The formulation for the coupled electromechanical problem of forced vibration of a simply supported inelastic sandwich beam with piezoelectric layers is developed. An approximate formulation for the problem in terms of the amplitudes of the main electromechanical field variables is produced by applying the monoharmonic (single-frequency) approach along with the concept of complex moduli to characterize the cyclic properties of the material. Accuracy of the developed monoharmonic approach is estimated. It is achieved through the comparison of the results computed for the transient response of the beam using the complete model with those found using the approximate model. Limitations on the approximate monoharmonic method application are specified. The effect of physically nonlinear behaviour of the passive layer on the beam response is investigated. The possibility of damping the forced vibrations of a structure with the help of harmonic voltages applied to the external piezoactive layers is also discussed.
Zhuk, Y. A., Guz, I. A., & Sands, C. M. (2011). Monoharmonic approximation in the vibration analysis of a sandwich beam containing piezoelectric layers under mechanical or electrical loading. Journal of Sound and Vibration, 330(17), 4211-4232. https://doi.org/10.1016/j.jsv.2011.04.012