A transfer matrix for shafts coupler with parallel misalignment (offset) was derived. The responses of a rotor system composed of flexible shafts, unbalanced disks, elastic supports and shafts coupler with misalignment were then investigated. Through the derivation, the boundary shears induced by a rotating shaft were first discovered to be coupled in two perpendicular directions. These coupling shears might reduce the first critical speed up to 50% in the free-free case. The studies showed that the shafts coupler altered the rotor's critical speeds and the misalignment played as an external load resulting through the whole driven shaft. The combined effects of disk unbalance and shaft misalignment showed that the misalignment predominated the response in most of the rotation speeds, but the unbalance could become significant at high speed. The whirling orbits before and after the misalignment were illustrated as well, and numerical results showed that the two ends of the misalignment whirled asynchronously as the rotation fell into some regions.
The vibration equations of a thick sandwich structure with a viscoelastic material core were derived. The host layer was assumed thick and the top layer could be thin or thick. This type of structures may apply to various cases and the particular application for which it fit is that of constrained layer damping treatment for vibration attenuating. The governing differential equations contained nine displacements for thick–thick surface layers. For cases of thin–thick, the number of displacement was significantly reduced to only five, which were one transverse displacement, two in-plane displacements, and two layer rotation angles, all associated with the host layer. The derived theory was general, and it could be not only specialized for many commonly seen structures such as beams, plates, and cylindrical shells but also degenerated into one- or two-layer structures. Specialization for a sandwich cylindrical shell was extensively illustrated, and numerical results of natural frequencies and damping were compared to those of thin shell theory. How each layer's thickness influenced the frequency and damping of the sandwich shell were particularly discussed.
In this paper a general transfer matrix method (TMM) for rotors containing global and local coupler offset was derived. Rotor response due to imbalances and offsets are then studied via the developed method. The studies showed both global and local offsets played as an external excitation that is a combined effect of all the elements behind the offset. Differences between global offset and local offset were compared and the results showed both types basically retain the same mode patterns but different jumps at the offset. The global offset, yet, imposed more significant dynamic effects since all the offsets accumulate thereafter. The whirling orbits in front and behind the offset were illustrated as well. The results, as expected, showed global offset appeared much larger radii especially after offset. The rotor's whirling orientation reversed, as rotation fell within a certain range and this feature was not changed by offsets. The TMM proposed by this study can be well applied to multiple global and local offsets.
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