Nonlinear energy harvesting systems based on multibody structures constitute a promising solution for autonomous devices powered by ambient vibrations. This paper presents the modeling and control of a nonlinear energy harvester employing a double pendulum configuration and BLDC motors operating as generators. The primary objective of the study was to develop a control strategy that enables the maximization of harvested power while simultaneously improving the energy conversion efficiency during the charging of the battery supplying the target system. The developed model incorporates the mechanical equations of motion of the double pendulum, an electrical model of the BLDC motors, and two independently controlled buck-boost converters, each connected to one joint of the pendulum. In addition, a perturb-and-observe (P&O) maximum power point tracking (MPPT) algorithm was implemented, which utilizes a portion of the computational resources of the target system's microcontroller and allows for dynamic adjustment of the electrical loads seen by the generators. Simulation results obtained in the Simulink environment confirm that the application of independent power converters combined with local MPPT control leads to an increase in the total harvested power and ensures more stable battery charging under conditions of variable mechanical excitation. The obtained results demonstrate the effectiveness of the proposed approach and indicate its potential applicability in self-powered systems operating in environments characterized by irregular and stochastic vibrations.

The efficiency of vibration-based energy harvesters is often constrained by low vibration amplitudes and limited responsiveness beyond the resonant frequency. To overcome these limitations, mechanical amplifiers and spring bumpers can be employed to enhance excitation amplitude and magnet velocity within a compact device. This study presents a nonlinear oscillator supported on pre-compressed coil springs with high-stiffness bumpers acting as motion limiters. The resulting collision effects and friction introduce hysteresis, significantly influencing the system's dynamic response. An electromagnetic model with position-dependent inductance is developed, and the identified system parameters enable numerical analysis of energy recovery and dynamic behaviour. Selected numerical predictions are compared with experimental observations, demonstrating the model's effectiveness.

The hinged – hinged beam with additional moments of inertia at the ends was modelled by finite element method. In the analysis, distribution of hinge's masses were taken into account. The beam was made of unidirectional pre-impregnate with a matrix of thermosetting epoxy resin reinforced with high-strength R-type glass fibres. For manufacturing the composite structures of selected layers arrangement, the autoclave technique was applied. The symmetrical and asymmetrical fibre configurations were analysed in layers configuration $+\alpha(5)/0/+\alpha(5)$ and $+\alpha(5)/0/-\alpha(5)$, where alpha is the angle of fibres orientation related to the axis of the beam. The considered boundary conditions lead to the nonlinear dynamic response in the vicinity of the primary resonance zones under harmonic kinematic excitation generated in the beam's plane of lower flexural stiffness. For selected fibres configurations, interactions in two orthogonal flexural (flexible and stiff) and longitudinal directions and also torsion due to beam's span responses were analysed. The numerical results were verified in the experimental investigation. The dedicated setup of the beam, which allows changing the boundary conditions (masses and inertia of the handles) was manufactured and then mounted on to the electromagnetic shaker. Good agreement in the numerical and experimental results was achieved. The influence of the fibres configuration on nonlinear behaviour of the structures was observed.

This paper presents a two-degrees-of-freedom system to describe the dynamics and behaviour of a vehicle driving on a road profile. It represents a simplified approximation of a quarter-car system, where the kinematical excitation is sourced from road roughness profiles. The description is provided using analytical and numerical approaches. Eliminating undesirable vibrations in an automobile is crucial for ensuring ride comfort and passenger safety. One of the most effective solutions is implementing vibration dampers, which play a key role in reducing the transmission of unwanted vibrations to the vehicle's body. Vibration dampers, as components of the suspension system, absorb energy from vibrations generated by road surface irregularities or other dynamic factors such as acceleration, braking, or steering maneuvers. With appropriately tuned damping characteristics, they effectively minimize vibration amplitudes and prevent their transmission to the vehicle body and interior. As a result, dampers not only enhance the vehicle stability and improve the tire-road contact but also reduce noise levels and vibrations perceived by passengers. The use of advanced dampers, such as shock absorbers with adaptive damping characteristics, further enables dynamic adjustment of their performance to current driving conditions. This allows for even more effective elimination of undesirable vibrations, translating into a higher level of comfort and increased durability of the suspension system and other vehicle components. This paper discusses the anti-resonance phenomenon that occurs when appropriate dampers and spring characteristics are introduced into the model. The results demonstrate the advantages of applying such dampers to avoid damaging conditions for the suspension during operation.

