## 1 Introduction
[16] introduced two piezoelectric microactuator devices that were fine-tuned for in-plane displacement using finite element technique simulations. Their research focused on optimizing actuation efficiency by conducting a comparative analysis of low-stiffness and high-stiffness actuators. They showed that the low-stiffness actuator outperformed the high-stiffness actuator because of its lower stiffness coefficient and greater responsiveness to applied voltage. In a similar vein, [PERSON] et al. [17] investigated the efficiency of in-plane piezoelectric unimorph microactuators comprising several material combinations, including AlN, PVDF, and polyimide. According to their research, soft material combinations were best suited for high-displacement applications since they provided the highest displacement per volt, particularly when thinner substrates were utilized. Piezoelectric energy harvesting devices were thoroughly analyzed by [PERSON] [18], who highlighted the possibility of nonlinear dynamics and material improvement to improve energy capture efficiency in low-frequency situations. Electromagnetic energy harvesting is efficient for extracting energy from low-frequency vibrations and utilizes the movement between a magnet and a coil to generate an electric current, according to [PERSON]'s Law of Electromagnetic Induction [19; 20; 21; 22]. [PERSON] et al. [23] created a prototype device that captures electromagnetic energy. The device consists of a vibrating beam with a permanent magnet. Their findings demonstrated that these systems could provide a significant amount of power with which to operate low-power sensors and wireless devices. This highlights the significance of adjusting the damping factor to achieve the highest possible energy conversion efficiency. [PERSON] et al. [24] conducted a comprehensive review of inerter-based vibration isolation systems, highlighting their applications across various fields such as automotive, civil, and ocean engineering. They particularly focused on the advantages of using inerters for both vibration suppression and energy harvesting, providing insight into the mechanical network's analogy to electrical systems and demonstrating the potential of inerters to improve system performance and reduce complexity. Electrostatic energy harvesting utilizes the movement between conducting surfaces and changes in capacitance to produce electrical energy. This technology's compatibility with microfabrication processes makes it extremely appropriate for MEMS applications [25; 26; 27]. [PERSON] et al. [28] introduced an electrostatic converter that transforms vibrations into electricity utilizing capacitors with adjustable capacitance. Their research demonstrated the practical application of these converters in settings with low frequency. It also explored the possibility of using other dielectric materials to improve the efficiency of these energy harvesters. Hybrid energy harvesters utilize multiple transduction processes to enhance energy conversion efficiency and expand the range of frequencies at which they may operate. These technologies are especially beneficial in circumstances where the attributes of surrounding vibrations exhibit substantial variations [29; 30; 31; 32]. [PERSON] et al. [33] created a hybrid energy harvester that combines piezoelectric and electromagnetic transduction methods. Their empirical findings demonstrated that the hybrid system had superior power generation capabilities when compared to individual harvesters, particularly in situations characterized by a diverse array of vibration frequencies. [PERSON] et al. [34] introduced a hybrid harvester that combines piezoelectric and electrostatic processes. Their research revealed that the hybrid method has the potential to greatly improve energy conversion efficiency and deliver a more consistent power output in different vibratory conditions. Numerical simulations and finite element method (FEM) evaluations are essential tools for optimizing the design and enhancing the performance of energy harvesters.