Active and passive damping patches on a thin rectangular plate: A refined analytical model with experimental validation

Concurrent placement of active and passive damping is an emerging area of research, though tractable analytical solutions to address such problems for plate-like structures are not readily available. Accordingly, a new analytical model is proposed using a Rayleigh–Ritz scheme for a thin elastic plate with side-by-side active and passive damping patches. Frequency-dependent properties of passive patch viscoelastic material are included in the formulation. The comprehensive model is found to be valid for the cases of either passive or active patches, as well as the combined case. The proposed formulation is verified with a commercial finite element code, and experiments are performed for limiting cases to validate proposed theory and results. The effect of passive patch location on modal loss factor and on the response due to a harmonic disturbance is analytically determined. The phase interaction between the active patches and the disturbance input, including the effect of damping on the required control parameters, is quantified. Finally, the side-by-side combination of active and passive damping is found to yield improved vibration reduction and to enhance the efficacy of active control.