## 1 Introduction  
Piezo technology is becoming essential in a world of smart devices that require the use of vibration sensors used in consumer electronics, automotive industries, architectural design, and other sectors where their extensive range of functionality extends to areas such as safety, fitness tracking, touch-free interaction [1], structural health monitoring [2], near-surface water detection in soils [3], air quality monitoring [4], food quality control [5], and energy harvesting applications [6, 7]. With the rise of technology, piezoelectric sensors are of utmost importance for a wide range of applications, such as skin-attachable devices for health monitoring and the detection of diseases. Piezoelectricity, a physical phenomenon known for decades, is defined as certain materials' ability to produce electric signals when mechanically stressed or conversely deform in the presence of electric potential. Many materials have been used in piezoelectricity. The most popular material is the perovskite structured (Pb[Zr(x)Ti(1\(-\)x)]O3) (PZT) [8], utilized for a wide range of applications in electromechanical sensors, actuators, and transducers. The polymer structured material, poly-vinylidene fluoride (PVDF), a viable alternative to PZT in wearable or implantable devices [9, 10], is also widely used in piezoelectricity. Studying piezoelectric systems is typically performed through experiments along with analytical and numerical approaches [11]. One of the most prominent numerical techniques that is vastly used in all major engineering industries is the finite element method (FEM). FEM enables the simulation and modeling of electromechanical coupling for the great majority of complicated geometries that cannot be handled with analytical approaches since it can accommodate the complete elements of multilayered structures and approximate the genuine solution to multiphysics systems. This way has been used to study a piezoelectric bridge transducer for energy harvesters utilizing the dissipated kinetic energy from traffic loads on roadways [12]. Another study used a finite element modeling approach to investigate the effectiveness of piezoelectric energy harvesters from asphalt pavements under various loads, various temperatures, buried depths, and traffic speeds [13]. COMSOL Multiphysics, the reliable finite element modeling tool, is comprised of many \"Multiphysics\" modules and is designed for research that spans multiple disciplines. The detailed design and flexibility to select various materials built-in in the software allow scientists and engineers to simulate different research topics in different applications before manufacturing, such as microscopy probes [14; 15], toxic gas absorption [16], piezoelectric and piezoresistive pressure sensors, optimization, and comparative studies [14; 17]. COMSOL is commonly used in piezoelectricity studies for sensing and energy harvesting applications such as bridge health monitoring [18], railway tracks [19], MEMS-based piezoelectric acoustic sensors [20], and others, using different materials. [PERSON] et al. revealed the static analysis of a 10-layered PZT-5H smart structure-based cantilever beam by studying the structure deformation and deflection direction [21]. Other work proposed a multi-layer structure-based sensor to study and enhance its electromechanical behavior [22; 23]. Different materials such as Polyvinylidene fluoride (PVDF) and Polydimethylsiloxane (PDMS) are also used in different designs for different applications (at-home breath monitoring of COVID-19 virus patients [24], nanodevice development [25], and tactile sensors [26]). Many other works have also developed their research on energy harvesting proposing a variety of materials such as PFCB W14 [27], PZT-4, PZT-5A, PZT-5J, PZT-7A [28], ZnO, ZnS, BGO [26; 29].