Effect of non-proportional damping on the torque roll axis decoupling of an engine mounting system

Several mounting system design concepts are conceptually used to decouple the engine roll mode though limited success has been observed in practice. One shortcoming of the existing theories or design methods is that they ignore non-proportional viscous damping in their formulations. It seems that the rigid-body vibrations are coupled whenever non-proportional damping is introduced to the mounting system even though the torque roll axis decoupling is still theoretically possible with proportional damping assumption. To overcome this deficiency, we re-formulate the problem for a non-proportionally damped linear system while recognizing that significant damping may be possible with passive (such as hydraulic) or adaptive mounts. The complex mode method is employed in our work and the torque roll axis decoupling paradigm is re-examined given mount rate ratios, mount locations and orientation angles as key design parameters. We derive a necessary axiom for a mode in the torque roll axis direction provided two eigenvalue problems, in terms of stiffness and damping matrices, are concurrently satisfied. Two numerical examples are chosen to examine both steady-state and transient responses and the extent of coupling or decoupling is quantified. Results show that the torque roll axis for a mounting system with non-proportional damping (under oscillating torque excitation) is indeed decoupled when one of the damped modes lies in the torque roll axis direction. Finally, eigensolutions are validated by using experimental data.