This article presents a comprehensive analysis of the energy efficiency and dynamics of a nonlinear magnetic rolling pendulum (MRP). The pendulum consists of a rolling magnet on a cylindrical track, suitably positioned bumpers, and coils, which allow for virtually any configuration. In this study, we determine the magnetic interactions in the system using (Finite Element Method) FEM to determine the characteristics of the force change over the entire range of pendulum movement. The design we propose has features that allow for the analysis of systems with one, two, and three wells, depending on the configuration of the magnetic bumpers. Then, we create a dimensionless mathematical model, which is verified on a laboratory stand by testing a prototype pendulum for selected excitation characteristics. The system’s displacement and voltage output responses are analyzed using nonlinear dynamics tools. For the analysis, we use tools such as bifurcation diagrams, Lyapunov exponents, Poincaré sections, and the amplitude frequency spectra. This allowed for the identification of periodic and chaotic solutions and transient chaos in the system for more than 1000 analyzed configurations. The impact of individual settings on energy efficiency is determined based on the author’s fill factor for the power value in a wide range of excitation parameters. The advantage of the proposed system for harvesting energy from mechanical vibrations, despite its apparent simplicity, is the possibility of many different configurations in terms of dynamics and efficiency, only by simple construction changes. We have shown that for the configurations considered, up to 15 mW of (Root Mean Square) RMS power and 20 mW of peak power is achieveable. The results demonstrate that the harvester maintains high efficiency even at low excitation levels, highlighting its potential for engineering applications.

Dynamical response of a double pendulum is studied and reported in this manuscript. The double pendulum system was innovated with a limiter (stopper) on the first pendulum, such that the rotation of the first pendulum is limited. The special focus is kept on the oscillations and rotations of the second element of the pendulum system. A simplified point mass model of the double pendulum system with the amplitude limiter on the first element of the pendulum is reported with harmonic horizontal excitation. Finally, the energy transfer to a twist damper is considered to show the possibility of energy harvesting. For relatively low frequencies, the results indicate resonance of the pendulum motion induced by the impact. In the higher frequency limit, we observe a good performance in the initial phase of motion. However, it is changed after transient time leading to the synchronized motion of the two elements of the pendulum system with fairly small amplitudes. We claim that the advantage of such a nonlinear structure with impact is related to the amplitude amplification mechanism designed in the first element of the pendulum system.

In the paper, an innovative system for energy harvesting is presented, based on a magnetic pendulum. The proposed system is characterized by nonlinear behaviour that depends on the initial conditions of vibration. The appearance of nonlinearities can provide a broadened bandwidth at resonance zones for energy harvesting. Usually the second resonance manifests a low output harvested electric energy in mechanical systems compared to a main resonance zone. In this work, the system is proposed, which provides high output parameters for energy harvesting in both primary and secondary resonance zones. The magnetic pendulum focuses on converting mechanical energy into electrical energy by utilizing a subsystem based on coils. The main concept of this solution involves the use of a permanent rolling magnet between two magnetic bumpers. The system provides behaviour corresponding to double solutions by sweeping up and sweeping down the excitation frequency within the first and the second resonances, and it is associated with initial conditions such as the angle of deflection and initial force of excitations. Introducing a variable distance between the bumpers of magnets, the energy harvesting efficiency is modified. Applying such a magnetic pendulum system with variable mechanical input parameters opens perspectives for effective energy harvesting in a way that can be adapted to variable environmental conditions.

Nonlinear kinetic energy harvesters are becoming more and more popular as well as advanced and efficient. This paper presents the study of the dynamics of such a system in a wide range of excitation parameters, assuming at the same time the possibility of a cyclical and smooth change of the potential function. We have designed a system that allows to obtain a wide spectrum of potential characteristics, from a single well to a three-well system, and we have analyzed its effectiveness. Next, we checked the influence of parameters characterizing the change of potential using bifurcation diagrams and their comparison with the effective voltage values. We also analyzed the behavior of the system in chaotic and periodic motion zones and presented selected sections of Poincare and Fourier amplitude-frequency spectra of chaotic solutions. The last element of the analysis was the impact of cyclic potential change on coexisting solutions. We have shown that the best effectiveness is achieved when the frequency of the external load is equal to the resonant frequency of the flexible cantilever beam and the change of potential is limited to extreme positions.

