Heonjun Yoon

Stochastic quantification of the electric power generated by a piezoelectric energy harvester using a time-frequency analysis under non-stationary random vibrations

Vibration energy, which is widely available, can be converted into electric energy using a piezoelectric energy harvester that generates alternating current in response to applied mechanical strain. For the last decade, there has been a strong surge of interest in developing an electromechanically-coupled analytical model of a piezoelectric energy harvester. Such a model is of great importance to enable understanding of the first principle of the piezoelectric transduction and to quantify harvestable electric power under a given vibration condition. However, existing analytical models that operate under an assumption of deterministic excitations cannot deal with the random nature present in realistic vibrations, even though this randomness considerably affects the variation in harvestable electric power. Furthermore, even when random vibrations are taken into account, existing stochastic analytical models can only be applied to stationary excitations, such as in the case of white Gaussian noise. This paper thus proposes a three-step framework for stochastic quantification of the electric power generated by a piezoelectric energy harvester under non-stationary random vibrations. First, we propose estimation of the time-varying power spectral density (PSD) of the input non-stationary random vibration using a statistical time‐frequency analysis. The second step is to employ an existing electromechanical model as the linear operator for calculating the output voltage response. The final step is to estimate the time-varying PSD of the output voltage response. Following this three-step process, the expected electric power can be estimated from the autocorrelation function which is the inverse Fourier transform of the time-varying PSD of the output voltage response. The merits of the proposed framework are two-fold in that it enables: (i) quantification of the time-varying electric power generated under non-stationary random vibrations and (ii) consideration of the randomness in the design process of the energy harvester. Four case studies are used to demonstrate the effectiveness of the proposed framework.

Kirchhoff plate theory-based electromechanically-coupled analytical model considering inertia and stiffness effects of a surface-bonded piezoelectric patch

As a compact and durable design concept, piezoelectric energy harvesting skin (PEH skin) has been recently proposed for self-powered electronic device applications. This study aims to develop an electromechanically-coupled analytical model of PEH skin considering the inertia and stiffness effects of a piezoelectric patch. Based on Kirchhoff plate theory, Hamiltons principle is used to derive the electromechanically-coupled differential equation of motion. Due to the geometric discontinuity of the piezoelectric patch, the Rayleigh–Ritz method is applied to calculate the natural frequency and corresponding mode shapes. The electrical circuit equation is derived from Gausss law. Output voltage is estimated by solving the equation of motion and electrical circuit equation, simultaneously. For the purpose of evaluating the predictive capability, the results of the electromechanically-coupled analytical model are compared with those of the finite element method in a hierarchical manner. The outstanding merits of the electromechanically-coupled analytical model of PEH skin are three-fold: (1) consideration of the inertia and stiffness effects of the piezoelectric patches; (2) physical parameterization between the two-dimensional mechanical configuration and piezoelectric transduction; (3) manipulability of the twisting modes of a cantilever plate with a small aspect ratio.

Analysis of Electromechanical Performance of Energy Harvesting Skin Based on the Kirchhoff Plate Theory

As a compact and durable design concept, energy harvesting skin (EH skin), which consists of piezoelectric patches directly attached onto the surface of a vibrating structure as one embodiment, has been recently proposed. This study aims at developing an electromechanically-coupled analytical model of the EH skin so as to understand its electromechanical behavior and get physical insights about important design considerations. Based on the Kirchhoff plate theory, the Hamilton’s principle is used to derive the differential equations of motion. The Rayleigh-Ritz method is implemented to calculate the natural frequency and the corresponding mode shapes of the EH skin. The electrical circuit equation is derived by substituting the piezoelectric constitutive relation into Gauss’s law. Finally, the steady-state output voltage is obtained by solving the differential equations of motion and electrical circuit equation simultaneously. The results of the analytical model are verified by comparing those of the finite element analysis (FEA) in a hierarchical manner.Copyright

Piezoelectric Energy Harvesting Analysis Under Non-Stationary Random Vibrations

Energy harvesting (EH), which scavenges electric power from ambient, otherwise wasted, energy sources, has received considerable attention for the purpose of powering wireless sensor networks and low-power electronics. Among ambient energy sources, widely available vibration energy can be converted into electrical energy using piezoelectric materials that generate an electrical potential in response to applied mechanical stress. As a basis for designing a piezoelectric energy harvester, an analytical model should be developed to estimate electric power under a given vibration condition. Many analytical models under the assumption of the deterministic excitation cannot deal with random nature in vibration signals, although the randomness considerably affects variation in harvestable electrical energy. Thus, predictive capability of the analytical models is normally poor under random vibration signals. Such a poor power prediction is mainly caused by the variation of the dominant frequencies and their peak acceleration levels. This paper thus proposes the three-step framework of the stochastic piezoelectric energy harvesting analysis under non-stationary random vibrations. As a first step, the statistical time-frequency analysis using the Wigner-Ville spectrum was used to estimate a time-varying power spectral density (PSD) of an input random excitation. The second step is to employ an existing electromechanical model as a linear operator for calculating the output voltage response. The final step is to estimate a time-varying PSD of the output voltage response from the linear relationship. Then, the expected electric power was estimated from the autocorrelation function that is inverse Fourier transform of the time-varying PSD of the output voltage response. Therefore, the proposed framework can be used to predict the expected electric power under non-stationary random vibrations in a stochastic manner.Copyright