Concurrent energy harvesting and vibration suppression utilizing PZT-based dynamic vibration absorber

Abstract

This paper investigates simultaneous vibration suppression and energy harvesting through a continuous dynamic vibration absorber (DVA) with piezoelectric coupling, both numerically and analytically. The proposed system is composed of a simply supported host beam that is under a periodic external forcing or transient excitation in the form of an initial condition. Besides, a DVA is attached to the host beam. First, the governing electromechanical equations of the coupled system are derived. Next, convergence analyses are performed to find the effects of the considering higher modes of the host and absorber beam. Furthermore, the frequency response curves of the mechanical and electrical responses are obtained. It is observed that the DVA can effectively annihilate the host structure vibrations, up to 98.5%, and at the same time harvest considerable levels of voltage/power. Moreover, comprehensive investigations on the role of various mechanical and electrical parameters on the system responses are carried out. To validate the numerical results, an analytical solution is provided and a great agreement between these solution schemes is observed. Also, the dynamics of the considered system under an initial condition is inspected. Finally, the effects of the PZT layers in vibration isolation performance are studied. Results divulged that, upon the proper tuning of the mechanical and electrical parameters, the proposed DVA can significantly scavenge energy and mitigate vibrations.

Appendix

The orthonormality condition of the upper and lower beams, characteristic equation of the absorber, and ${\text{\rm Z}}_{i}$ relationship are provided in Eqs. (45–48).

$$\rho_{m} A_{m} \mathop \int \limits_{0}^{{L_{m} }} \overline{{C_{I} }} \sin \left( {\frac{I\pi }{{L_{m} }}S} \right) \cdot \overline{{C_{J} }} \sin \left( {\frac{J\pi }{{L_{m} }}S} \right)dS = \delta_{IJ} \to \overline{{C_{I} }} = \sqrt {\frac{2}{{\rho_{m} A_{m} L_{m} }}}$$

(45)

$$\mathop \int \limits_{0}^{{L_{a} }} \phi_{i} \left( s \right)m_{a} \phi_{j} \left( s \right)ds + \left\{ {\phi_{i} \left( s \right)M_{t} \phi_{j} \left( s \right)} \right\}_{{s = L_{a} }} = \delta_{ij}$$

(46)

$$\frac{{M_{t} }}{{m_{a} L_{a} }}\left( {\sinh \lambda_{i} \cos \lambda_{i} - \cosh \lambda_{i} \sin \lambda_{i} } \right)\lambda_{i} + \left( {1 + \cos \lambda_{i} \cosh \lambda_{i} } \right) = 0$$

(47)

$${\rm Z}_{i} = \frac{{\left( {\sin \lambda_{i} - \sinh \lambda_{i} } \right) + \frac{{M_{t} }}{{m_{a} L_{a} }}\lambda_{i} \left( {\cos \lambda_{i} - \cosh \lambda_{i} } \right)}}{{\left( {\cos \lambda_{i} + \cosh \lambda_{i} } \right) - \frac{{M_{t} }}{{m_{a} L_{a} }}\lambda_{i} \left( {\sin \lambda_{i} - \sinh \lambda_{i} } \right)}}$$

(48)