Analysis of Piezoelectric Energy Harvesters of a Moderate Aspect Ratio With a Distributed Tip Mass

Abstract

Various mathematical beam models have been proposed for the efficient analysis of a piezoelectric energy harvester (PEH) and carrying out parameter study but there appears no beam model suitable for a PEH of a moderate width-to-length aspect ratio with a distributed tip mass, and so, moderate width-to-length aspect ratios and distribution effects of a tip mass over a finite length will be mainly focused on in the present beam analysis. To deal with a wide range of aspect ratios, the material coefficients appearing in the constitutive equations of a PEH beam will be interpolated by those of the limiting plane-strain and plane-stress conditions. The key idea in the interpolation is to derive the interpolation parameter analytically by using the fundamental frequency of a cantilevered beam of moderate aspect ratios. To deal with the distribution effects of a tip mass over a finite length, the use of a set of polynomial deflection shape functions is proposed in the assumed mode approach. The equations to predict the electrical outputs based on the proposed enhanced beam model are explicitly expressed in template forms, so one can calculate the outputs easily from the forms. The validity and accuracy were checked for unimorph and bimorph PEHs by comparing the results from the developed beam model, the conventional beam model, and a three-dimensional finite element model. The comparisons showed substantial improvements by the developed model in predicting the electrical outputs.

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

“…It is known that electrical outputs of a PEH with an attached load resistance can be well predicted using finite element analysis. 22 Here, the fabricated PEH was modeled with the threedimensional coupled-field SOLID5 elements. The properties of the aluminum, brass and piezoelectric material used for the finite element analysis are listed in Table 3.…”

“…(6) can also be applied to plate-type PEHs as long as the relevant parameters can be properly evaluated. 22 Therefore, starting from Eq. (6), it is transformed into the following equation after some manipulations: (7) where Q m is the quality factor equal to 1/2ζ m and V b denotes the amplitude of the velocity of a vibrating base.…”

“…The average output power across a load resistance R L , which is calculated as V 2 /2R L , can be derived as (see, e.g. 22 ): (2) where A b denotes the magnitude of the acceleration of a base excitation, ζ m is the mechanical modal damping ratio measured at the short-circuit condition, and ω sc (ω oc ) is the angular short-circuit (open-circuit) resonant frequency in rad/s. The parameter , which represents the electro-mechanical coupling coefficient (EMCC) of piezoelectric devices, 27 is defined as:…”

“…These limitations occur because the mathematical models are based on the one-dimensional beam assumptions and thus cannot correctly assess the performance of platetype PEHs that have large effective area for the energy harvesting. To address the issue, a plate finite element model 21 and an enhanced beambased analysis model 22 were proposed, the latter of which also considered the distribution effects of a tip mass in contrast to the conventional assumption of a concentrated tip mass. As an alternative to the above-mentioned modeling techniques, an equivalent electrical circuit method can be used to find DC electrical outputs as well as frequencyswept AC outputs.…”

Power enhancing by reversing mode sequence in tuned mass-spring unit attached vibration energy harvester

“…For all simulations conducted here, ANSYS (a commercial finite element program) was used as in earlier study. 22 As for material data, brass (Young's modulus of 110 GPa and mass density of 8470 kg/m 3 ) was used for tip mass elements of both TMS and PEH units while aluminum (Young's modulus of 69 GPa and mass density of 2700 kg/m 3 ) was used for the substrate of the PEH unit and the beam part of the TMS unit. The piezoelectric material used to make PEH was chosen to be PZT 5H4E made by Piezo Systems, Inc. because it has high energy density 23 among polycrystalline piezoelectric ceramics.…”