VIBRATION TRANSMISSION THROUGH AN ISOLATOR MODELLED BY CONTINUOUS SYSTEM THEORY

This article focuses on the flexural motion of an elastomeric isolator but the longitudinal motion is also considered. The continuous system theory is used to describe mobility or stiffness characteristics and power-based vibration isolation measures. The scope of this study is limited to the frequency domain analysis of a linear time-invariant (LTI) system with a single isolator that is placed between a rigid body and a finite or infinite beam receiver. The upper limit of the frequency range is 4 kHz. Two types of solutions to the Timoshenko beam for a rubber material are critically examined, and the Timoshenko and Euler beam solutions are compared for vibration power measures. Our analysis shows that the shear deformation and rotary inertia must be considered in order to properly describe a thick isolator that effectively transmits flexural motions at higher frequencies. The shear deformation effect is, however, found to be more pronounced as evaluated by the power-based vibration isolation measures at higher frequencies. Further, the roles of isolator parameters such as the static stiffness ratios, shape factors and material properties are investigated. The continuous system theory clearly accounts for the cross-axis coupling terms and it may be further utilized for optimizing vibration isolation schemes over a wide range of frequencies.