Amplitude Of External Excitation Research Articles

Study of vibration suppression and energy harvesting for a Vibration-based Piezoelectric–Electromagnetic energy harvester with nonlinear energy sink

Vibration-based energy harvesting devices are prone to excessive displacement response. The effective vibration suppression is critical to the longevity and safety of energy harvesting systems. In this work, the vibration-based Piezoelectric–Electromagnetic energy harvester with nonlinear energy sink (NES-VBPEEH) is proposed to achieve the dual efficacy goals of vibration suppression and vibration energy harvesting. The electromechanical-coupled distributed governing equations are derived through Hamilton’s principle, Euler’s Bernoulli theory, Gauss’s law and Faraday’s law of electromagnetic induction. The output performances of the degradation model of the NES-VBPEEH are validated by previous work. Parameter analysis indicates that the external resistance of the piezoelectric energy harvester significantly affects the electrical damping of the system and ultimately affects the output response of the NES-VBPEEH. The external resistance and coil turns of the electromagnetic vibration energy harvester can significantly affect the output response of the NES-VBPEEH. The output power of both types of energy harvesters is maximized with respect to the resistance and the coil turns. The output response of the NES-VBPEEH exhibits certain nonlinear characteristics as the external excitation amplitude increases to a certain value. The damping and nonlinear stiffness of the NES can significantly affect the output power of the NES-VBPEEH, and appropriate parameter selection can help to achieve the dual efficacy goals of vibration suppression and vibration energy harvesting for the energy harvester.

Nonlinear dynamic analysis of a spring coupled double beam based piezoelectric energy harvester under parametric base excitation

This paper proposes a base excited, spring coupled double cantilever beam with attached tip mass based piezoelectric energy harvester. The dimensions of the beams are so chosen that the system experiences 1:1 internal resonance. The governing coupled electro-mechanical equations of motion of the system are obtained by using the Lagrange principle which is reduced to the temporal form by using generalized Galerkin’s method. The governing temporal equations of motion are in the form of that of a parametrically excited coupled system with geometric and inertial nonlinearities. These nonlinear equations are solved using the method of multiple scales and the results are compared with those solved by numerical method (4th order Runge Kutta method) for principal parametric resonance conditions. Parametric studies are conducted by varying the tip masses of the beams, coupled spring stiffness, load resistance, external excitation frequency and excitation amplitude. Results show that by introducing spring coupling, the system operational frequency range increases significantly and also energy transfer process takes place due to the internal resonance. Significant enhancement of voltage and power are observed in the present work in comparison to the earlier studied equivalent single beam-based energy harvester.

Design and experimental investigation of a positive feedback magnetic-coupled piezoelectric energy harvester

A positive feedback magnetic-coupled piezoelectric energy harvester (PFM) is proposed to address the limitations of current piezoelectric energy collectors, including restricted acquisition direction, limited acquisition bandwidth, and low energy output. Firstly, the dynamic theoretical model of the energy harvester was established, and the optimization factors were explored, providing a solid theoretical foundation for subsequent research endeavors. The energy capture characteristics of rectangular beam and compound trapezoidal beam were compared through finite element simulation analysis. Subsequently, an experimental platform was constructed and an optimized experimental methodology was devised to analyze the energy capture characteristics and enhance the performance of the energy harvester. The results demonstrate that the positive feedback magnetic-coupled PFM with a trapezoidal beam exhibits superior energy capture efficiency. Furthermore, it is observed that the optimized energy harvester possesses wide frequency coverage, multi-directional capabilities, low-frequency adaptability, and facilitates easy vibration. When the 45 kΩ resistor is connected in series and subjected to a longitudinal external excitation amplitude of 0.5 g, it is capable of generating an average voltage and power output of 4.20 V and 0.39 mW respectively at a vibration frequency of 9 Hz. Similarly, when exposed to a transverse external excitation amplitude of 1 g, it can produce an average voltage output of 6.2 V and power output of 0.85 mW at a vibration frequency of 19 Hz. When the inclination angle of the energy harvester is set to 35 degrees, the maximum voltage output occurs at a frequency of 18 Hz and the Z-axis to X-axis force ratio of the energy harvester is 1.428. These research findings can serve as valuable references for piezoelectric energy harvesting applications in self-powered microelectronic systems.

