An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations

Abstract

Piezoelectric transduction has received great attention for vibration-to-electric energy conversion over the last five years. A typical piezoelectric energy harvester is a unimorph or a bimorph cantilever located on a vibrating host structure, to generate electrical energy from base excitations. Several authors have investigated modeling of cantilevered piezoelectric energy harvesters under base excitation. The existing mathematical modeling approaches range from elementary single-degree-of-freedom models to approximate distributed parameter solutions in the sense of Rayleigh-Ritz discretization as well as analytical solution attempts with certain simplifications. Recently, the authors have presented the closed-form analytical solution for a unimorph cantilever under base excitation based on the Euler-Bernoulli beam assumptions. In this paper, the analytical solution is applied to bimorph cantilever configurations with series and parallel connections of piezoceramic layers. The base excitation is assumed to be translation in the transverse direction with a superimposed small rotation. The closed-form steady state response expressions are obtained for harmonic excitations at arbitrary frequencies, which are then reduced to simple but accurate single-mode expressions for modal excitations. The electromechanical frequency response functions (FRFs) that relate the voltage output and vibration response to translational and rotational base accelerations are identified from the multi-mode and single-mode solutions. Experimental validation of the single-mode coupled voltage output and vibration response expressions is presented for a bimorph cantilever with a tip mass. It is observed that the closed-form single-mode FRFs obtained from the analytical solution can successfully predict the coupled system dynamics for a wide range of electrical load resistance. The performance of the bimorph device is analyzed extensively for the short circuit and open circuit resonance frequency excitations and the accuracy of the model is shown in all cases.

Numerical Modeling of Flow-Driven Piezoelectric Energy Harvesting Devices

“…It was shown that the load-resistance depen-dent variation of the resonance frequency and amplification of the motion at opencircuit frequency are indicators for the need for better representation of the effect of harvesting circuits. In one of the most important works in the field, [7,8] presents a mathematical model with distributed parameter solution based on Euler-Bernoulli assumptions, and comparisons with several SDOF models are made to point out the inaccuracies in popular SDOF models. Several flaws in SDOF models, ranging from the neglect of base rotary motion up to the simplified modeling of damping induced by piezoelectric coupling, are addressed in this work and correction factors are introduced, where necessary, to the SDOF models.…”

“…where (7) is the momentum balance equation, (8) gives the non-linear kinematic relation, and (9) depicts the coupled constitutive relation in rate form for the direct piezoelectric effect. S is the second Piola-Kirchoff tensor,Ė is the strain rate tensor, sD is the compliance matrix measured at constant electric displacement, [g] is the piezoelectric coefficient, andD is the dielectric displacement of the piezoelectric structure.…”

“…The expressions for mechanical strain rate (Ė) in (8) and electric field rate (Ė) in (13) can be obtained by differentiating (36d) and (36b) respectively, and expressed asĖ…”

“…The bimorph cantilever beam considered in this numerical example is also discussed in [8], and the basic setup is shown in Fig. 7 The substructure is sandwiched between two identical piezo patches which are fully covered with conductive electrodes.…”

An Energy conversion model for cantilevered piezoelectric vibration energy harvesters using only measurable parameters

“…For example, the single-degree-of-freedom modeling approach (lumped parameter modeling) was developed by Roundy and Wright 15 duToit et al. 16 Since then, the variational principle combined with the Rayleigh-Ritz method 16,17 and the continuous distributed parameter approach 18,19 have been the two primary mathematical modeling approaches used to predict the electrical performance of cantilevered PEHs. More detailed discussions about the existing mathematical modeling approaches can be found in Erturk and Inman.…”