“…The literature review shows that the main element of piezoelectric energy harvesters are often a cantilever beam with a bluff body in its tip. Therefore, the nonlinear effect due to middle layer stretching effect has been neglected in the previous works (Abdelkefi et al, 2012;Akaydin et al, 2010;Dai et al, 2016;Ewere and Wang, 2014;Gao et al, 2013;Hou et al, 2020Hou et al, , 2022Jia et al, 2018;Li et al, 2022aLi et al, , 2022bLi et al, , 2023Ma et al, 2023;Mehmood et al, 2013;Rezaei and Talebitooti, 2019;Seyed-Aghazadeh et al, 2020;Skop and Griffin, 1973;Sui et al, 2022;Sun et al, 2019;Wang et al, 2020;Yang and He, 2019;Zhang et al, 2022;Zhang and Wang, 2016;Zhao et al, 2012Zhao et al, , 2016Zhao et al, , 2019.…”