Natural and forced vibrations of solid bodies with account for damping and prestressed state induced by piezoelectric elements
DOI:
https://doi.org/10.7242/1999-6691/2025.18.4.29Keywords:
natural and forced vibration, electro-viscoelasticity, prestress, viscous and Rayleigh damping, finite element methodAbstract
The widespread use of thin-walled structures subjected to undesirable dynamic phenomena necessitates the development of effective methods for controlling their vibrational characteristics to prevent resonance. A promising approach to solving this problem is the application of smart materials, particularly, piezoelectric elements, enabling the implementation of passive, active, and hybrid damping systems. This work investigates the natural and forced vibrations of piecewise-homogeneous electro-elastic and electro-viscoelastic bodies using the finite element method. A distinctive feature of the study is the consideration of the prestressed and predeformed state caused by an embedded piezoelectric element as a result of the reverse piezoelectric effect due to DC voltage supply. A mathematical formulation of the problem, interpreting the prestress state in terms of geometric stiffness, and accounting for viscous and Rayleigh damping mechanisms is developed based on the principle of virtual displacements. Using a plate with an embedded piezoelectric element as an example, the influence of the control voltage and the type of damping on the complex natural frequencies and amplitude-frequency responses is studied. It has been established that both viscous and Rayleigh damping have slight effect on the shift of resonant frequencies caused by the prestressed state. The results of solution of the forced vibration problem allow us to quantify a decrease in the vibration amplitude of the plate in the prestressed state caused by the piezoelectric element in the case of external excitation with frequency corresponding to the resonance frequency of the unloaded plate. The results presented demonstrate the influence of the prestressed state on the amplitude-frequency response of a plate with closely spaced natural frequencies at different values of the electric potential on the piezoelectric element.
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