Results in Engineering (Mar 2025)

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

  • A. Almusallam,
  • M.A. Belaid

Journal volume & issue
Vol. 25
p. 103813

Abstract

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This paper presents a detailed 3D mathematical model for the representative volume element (RVE) of bimorph d33-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 Ep, 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 Ep. Furthermore, the fringe effect doubles the Ep 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 S3. Further investigation, adjusting the piezoelectric thickness tp, electrode width we, electrode separation d, and electrode length le while keeping the RVE width constant w=400μm, revealed the dependency of strain S3 on the electrode dimensions. It was shown that increases in we and reductions in tp enhance strain at any point (a,c,z) of the weak Ep mentioned earlier. Conversely, peak values of S3 were observed within tp=0−20μm and at electrode width extremities scale with a=0,−we when coordinates were assessed relative to a constant width w. le variation had negligible impact on S3 (2.5% increase from 4mm to 4cm). Uniform Ep 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 d33-actuators.

Keywords