The aim of this study is to determine the effect of environmental factors in the form of UV radiation and temperature on the amplitude-frequency behaviour of polymer composites (prepregs) based on a framework of thermosetting epoxy resin reinforced with high-strength R-glass fibres. Two series of composites with different fibre arrangements were prepared. The series had fibres arranged at angles of 30°, 45°, and 60°, at symmetric and asymmetric orientations in relation to the central layer. The composites were subjected to conditioning which simulated a six-month period of use in the spring and summer in the temperate warm transitional climate of Central and Eastern Europe. An UV QUV/SPRAY/RP accelerated aging chamber manufactured by Q - Lab Corporation was used for this purpose, and UV-A 340 lamps were used to simulate daylight. In addition, varying loads caused by sudden temperature changes were simulated using the Thermal Shock Chamber T/60/V2 Weisstechnik. Conditioned samples were tested using a TIRAvib 50101 electromagnetic exciter in combination with an LMS Scadias III controller and Test.Lab software. The results of the tests, in the form of amplitude-frequency diagrams in resonance regions, indicated that certain changes occurred as a result of the conditioning, which is a new development in the area of material tests. The results shed light on the effects of environmental conditions on the stiffness characteristics of composites, causing dynamic nonlinearities when operating at resonant frequencies.

We examine the nonlinear response of two planar pendula under external and kinematic excitations, which are very relevant as paradigmatic models in nonlinear dynamics. These pendula act under the action of an additional constant torque, and are subjected to one of the following excitations: a further external periodic torque, and a vertically periodic forcing of the point of suspension. Here, we show the influence of the constant torque strength on the transition to chaotic motions of the pendulum using both Melnikov analysis and the computation of the basins of attraction. The global bifurcations are illustrated by the erosion of the corresponding basins of attraction.

We use friction to simultaneously damp and excite a pendulum system. A Froude pendulum attached to a suspension shaft is subjected to a frictional load. We investigate two types of response of the system: regular and chaotic responses, depending on the excitation frequency. A transient chaotic solution was also obtained. We identify the motions using phase portraits, Poincaré maps, and Fourier spectra. Finally, the composite multiscaled entropy was estimated for the specified cases to confirm the preliminary classification.

The external environments have significant influence on the materials, especially for its structures exposed on harmful conditions.The main goal of this work is the determination of environmental factors which influenced on the dynamical behaviour of composite structures.In the paper is discussing the effects of UV and temperature on amplitudefrequency responses of analysed material.The dynamics is experimentally tested on polymer composites based on a thermosetting matrix of epoxy resin, reinforced by high-strength R-type glass fibres.There was provided series of cantilever beam samples consisting of 11 plies layer at different stacking sequence, which secured both, symmetric (+/+) and antisymmetric (+/-) configurations of beam samples.In the experiment were applied the composite samples with fibres configuration at 30º, 45º and 60º angles.For each angel set the amplitudefrequency responses were recorded within the first three base translational resonance zones from 10Hz to 320Hz at sweep up frequencies.The experiments have been carried out on electro-dynamical shaker TIRA Vib which assured the conditions of vibration.The measurements were repeated after the conditioning processes which simulated the separate time range corresponded to two-month periods.The first test was limited directly to the beams after manufactured in autoclave system.Then the initial results of amplitudefrequency responses were compared to the next tests of the same beams but conditioned by UV lights and temperature influence.It turned out the significant differences of results are visible between the beams with symmetric and anti-symmetric fibres configurations.Additionally the dynamics of conditioned composite beams varied from each other in both cases of fibres layout.Both conditioning, UV lights and temperatures caused the resonance zones moved from the origin position, significantly changing the dynamic properties of composite structures into softening or hardening features.

Forecasting is one of the cognitive methods based on empirical knowledge supported by appropriate modeling methods that give information about the way the relations between factors and how the phenomenon under study will develop in the future. In this article, a selection is made of a suitable architecture for a predictive model for a set of data obtained during testing of the properties of polymer composites with a matrix in the form of epoxy resin with trade name L285 (Havel Composites) with H285 MGS hardener (Havel Composites), and with the addition of the physical modifier noble alumina with mass percentages of 5%, 10%, 15%, 20% and 25% for the following grain sizes: F220, F240, F280, F320, F360, respectively. In order to select the optimal architecture for the predictive model, the results of the study were tested on five types of predictive model architectures results were tested on five types of prediction model architectures, with five-fold validation, including the mean square error (MSE) metric and R2 determined for Young's modulus (Et), maximum stress (σm), maximum strain (εm) and Shore D hardness (⁰Sh). Based on the values from the forecasts and the values from the empirical studies, it was found that in 63 cases the forecast should be considered very accurate (this represents 63% of the forecasts that were compared with the experimental results), while 15 forecasts can be described as accurate (15% of the forecasts that were compared with the experimental results). In 20 cases, the MPE value indicated the classification of the forecast as acceptable. As can be seen, only for two forecasts the MPE error takes values classifying them to unacceptable forecasts (2% of forecasts generated for verifiable cases based on experimental results).

