In this paper we present a calculation method in the time domain for vibration systems including hydraulic engine mounts (HEMs) to evaluate the vibrations of a body that is a sprung mass in bounce and roll modes. A fractional derivative model is used to describe the frequency-dependent dynamic properties of a HEM. A two degree-of-freedom vibration system with two mounts is considered to demonstrate the use of the method. An optimization method is proposed to suppress body vibrations in the two modes. Optimization results show that body vibrations can be effectively suppressed using the HEMs designed on the basis of the optimization method.
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