## 2 Energy Conversion Mechanisms  
In the phenomenon of piezoelectricity, energy generation can occur through three conversion mechanisms: piezoelectric, electromagnetic, and electrostatic. In the case of conversion using the piezoelectric effect, a piezoelectric material can be employed in a spring system, converting kinetic energy into electrical energy through the pressure exerted by the mass on the material induced by vibrations in the system [14]. Due to the advantages of not requiring an external voltage source, allowing the use of high voltages, and providing greater electrical generation capacity, the behavior of two piezoelectric transducers was evaluated in a cantilever-free structure, which is the most used configuration due to its advantages. The most suitable mechanical mode for this type of configuration is mode 31, as it offers efficient electromechanical coupling and can generate higher mechanical deformations with a relatively low mechanical force. Additionally, this configuration is easy to construct and has a relatively low resonance frequency. A vibration-based energy harvesting system, which converts mechanical energy into electrical energy, consists of a piezoelectric transducer coupled to a cantilevered beam, modeled as a mass-spring-damper system (Figure 1a). For energy dissipation, a load resistor is employed, as depicted in Figure 1b. In the configuration where the system has a mass element fixed at the end, the objective is to reduce the resonance frequency and increase mechanical deformation. To achieve this, it is necessary for the excitation frequency to approach the natural frequency of the mechanical system, ensuring a greater deformation in the beam. Therefore, the excitation frequency should be close to the resonance frequency to achieve maximum potential generation [14; 15], as illustrated in Figure 1c. Signal conditioning circuits play a crucial role in the operation of the energy harvesting system as they are responsible for converting the alternating current (AC) signal generated by the piezoelectric transducer into direct current (DC), which is widely used by electronic devices. The goal is to maximize power generation while keeping the power consumption of these circuits as low as possible, aiming for maximum efficiency. To achieve this, two circuits will be modeled: one using a load resistor and another using a diode bridge circuit. Additionally, a comparative analysis of the LTC-3588 integrated circuit will be conducted in relation to the previous methods of extracting electrical energy and applying it to a temperature monitoring system. Table 1 presents the mechanical and electrical parameters, which will be used to determine the equivalent circuit based on the mechanical system in question. Input energy comes from the base vibration, represented by y(t), while the output energy, z(t), is the electrical energy generated through the voltage and current across the load resistor due to mechanical efforts on the piezoelectric transducer. For a single-degree-of-freedom (1-DOF) piezoelectric system with a constant excitation amplitude as a function of frequency, as illustrated in Figure 1a, the governing equations of the system are as follows:  
\[\mathrm{M\ddot{z}+c\dot{z}+Kz}=-\mathrm{M\ddot{y}-\alpha V} \tag{1}\]  
Figure 1: System models and output: system models. (**a**) Electromechanical collection system, (**b**) electric power harvesting circuit, and (**c**) system behavior at resonance. The electrical equation is as follows:  
\[\mathrm{I}=\alpha\dot{x}-\mathrm{C}_{0}\dot{V}, \tag{2}\]  
where y is the base excitation displacement, \(z=x-y\) is the relative displacement of the transducer with respect to the base, and \(I\) is the output current of the extraction circuit.