Nonlinear vibrations of porous-hyperelastic cylindrical shell under harmonic force using harmonic balance and pseudo-arc length continuation methods

The resonant responses are investigated for the porous-hyperelastic Mooney–Rivlin cylindrical shell subjected to a radial harmonic excitation. Considering the higher-order shear deformation theory (HSDT), fourth-order strain-displacement relations are derived, which include the radial geometric imperfections varying along the thickness direction. Using the porous-hyperelastic Mooney–Rivlin constitution relation and Lagrange equation, the differential governing equations of motion are obtained for the porous-hyperelastic cylindrical shells. The resonant conditions are presented and the accuracy of the mathematical models is verified. The harmonic balance and pseudo-arc length continuation methods are used to obtain the amplitude-frequency and forced-amplitude curves. The stability of the solutions is analyzed by Floquet theory. The effects of the external excitation amplitudes, structure parameters and porosity infill parameters on the linear frequencies, amplitude-frequency responses and force-amplitude responses are discussed for the imperfect porous-hyperelastic cylindrical shells. The results show that the linear frequencies of the porous-hyperelastic cylindrical shells increase obviously as the uniform and sigmoid function porosity parameters reach the certain values. The increase of the structure parameters enhances the response amplitudes of the first-order mode and minified response amplitudes of the second-order mode. The decreasing porosity ratios weaken the softening nonlinear behaviors of the porous-hyperelastic cylindrical shells. With the changes of the external excitation amplitudes and structure parameters, the motion of the porous-hyperelastic cylindrical shell indicates that the synchronous vibrations occur with the period and chaotic vibrations alternately.

Energy harvesting from low-frequency vibrations of hanger using PVDF: An experimental study and performance analysis

Piezoelectric energy harvesters (PEH) are widely used to collect piezoelectric energy. However, adapting to different engineering application environments is difficult for traditional PEHs. To improve the engineering application value of PEH, a hanger piezoelectric energy harvester (HPEH) based on low frequency vibration of hanger is proposed in this paper. A dynamic electromechanical coupling model was established for hanger structure, and the effects of the external load resistance, the polyvinylidene fluoride (PVDF) piezoelectric film installation location, the stability of the PVDF piezoelectric film with different winding methods, and the external excitation amplitude on the energy output performance of the HPEH were studied. Results indicate that the optimal load resistance of the HPEH studied in this paper is 1.0 MΩ; the PVDF piezoelectric film location has a significant impact on the performance of the HPEH, and the output power is highest at hanger Lc/4; the PVDF piezoelectric films during ring winding is better than those in spiral winding for the same external cycle excitation; in the external excitation amplitude range of 2d–6d (d: hanger diameter), appropriately increasing the external excitation amplitude is conducive to improving the output voltage of the HPEH, with the root mean square voltage increasing by 95.11 % at external excitation amplitude A = 6d compared with that at the initial excitation amplitude. It provides an innovative solution for the field of cable structures and new energy sources, and the further research and application of this technology is expected to have a profound impact in the field of energy sustainability and engineering technology.

Nonlinear combined resonance of axially moving conical shells under interaction between transverse and parametric modes

The purpose of present paper is to establish a conical shell model for exploring combined resonance response of axially moving graphene platelets reinforced metal foams (GPLRMF) conical shells subjected to coupled external and parametric excitations in thermal environments. The Reddy's higher order shear deformation theory (HSDT) is applied to derive the stress-strain relationship, and the governing equations of the shell structure are obtained using Hamilton's principle. The displacements and boundary conditions are characterized by a set of displacement shape functions with orthogonal properties. Then, the combined resonant for the conical shell are solved, where the method of varying amplitude (MVA) is adopted for discretizing and formulating the nonlinear governing motion equations. The correctness of the steady-state approximate solutions is verified by conducting comparative analysis, where the existing valuable literature is served as reference. In addition, the effects of initial phase angle, damping interference, material property, axially moving velocity, temperature change, coning angle as well as external excitation amplitude on the vibrational mechanism are analyzed, and the jumping phenomenon, bifurcation behavior, and chaotic characteristics are discussed in detail.

Numerical study of liquid sloshing using smoothed particle hydrodynamics with adaptive spatial resolution

Liquid sloshing is a typical problem of free surface flow in a number of engineering applications. The efficient simulation of liquid sloshing, particularly the large deformation and breakup of free surface, is a challenge for numerical methods. This paper presents a numerical method based on smoothed particle hydrodynamics with adaptive spatial resolution (SPH-ASR) for liquid sloshing. The SPH-ASR method can adaptively adjust the spatial resolution based on the distance to the free surface and the moving boundary. The numerical method was validated against experimental results from literature. Then the SPH-ASR method was applied to study the liquid sloshing problem in a prismatic tank and a rectangular tank. The effects of liquid fill level, external excitation frequency and amplitude on liquid sloshing were investigated. The pressure at different points on the tank wall and the total moment on the rotating shaft of the tank were compared and analyzed.