In this paper, the dynamical behavior of composite material is analyzed, including the energy harvesting effect. The composite is modeled by the Finite Element Method (FEM) and is made of pre-impregnate with a matrix of thermosetting epoxy resin reinforced with high-strength R-type glass fibers, and it is designed as a beam structure that is exposed to mechanical vibrations. The structure assumed the form of a beam with a substantially rectangular cross section. The couplings of motion occurring between mode shapes at properly selected fiber orientations are investigated. The beams with determined sets of composite layers and a coupling effect are used to recover electricity from the mechanical vibrations in the vicinity of the first resonance zone. The composite with a certain number of fiber glass layers has assumed an orientation relative to the beam axis. The new values found in this paper are the intensity of the coupling between the bending in the stiff and flexible directions of the beam for a chosen fiber layer stacking sequence. Additionally, the influence of layer configuration on the energy harvesting efficiency of the Macro-Fiber Composite (MFC) piezoelectric element is assessed.

The aim of this study was to determine the effect of a selected physical modifier with different granularity and mass percentage on the dynamics of aerospace polymer composites. The tests were carried out on samples made of certified aerospace materials used, among other purposes, for the manufacture of aircraft skin components. The hybrid composites were prepared from L285 resin, H286 hardener, GG 280T carbon fabric in twill 2/2 and alumina (Al2O3, designated as EA in this work). The manufactured composites contained alumina with grain sizes of F220, F240, F280, F320 and F360. The mass proportion of the modifier in the tested samples was 5% and 15%. The tested specimens, as cantilever beams fixed unilaterally, were subjected to kinematic excitation with defined parameters of amplitude and frequency excitation in the basic resonance zone of the structure. The results, obtained as dynamic responses, are presented in the form of amplitude–frequency characteristics. These relationships clearly indicate the variable nature of composite materials due to modifier density and grain size. The novelty of this study is the investigation of the influence of the alumina properties on system dynamics responses.

In the paper, a new 3D energy harvesting system is provided. This work discussed the Lagrange approach to derive the differential equations of motion in the case of energy harvesting systems. An electromechanical system consists of a mechanical resonator, a piezoelectric transducer and electrical circuit with the load resistor. A flexible slender rod clamped at the bottom and loaded by the tip mass is proposed as the resonator. Moving in the 3D space, it enables the system to avoid the gravitational potential barrier of the straight vertical shape in case of buckling. This paper investigates the response of the rod deflection and the root mean square power output of selected vibration mode shapes with an attached tip mass.

In this research, an analysis of polymer composite with the matrix of L285-cured hardener H286 and six reinforcement layers of carbon fabric GG 280 T was provided. It involved a comparison of the dynamical behavior responses for three cases of composite structures in the context of the presence of the mass share modifier. The samples with the addition of a physical modifier with varying mass percentages were investigated by being subjected to dynamic tests with specific parameters, i.e., constant excitation amplitude and vibration frequency in the vicinity of the base resonance zone. The analysis allowed for indicating the relationship between the composition of the prepared composites and their dynamic response via stiffness characteristics. In addition, the investigation resulted in determining the range of harmful dynamical operating conditions, which may contribute to damage to the composite structures.

The vibrations of the mechanical system in resonance areas manifest both, the risk amplitudes of device response and the relatively high efficiency of energy harvesting. In laboratory conditions to keep the relatively high energy harvesting productivity, the assumed parameters of the shakers have to be secured. Unfortunately, the technical parameters of excitation source devices are restricted by their electrical and mechanical limitations. Hence in this work, the influence of the excitation in the rigid beam direction is analyzed for the composite beam response in the perpendicular flexible direction. We modeled the beams with determined sets of composite layers, and simulated the appeared effect of perpendicular vibrations to the excitation direction. Dissimilar dynamical behavior is observed while the configurations of the layers differ. We focused on the mechanical coupling of the sets of composite beam layers to get an optimal configuration. The energy harvesting is realized by the piezo element attached to the surface of the composite beam.