The development of bulk piezoelectric ceramics with high energy conversion efficiency is of decisive importance for the requirements of the advanced energy harvesting devices toward miniaturization and integration. There is an additional motivation in the piezoelectric ceramics, lead titanate-zirconate (PZT) ceramics are the most widely used energy harvesting (EH) materials. This fact is important because legal restrictions on the use of lead in electronic devices have led to greater efforts being made to develop leadfree alternatives to PZT-based materials. Here, we propose the Bi0.5(Na0.8K0.2)0.5TiO3 (BNKT) lead-free piezoceramics as a good candidate for the replacement of toxic lead compounds for energy harvesting applications. For that, we have carried out a systematic study of the voltage generation of BNKT-based piezoceramics for (EH) purposes. Specifically, our results reveal that the BNKT-based lead-free piezoceramics show adequated effective capacitance and output energy due to more effective performance with a piezoelectric charge coefficient and a maximum generated output voltage as high as 12.8 pC/N and 19.9 V, respectively. Finally, we consider that the design of new leadfree piezoceramics with superior property coefficients and functionalities, such as the BNKT-based piezoceramics, should be seriously considered as candidates for the replacement of the current toxic lead-based compounds.

In this paper we show the importance of double impact in an up-converting mechanism by using a resonant low-frequency driving beam across a high-frequency piezoelectric beam, to enhance the electrical output power in a vibration energy harvesting (VEH) system suitable for ambient vibrations. The main advantage of this device is its nearly constant output voltage between impacts compared to other VEH systems using up-converting mechanisms whose output voltages decay abruptly after impact. With the proposed design, the optimum electrical load of the system is substantially lower compared to traditional low-frequency VEH systems. This mechanism improves the energy transfer to some transducers and electronic interfaces with low input impedances, attaining optimal efficiency.

To predict electrical generation in piezoelectric small-scale beam energy harvesting devices, it is important to have a complete mathematical model that captures the different associated phenomena. In the literature, some authors propose several alternatives of nonlinear mathematical formulations, with non-linearities coming from different physical aspects. All these formulations present good aptitudes to predict the nonlinear behavior of the system under different values of accelerations, geometry and boundary conditions. At the same time, they do not represent a unified general proposal for modeling multimodal energy harvesting devices of any type of mode generation and boundary conditions at large excitations. In this sense, this paper presents a mathematical description of inextensional nonlinear Euler-Bernoulli piezoelectric beams that combines the best contributions of the literature to the voltage generation of multimodal nonlinear piezoelectric energy harvesters (geometric, material and damping non-linearities). The developed analytical model yields a total set of N + 1 ordinary differential equations for the first N modes and for the output voltage. However, direct solution of this ordinary nonlinear differential system of N equations is computationally costly. Instead, a reduced algebraic system of 2(𝑁 + 1) algebraic equations is proposed applying the method of averaging. Its main advantage is that it makes more suitable and computationally economical for the implementation of a parameter identification process involving any number of piezoelectric inserts (unimorph or bimorph) and mode of generation (d33 or d31). Two types of validations are presented for some selected physical systems to test the validity of the assumptions: a numerical one, by the direct integration of the equations of motion and an experimental one. A final comparison between the results demonstrates the importance of the having a unified nonlinear model to predict the generated voltage in multimodal energy harvesters.

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