Combined resonance of graphene platelets reinforced metal foams cylindrical shells with spinning motion under nonlinear forced vibration

The recent studies on dynamical behavior of spinning cylindrical shells are mainly concerned on the principal and internal resonances, however, there is a lack of study on coupled resonance of spinning graphene platelets reinforced metal foams (GPLRMF) cylindrical shells. To remedy this defect, the present work attempts to investigate the combined resonances of spinning cylindrical shells under multi-source excitations. Considering Reddy's higher order shear deformation theory (HSDT), the highly dimensional nonlinear governing motion equations is derived and then discretized through Galerkin truncation. Afterwards, the method of varying amplitudes (MVA) is applied to obtain the steady-state approximate solution, in which the jump phenomenon and bifurcation behavior are discussed. Additionally, the dynamic model is confirmed via comparing with existing literature. Eventually, numerical analyses indicate the internal stable/unstable loops may appear unexpectedly, and the existence of the loop mainly depends on the variations of initial phase angle, external excitation amplitude, damping coefficient and so on. In addition, the amplitude frequency response curve of nonlinear vibration can be adjusted and supported through parametric resonance, and different from internal resonance, the multi-jump phenomenon of combined resonance will take place in the spinning cylindrical shells.

Quasi-periodic oscillation characteristics of a nonlinear energy sink system under harmonic excitation

Quasi-periodic oscillation characteristics of a nonlinear energy sink (NES) system under harmonic excitation are studied in this work. It is found that there exist uniformly distributed sidebands in frequency spectra of quasi-periodic oscillations. The traditional incremental harmonic balance (IHB) method and the IHB method with two time-scales are used to obtain accurate frequency components and amplitudes of periodic responses and two different quasi-periodic oscillations of the system, respectively, with variations of the external excitation frequency and amplitude. The two different quasi-periodic oscillation characteristics are analyzed; energy absorption of the NES system under different excitation frequencies and amplitudes is also analyzed. Stability of quasi-periodic solutions obtained from the IHB method with two time-scales is analyzed by the Floquet theory. Analytical results obtained from the traditional IHB method and the IHB method with two time-scales agree very well with those from numerical integration using the fourth-order Runge–Kutta method. Results show that the efficiency of energy absorption of a strongly quasi-periodic oscillation is greater than those of a periodic response and a weakly quasi-periodic oscillation.

Analysis on the symmetric fast-slow behaviors in a van der Pol-Duffing-Jerk oscillator

The study of bursting oscillations induced by frequency-domain multiscale effect is one of the key scientific issues in the theoretical analysis of circuit systems. In this paper, we explore the mechanism of the bursting oscillations of a van der Pol-Duffing-Jerk circuit oscillator with slow-changing parametric and external periodic excitations. Three typical bursting modes, namely, left-right symmetric ‘subHopf/fold limit cycle’ bursting, origin symmetric ‘fold/fold limit cycle’ bursting and origin symmetric ‘fold/subHopf/fold limit cycle’ bursting, are presented. The slowly changing excitation is treated as a generalized state variable to analyze the influence on the critical manifolds of the equilibria and bifurcations. The critical conditions of fold and Hopf bifurcations are computed by using the bifurcation theory, and two typical bifurcation structures are obtained according to the position of different bifurcation curves. Based on the bifurcation analysis, we investigate the appearance and dynamicalal evolutions of the different bursting oscillations with the variation of the external excitation amplitude. It is pointed that not only the bifurcation structures but also the distance between the fold and Hopf bifurcation points can affect the bursting patterns. We find the directions of the trajectories and the bursting types are sensitive to the values of the external excitation amplitude. Furthermore, we reveal the mechanism of the bursting oscillations by overlapping the trajectories on (θ, x)-plane onto the corresponding bifurcation structures. Numerical simulations are also presented to prove the correctness of the theoretical analysis in our study.

Design optimization of sloshing tank using weakly compressible mesh free model

The sloshing effects from baffle and non-baffled water tank was investigated under different external excitation frequencies and amplitudes. It was simulated and analyzed using the Weakly Compressible Moving Particle Explicit (WCMPE) method under condition of high-precision simulation data. The effects from different baffle configuration, external excitation frequency and amplitude, and the behaviour of liquid sloshing were analyzed through the conversion of simulated data and images. The results showed that half-proportional baffles resulted in a highly complex water motion, which resulted in the damping of the liquid slosh. On the other hand, the sloshing of the water in the tank at non-natural frequency resulted in mutual cancellation of the particle velocities. With greater understanding of the sloshing and damping effects, the use of half-scale baffle and liquid depth at different position were further examined. Three case scenarios were simulated and analyzed. First, the length of the baffle was kept constant with gradual lifting of the baffle from the bottom of the tank until it protrudes the water surface. Secondly, the length of the baffle was gradually increased from bottom of tank until it protrudes above the water surface to explore the optimal damping effect. Lastly, the top of the baffle is situated immediately below the water surface. Determination of the optimal ratio of baffle length and liquid depth was completed from the three hypothetical case studies.

