Revisit on the distributions of electric field and electric displacement in a three-layer beam-like piezoelectric harvester

In this paper, the distributions of electric field and electric displacement in a three-layer beam-like piezoelectric harvester are revisited from the accurate piezoelectricity theory. The electric displacement D₃ is obtained from the Gauss theorem in electrostatics and found to be uniformly distributed along the thickness direction. The electric field is observed linearly dependent on x₃. The efficiency is calculated finally and found to be always less than one, which eliminates a paradox that may appear for piezoelectric harvesters with large electromechanical coupling coefficients when calculated from the assumption of uniform electric field.