This paper proposes a new analytical model for a thin cylindrical shell that utilizes a homogeneous cardboard liner to increase modal damping. Such cardboard liners are frequently used as noise and vibration control devices for cylindrical shell-like structures in automotive drive shafts. However, most prior studies on such lined structures have only investigated the associated damping mechanisms in an empirical manner. Only finite element models and experimental methods have been previously used for characterization, whereas no analytical studies have addressed sliding friction interaction at the shell-liner interface. The proposed theory, as an extension of a prior experimental study, uses the Rayleigh-Ritz method and incorporates material structural damping along with frequencydependent viscous and Coulomb interfacial damping formulations for the shell-liner interaction. Experimental validation of the proposed model, using a thin cylindrical shell with three different cardboard liner thicknesses, is provided to validate the new model, and to characterize the damping parameters. Finally, the model is used to investigate the effect of the liner and the damping parameters on the modal attenuation of the shell vibration, in particular for the higher-order coupled shell modes.

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This article extends a recent publication [MSSP (2016), 176−196] by developing a Rayleigh-Ritz model of a thin cylindrical shell to predict its response subject to concurrent active and passive damping treatments. These take the form of piezoelectric patches and a distributed cardboard liner, since the effects of such combined treatments are yet to be investigated. Furthermore, prior literature typically considers only the-bimorph‖ active patch configuration (with patches on the inner and outer shell surfaces), which is not feasible with an interior passive liner treatment. Therefore, a novel configuration-termed as-unimorph‖-is proposed and included in the model. Experiments are performed on a shell with active patches (under harmonic excitation from 200 to 2000 Hz) in both the bimorph and unimorph configurations to provide evidence for the analytical model predictions. The proposed model is then employed to assess competing control system designs by examining local vs. global control schemes as well as considering several alternate active patch locations, both with and without the passive damping. Non-dimensional performance metrics are devised to facilitate comparisons of vibration attenuation among different designs. Finally, insertion loss values are measured under single-frequency excitation to evaluate several vibration control designs, and to compare the effects of alternate damping treatments.

Combined active and passive damping is a recent trend that can be an effective solution to challenging NVH problems, especially for lightweight vehicle components that demand advanced noise and vibration treatments. Compact patches are of particular interest due to their small size and cost, however, improved modeling techniques are needed at the design stage for such methods. This paper presents a refined modeling procedure for side-by-side active and passive damping patches applied to thin, plate-like, powertrain casing structures. As an example, a plate with fixed boundaries is modeled as this is representative of real-life transmission covers which often require damping treatments. The proposed model is then utilized to examine several cases of active and passive patch location, and vibration reduction is determined in terms of insertion loss for each case. Results are compared to an experiment with an actual transmission casing for validation, using piezoelectric active patches and constrained-layer passive patches with a viscoelastic core. Conclusions are drawn about patch size and location in terms of NVH reduction capability, and guidelines are suggested for the dynamic design process.

Concurrent placement of compact active and passive damping patches for vibration reduction is a developing area of research. Analytical and computational models to evaluate alternate patch configurations and structural geometries are not widely available. To overcome this void, this paper presents a simplified discrete-system model for vibrations of a beam-like structure. A disturbance input is included in the model, along with a control input from an active patch. Localized structural damping resulting from a passive patch is modeled with an equivalent loss factor. Results from the simplified model are verified using a more detailed analytical formulation, which is based on the Ritz approximation. Verification studies include the effect of a passive damping patch on modal loss factors and broadband attenuation. Finally, a few case studies are proposed which show the efficacy of the reduced-order model for parametric design studies. These studies include determining the effect of localized damping on the control system parameters that are required for attenuation of localized and global motions. The effect of patch locations on system response is also studied. This work has potential applications in industry since compact damping patches are attractive NVH treatments that add minimal weight and complexity.