# Influence of the Motion of a Spring Pendulum on Energy-Harvesting Devices
## 1 Introduction
A new flexoelectric energy harvester and broadband piezoelectric in the presence of an applied axial compressive load with an excitation base is investigated in [22], where the energy harvester operates in either a pre-torsion configuration or a post-configuration, depending on the axial load's amplitude. Moreover, a converter is used in [23] to transform the piezoelectric vibration into electricity as a power source for wireless electronics. A simple piezoelectric spring configuration depending on a standard binder clip structure is studied in [24]. The harvester consists of a spring's pendulum that converts the mass's energy into an electrical one in the piezoelectric transducer. Two degrees of freedom (DOF) mechanical model with developed glands was examined in [25] by simulating the impact behavior as linear stiffness piecewise. A new horizontal asymmetric U-shaped vibration-based PEH is presented in [26], in which the nonlinearity is combined with multimodality. [PERSON] et al. [27] examined the high-energy orbits in the piezo-magneto-elastic energy harvester theoretically and experimentally over the excitation frequencies area. A comparison between an electromagnetic PEH and a PEH with distinct interface circuits is found in [28]. Furthermore, it is shown in [29] that the effect of the backward electromechanical coupling on the mechanical vibrations of the energy harvesters can be approximated using the different values of the excitation frequency and damping coefficient. The periodic and quasi-periodic vibration of a dynamical model connected to a piezoelectric circuit was studied in [30]. The approximate solutions were obtained using the complexification-averaging method. A special EH designed system was examined asymptotically using the harmonic balance method in [31], in which the attained results are verified numerically and experimentally. In contrast, the author in [32] designed another nonlinear system that suppressed the vibration and EH at the same time. It is concluded that the starting area of resonance is the best area for suppression. The dynamical motion of a damped spring pendulum with two or three DOF in the presence of excitation forces and moments is investigated in several works, e.g., [33; 34; 35; 36; 37; 38; 39; 40]. The damped motion of a spring pendulum, in which its suspended point moves in a circular trajectory, is investigated in [33]. The authors provided a numerical example for the model's physical parameters to study the examined model's chaotic behavior. The planar motion of a linear spring-rigid-body pendulum with fixed pivot is studied in [34], and its generalization is found in [35] and [36] when the fixed point is constrained to move on an ellipse with a constant angular velocity for a linear and nonlinear spring stiffness, respectively. The authors provided other motions as additional examples in [36] for the motion of the fixed point in horizontal and vertical paths. The chaotic motion of an elastic pendulum is explored in [37], the movement of its suspension point in a circular route. It is observed that the approximated system has a bifurcation that leads to chaotic motion via a series of period-doubling bifurcations. The nonlinear motion of a double pendulum system with 3 DOF in the presence of one external force and two moments is examined in [38]. The effects of absorber motion on the 3 DOF dynamical system is studied in [39]. On the other hand, nonlinear movements of an elastic pendulum under the influence of two perpendicular excitation forces are investigated in [40]. The pivot points of the pendulums considered in [38; 39; 40] are considered to move in elliptic trajectories. The asymptotic solutions are obtained up to higher order of approximation using the approach of multiple scales (AMS). The solvability conditions and the modulation equations (ME) are achieved in line with the examined resonance cases.