertical displacement and the roll angle of the supported object in time domain. Calculation and test results demonstrate that the five-parameter fractional derivative model can describe the frequency-dependent dynamic properties of the HEMs efficiently. The time-domain response analysis method based on the block diagram can be used to analyze the dynamic responses of the vibration systems including HEMs, and the optimization method developed in this paper can be used to optimize the dynamic properties of the HEMs.

Key words: Dynamic response calculation, Fractional derivative model, Hydraulic engine mount, Optimization design method