This paper is to propose a viable hybrid damping design that integrates active and passive dampings through intelligent constrained layer (ICL) treatments. This design consists of a viscoelastic shear layer sandwiched between a piezoelectric constraining cover sheet and the structure to be damped. According to measured vibration response of the structure, a feedback controller regulates axial deformation of the piezoelectric layer to perform active vibration control. In the meantime, the viscoelastic shear layer provides additional passive damping. The active damping component of this design will produce adjustable and significant damping. The passive damping component of this design will increase gain and phase margins, eliminate spillover, reduce power consumption, improve robustness and reliability of the system, and reduce vibration response at high frequency ranges where active damping is difficult to implement. To model the dynamics of ICL, an eighth-order matrix differential equation governing bending and axial vibrations of an elastic beam with the ICL treatment is derived. The observability, controllability, and stability of ICL are discussed qualitatively for several beam structures. ICL may render the system uncontrollable or unobservable or both depending on the boundary conditions of the system. Finally, two examples are illustrated in this paper. The first example illustrates how an ICL damping treatment, which consists of an idealized, distributed sensor and a proportional-plus-derivative feedback controller, can reduce bending vibration of a semi-infinite elastic beam subjected to harmonic excitations. The second example is to apply an ICL damping treatment to a cantilever beam subjected to combined axial and bending vibrations. Numerical results show that ICL will produce significant damping.

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