Modal and Forced Response Analysis of Vehicle Systems With Latent Vibration Modes Due to Hydraulic Mounts

Abstract

Hydraulic mounts used in vehicles for better isolation of vibrations were often approximated by lumped or mechanical mass-damper-spring (m-c-k) models, although deficiency in such modeling was pointed out and “hydraulic” modeling was proposed as an alternative. In this paper, a brief review on the mechanical m-c-k modeling and “hydraulic” modeling of the hydraulic mounts is presented. A simplest system consisting of a single mass and a hydraulic mount is used to illustrate both equivalence and difference in a closed form between the two modeling approaches. Then, modal analyses are done on an apparently three degrees-of-freedom (DOF) quarter car with a hydraulic mount, where the key idea is to use an internal variable for the movement of fluid mass which is responsible for a “latent” vibration mode. Equations of motion for the apparently 3DOF system, 4DOF system in fact, by the two modeling are formulated. Modal parameters by the proposed “hydraulic” modeling of the hydraulic mount are compared with those by the m-c-k modeling. Forced responses to transient base excitations are also compared between the two modeling approaches to illustrate how much errors can arise in the frequency and time domain analysis. To be more realistic, the modal and forced response analysis on a full car of an apparently 10DOF (3DOF for powertrain, 3DOF for car body, and 4DOF for knuckles and tires) with two more DOF internally for two hydraulic mounts between the powertrain and car body is presented.