A novel 3D analytical model and numerical study of bimorph piezoelectric actuators in d33 mode

This paper presents a detailed 3D mathematical model for the representative volume element (RVE) of bimorph d 33-mode piezoelectric actuators, to examine the intensity and distribution of the electric field EP and strain S within the piezoelectric material across different planes and under varying conditions. By maintaining constant dimensions, the analysis demonstrates a notable decrease in the orthogonal planar component of E-P , under electrode and electrode separation (60-80% and 50-70% in the corresponding cross-sections of x - z and x - y planes, and 80% in the y - z plane) and under electrode areas (40-30%, 50-90%, and 80% corresponding to the x - z , x - y , and y - z planes, respectively). These results show a dominant x-component of E-P . Furthermore, the fringe effect doubles the E-P intensity along the x - y plane at the edges of the electrode and reduces it by 40% in the x - z and y - z planes, affecting actuator performance, durability and structural integrity due to the localized strain intensification S 3 . Further investigation, adjusting the piezoelectric thickness t P , electrode width w e , electrode separation d , and electrode length le while keeping the RVE width constant w = 400 mu m , revealed the dependency of strain S-3 on the electrode dimensions. It was shown that increases in we and reductions in t(P) enhance strain at any point ( a, c, z) of the weak EP mentioned earlier. Conversely, peak values of S-3 were observed within tP = 0 - 20 mu m and at electrode width extremities scale with a = 0 , - w(e) when coordinates were assessed relative to a constant width w . l(e) variation had negligible impact on S-3 (2.5% increase from 4 mm to 4 cm ). Uniform E-P theoretically maximize strain but are practically unattainable due to dependencies on charge distribution location, distance, and material and geometric limitations. The analysis reveals the interplay between the electric field, strain, and geometry in optimizing the bimorph d 33-actuators.