In this paper, an energy harvesting model based on a portal frame structure, modeled as a duffing system, with a non-ideal excitation force, DC motor with an unbalanced mass, is presented and the piezoelectric coupling is designed to exhibit nonlinear characteristics. Nonlinearity included provides higher power output over a wide frequency range. This analysis was carried out by numerical simulation of the proposed mathematical formulation. Thus, the bifurcation diagram and the largest Lyapunov exponents are plotted to investigate the dynamic behavior by ranging the voltage applied to the DC motor. In this way, power harvesting is analyzed for two different dynamic responses: periodic and chaotic behavior. Furthermore, this work exhibits an application of frequency-domain techniques, such as short-time Fourier transform, continuous wavelet transform, synchrosqueezed wavelet transform, and Wigner-Ville distribution methods. These methods are often used to analyze non-stationary signals, allowing the verification of dynamic behavior and power harvesting. Therefore, this paper aims to apply the time-frequency methods, mentioned previously, to analyze the mechanical system response in different behaviors.

中文翻译：

---

能量收集模型中非线性动力学和混沌分析的时频方法比较

在本文中，提出了一种基于门式框架结构的能量收集模型，建模为达芬系统，具有非理想激振力，具有不平衡质量的直流电机，压电耦合设计为具有非线性特性。包含的非线性可在较宽的频率范围内提供更高的功率输出。该分析是通过所提出的数学公式的数值模拟来进行的。因此，绘制了分岔图和最大的李雅普诺夫指数，以通过调整施加到直流电机的电压来研究动态行为。通过这种方式，可以针对两种不同的动态响应分析功率收集：周期性行为和混沌行为。此外，这项工作展示了频域技术的应用，例如短时傅立叶变换，连续小波变换、同步压缩小波变换和 Wigner-Ville 分布方法。这些方法通常用于分析非平稳信号，从而可以验证动态行为和功率收集。因此，本文旨在应用前面提到的时频方法来分析不同行为下的机械系统响应。