Finite element analysis of optimized piezoelectric bimorphs for vibrational “energy harvesting”

Marco Gallina, Denis Benasciutti
University of Udine

The concept of “energy harvesting” is to design smart systems to capture the ambient energy and to convert it to usable electrical power to supply small electronics devices and sensors. The goal is to develop autonomous and self-powered devices that do not need any replacement of traditional electrochemical batteries. Among the available energy sources (solar energy, waste heat, electromagnetic waves, vibrations, etc..) and transduction mechanisms, great attention has been focused on vibrational energy harvesting with piezoelectric materials, due to their excellent electromechanical coupling, high conversion efficiency and favorable frequency response. The purpose of this paper is to numerically analyze the electromechanical response of piezoelectric bimorphs subjected to vibrations. The bimorph is made up of two layers of piezoelectric material glued on a stainless steel shim, which form a cantilever beam with a tip mass that has the capability to convert the mechanical bending strain within the piezoelectric layers into electric charges on its external surface. The bimorph can be used to continuously generate electrical energy to supply connected devices (e.g. sensors, RF transmitters), especially when batteries replacement could be unfeasible. The strategy here used to increase the average mechanical strain, and hence the generated power output, is to modify the geometry of rectangular piezoelectric beam, which is traditionally used in applications. Optimized configurations with trapezoidal shapes (direct and reversed), with either constant width or constant volume, have been proposed and numerically analyzed. A detailed 3D finite element model is used to evaluate and to compare the electromechanical response of the proposed optimized bimorphs, in terms of resonant frequency, harmonic transfer function, output voltage and power. The electromechanical vibration response has been studied with a modal analysis and a harmonic coupled simulation with imposed base acceleration. An original modeling approach is proposed to impose a constant base acceleration to the vibrating bimorph during the frequency sweep over a wide frequency range. The anisotropic mechanical (stiffness matrix) and electrical (piezoelectric coupling, permittivity matrix) properties of the piezoelectric material, poled along the direction transverse to bending, have also been characterized by suitable electromechanical constitutive matrices. Missing any specific experimental result, the value of the mechanical damping ratio, which represents a parameter that is generally difficult to assess, is preliminary evaluated with reference to literature data.
Coupled harmonic simulations have been carried out with a wide set of electrical resistances connected to the piezoelectric bimorph, to investigate the electromechanical response in a range of electrical loads ranging from closed to opened circuit conditions. The obtained results confirm an increment in the electric performance of the proposed optimized bimorphs, with a net increase in electric power compared to the traditional rectangular configuration.