Microelectromechanical system (MEMS)-based piezoelectric energy harvesting (PEH) devices can convert the mechanical vibrations of their surrounding environment into electrical energy for low-power sensors. This electrical energy is amplified when the operation resonant frequency of the PEH device matches with the vibration frequency of its surrounding environment. We present the electromechanical modeling of two MEMS-based PEH devices to transform the mechanical vibrations of domestic washing machines into electrical energy. These devices have resonant structures with a T shape, which are formed by an array of multilayer beams and a ultraviolet (UV)-resin seismic mass. The first layer is a substrate of polyethylene terephthalate (PET), the second and fourth layers are Al and Pt electrodes, and the third layer is piezoelectric material. Two different types of piezoelectric materials (ZnO and PZT-5A) are considered in the designs of PEH devices. The mechanical behavior of each PEH device is obtained using analytical models based on the Rayleigh–Ritz and Macaulay methods, as well as the Euler–Bernoulli beam theory. In addition, finite element method (FEM) models are developed to predict the electromechanical response of the PEH devices. The results of the mechanical behavior of these devices obtained with the analytical models agree well with those of the FEM models. The PEH devices of ZnO and PZT-5A can generate up to 1.97 and 1.35 µW with voltages of 545.32 and 45.10 mV, and load resistances of 151.12 and 1.5 kΩ, respectively. These PEH devices could supply power to internet of things (IoT) sensors of domestic washing machines.

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Resonators based on micro and nanoelectromechanical systems (MEMS/NEMS) are used in many applications, including biological and gas sensors, magnetic field sensors, RF switches, accelerometers, piezoelectric micro and nanogenerators, and viscosity sensors. The design of these resonators requires analytical models to predict their mechanical behavior and optimize the sensitivity and resolution. However, most of these models are only applied to resonators with rectangular and uniform cross-sections. In this paper, we present the analytical modeling to determine the first bending resonant frequency, out-of-plane deflections, and normal stresses of MEMS/NEMS-based multilayered resonators with variable cross-sections and multiple fixed supports. The proposed modeling is derived using the well-known Rayleigh and Macaulay methods, as well as the Euler-Bernoulli beam theory. This analytical modeling is applied to four multilayered resonators with different clamped supports and non-uniform cross-sections. The results of our analytical modeling agree well with respect to those of finite element method (FEM) models and experimental data reported in the literature. The proposed analytical modeling can be used to estimate the frequency shift of resonators due to variations of their geometric parameters, number of clamped-supports or mechanical properties of the materials. Furthermore, this modeling can be used to obtain optimal designs of resonators that ensure safe operations and enhanced performance for sensors and energy harvesters in telecommunications, automotive sector, aerospace industry, consumer electronics, non-destructive testing, and navigation.

Piezoelectric nanogenerators can convert energy from ambient vibrations into electrical energy. In the future, these nanogenerators could substitute conventional electrochemical batteries to supply electrical energy to consumer electronics. The optimal design of nanogenerators is fundamental in order to achieve their best electromechanical behavior. We present the analytical electromechanical modeling of a vibration-based piezoelectric nanogenerator composed of a double-clamped beam with five multilayered cross-sections. This nanogenerator design has a central seismic mass (910 μm thickness) and substrate (125 μm thickness) of polyethylene terephthalate (PET) as well as a zinc oxide film (100 nm thickness) at the bottom of each end. The zinc oxide (ZnO) films have two aluminum electrodes (100 nm thickness) through which the generated electrical energy is extracted. The analytical electromechanical modeling is based on the Rayleigh method, Euler–Bernoulli beam theory and Macaulay method. In addition, finite element method (FEM) models are developed to estimate the electromechanical behavior of the nanogenerator. These FEM models consider air damping at atmospheric pressure and optimum load resistance. The analytical modeling results agree well with respect to those of FEM models. For applications under accelerations in y-direction of 2.50 m/s2 and an optimal load resistance of 32,458 Ω, the maximum output power and output power density of the nanogenerator at resonance (119.9 Hz) are 50.44 μW and 82.36 W/m3, respectively. This nanogenerator could be used to convert the ambient mechanical vibrations into electrical energy and supply low-power consumption devices.