TY - JOUR
T1 - Semi-analytical model of an acoustic black hole piezoelectric bimorph cantilever for energy harvesting
AU - Deng, Jie
AU - Guasch, Oriol
AU - Zheng, Ling
AU - Song, Tingting
AU - Cao, Yanshu
N1 - Funding Information:
This work has been completed while the first author was performing a two-year Ph.D. stay at La Salle, Universitat Ramon Llull, funded by the National Natural Science Foundation of China under Grant (51875061) and the China Scholarship Council (CSC no. 201806050075). The authors gratefully acknowledge this support as well as the in-kind assistance from La Salle, Universitat Ramon Llull, and the Chongqing University to make that collaboration possible.
Funding Information:
This work has been completed while the first author was performing a two-year Ph.D. stay at La Salle, Universitat Ramon Llull, funded by the National Natural Science Foundation of China under Grant ( 51875061 ) and the China Scholarship Council (CSC no. 201806050075 ). The authors gratefully acknowledge this support as well as the in-kind assistance from La Salle, Universitat Ramon Llull, and the Chongqing University to make that collaboration possible.
Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2021/3/3
Y1 - 2021/3/3
N2 - An acoustic black hole (ABH) beam termination can be achieved by decreasing its thickness according to a power-law profile. Waves entering the ABH slow down and vibrational energy strongly concentrates at the tip of the beam. This can be exploited for energy harvesting, as suggested in some recent works. The finite element method (FEM) is commonly used to carry out the simulations, which hampers long parametric analyzes. In this paper, we develop a semi-analytical approach to characterize the performance of a piezolectric bimorph cantilever with an ABH termination. The method can be easily extended to further configurations and allows one to determine ABH harvesting capabilities when varying system parameters, in a fast and efficient way. The Lagrangian of the ABH beam plus piezoelectric layers is constructed and the coupled equations for the flexural vibrations and voltage are derived from it. The flexural displacement field is expanded in terms of Gaussian basis functions. Vibration shapes and harvested power are computed with the proposed method and validated against FEM simulations. The ABH piezolectric bimorph cantilever is shown to substantially enhance the harvesting capabilities of a cantilever with uniform cross-section. The semi-analytical approach is then used to examine the influence of several ABH and piezoelectric layer parameters on energy harvesting efficiency. As regards the former, the effects of the tip truncation thickness and ABH order are explored. In what concerns the piezoelectric layer, we investigate the effects of its location, thickness, splitting it into several patches and varying the load resistors to enhance its performance in a broad frequency range. The proposed method constitutes a valuable tool for the design of ABH energy harvesting devices.
AB - An acoustic black hole (ABH) beam termination can be achieved by decreasing its thickness according to a power-law profile. Waves entering the ABH slow down and vibrational energy strongly concentrates at the tip of the beam. This can be exploited for energy harvesting, as suggested in some recent works. The finite element method (FEM) is commonly used to carry out the simulations, which hampers long parametric analyzes. In this paper, we develop a semi-analytical approach to characterize the performance of a piezolectric bimorph cantilever with an ABH termination. The method can be easily extended to further configurations and allows one to determine ABH harvesting capabilities when varying system parameters, in a fast and efficient way. The Lagrangian of the ABH beam plus piezoelectric layers is constructed and the coupled equations for the flexural vibrations and voltage are derived from it. The flexural displacement field is expanded in terms of Gaussian basis functions. Vibration shapes and harvested power are computed with the proposed method and validated against FEM simulations. The ABH piezolectric bimorph cantilever is shown to substantially enhance the harvesting capabilities of a cantilever with uniform cross-section. The semi-analytical approach is then used to examine the influence of several ABH and piezoelectric layer parameters on energy harvesting efficiency. As regards the former, the effects of the tip truncation thickness and ABH order are explored. In what concerns the piezoelectric layer, we investigate the effects of its location, thickness, splitting it into several patches and varying the load resistors to enhance its performance in a broad frequency range. The proposed method constitutes a valuable tool for the design of ABH energy harvesting devices.
KW - Acoustic black holes
KW - Energy harvesting
KW - Gaussian expansion method
KW - Piezoelectric bimorph cantilever
KW - Piezoelectric effect
UR - http://www.scopus.com/inward/record.url?scp=85097353753&partnerID=8YFLogxK
U2 - 10.1016/j.jsv.2020.115790
DO - 10.1016/j.jsv.2020.115790
M3 - Article
AN - SCOPUS:85097353753
SN - 0022-460X
VL - 494
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
M1 - 115790
ER -