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Hybrid damping of structural vibration using a combination of active and passive layers is found to have high application potential due to the requirement of a lower power supply and guaranteed stability. Use of hard-coating layers as a passive damping treatment is found to be industrially acceptable for turbine blades etc, due to the high damping capacity and large service temperature range. However, such damping materials also have high strain dependence. In a way that is similar to active constrained layer damping, by using an active material the strain in the passive damping can be controlled, and thereby the damping performance of the passive layer. This paper proposes a semi-analytical method to estimate structural damping in such a system and obtain the response of a smart hybridly damped system. The paper delves into the closed-form solution of all common boundary conditions of a vibrating beam, namely cantilever, hinged-hinged, free-free, hinged-free, and fixed-fixed beams. It also compares the damping performance of a beam with only a passive damping layer to that of beams comprising both active and passive damping layers.

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