Toward self-powered integrated smart packaging system − Desiccant-based triboelectric nanogenerators

Smart packaging plays a crucial role in safeguarding products, monitoring their quality, and ensuring supply chain efficiency during distribution and transportation. However, the extensive use of sensors in smart packaging systems requires a sustainable power supply for long-term monitoring. Unfortunately, portable batteries may not meet the needs for next-generation smart packaging as they have a limited lifetime, are heavy, and may cause environmental pollution after use. To address this issue, we propose a self-powered integrated smart packaging system driven by a novel desiccant-based triboelectric nanogenerator (D-TENG). The D-TENG is designed using a contact-separation mode and includes a paperboard-based honeycomb frame, two PTFE/Cu triboelectric layers, and desiccants stored in the honeycomb holes as the freestanding triboelectric material. We systematically investigate the significant parameters affecting the energy harvesting performance of the D-TENG, including the type of desiccants, frame height, number of honeycomb holes, frequency and amplitude of external excitation, and device orientation with the vibration direction. Furthermore, we demonstrate a self-powered integrated smart packaging system based on the D-TENGs that harvests vibration energy to power sensors integrated into the package. This research provides a practical strategy to continuously monitor the status and quality of packaged products throughout the supply chain for an extended period, reducing food waste and ensuring a complete record of logistics history in vaccine delivery.

Nonlinear resonant responses of hyperelastic cylindrical shells with initial geometric imperfections

The resonant responses of the hyperelastic cylindrical shell with the initial geometric imperfections are investigated by considering both geometric and material nonlinearities. The hyperelastic cylindrical shell is subjected a radial harmonic excitation. Based on Donnell's theory, hyperelastic constitutive relations and Lagrange equation, the differential governing equations of motion are derived for the hyperelastic cylindrical shell with the initial geometric imperfections. Using the multiple scale method, the perturbation analysis for the governing equations of motion is conducted under the 2:1 internal resonance condition. The amplitude-frequency and force-amplitude response curves are obtained for the hyperelastic cylindrical shell. The effect of different parameters on the linear frequencies, amplitude-frequency response curves, force-amplitude response curves and chaotic responses of the hyperelastic cylindrical shell are discussed. The numerical results indicate that the existence of the geometric imperfections leads to the increase of the linear frequencies of the hyperelastic cylindrical shell. The amplitude-frequency response curves have the typical double-jumping phenomena and the response amplitudes increase with the increase of the external excitation amplitudes. The imperfection amplitudes, imperfection forms and structure parameters have the obvious influences on the resonant peaks evolutions. The vibrations of the first-order and second-order modes have the synchronization phenomena. With the changes of the parameters, the dynamic responses of the hyperelastic cylindrical shell with the imperfections change the period to chaotic vibrations alternately.

Three-dimensional mapping analysis of a capsule system with bilateral elastic constraints

The three-dimensional mapping of the capsule system with bilateral elastic constraints is studied, which is rarely seen in the literature at present. The bilaterally constrained elastic system is suitable for small-scale capsule models. Compared with the unilaterally constrained elastic capsule system, the bilaterally constrained elastic system has a more complex switching mechanism on the boundary, a larger number of local mappings, and a richer whole motion process and bifurcation. The detailed analysis of the bilaterally constrained elastic capsule models can provide more effective theoretical support for the practical application of small-scale capsule models. In this paper, the local dynamics of non-smooth boundaries caused by dry friction and contact and global dynamics in a bilaterally constrained elastic capsule system are analyzed. By considering the vector fields near the boundary surfaces and boundary lines, we get the switching mechanisms on the boundary surfaces and boundary lines and find all possible local mappings. Under the guidance of theoretical analysis, we obtain the sliding bifurcations and boundary-intersection crossing bifurcations by changing the external excitation amplitude. The numerical simulation shows that the bifurcation points and the change of the motion state before and after the bifurcation are consistent with the theoretical results, indicating that this analysis method can be used to accurately discuss the dynamic behaviors of the bilaterally constrained elastic capsule system and mappings can express the dynamic behaviors.

The dynamic regimes and the energy harvesting of the energy harvester based on the bistable piezoelectric composite laminate

The dynamic regimes and the energy harvesting of the bistable energy harvester based on the bistable piezoelectric composite laminate are elaborated here. To identify the all-around dynamic regimes and assess the bistable energy harvesting performance, the forward frequency sweep, the reverse frequency sweep and the resistance sweep are conducted. The peak-to-peak frequency–amplitude response curves on the displacement and the voltage output are graphically presented. The single-well vibration, the limit cycle oscillations, the intermittency between the limit cycle oscillations and the chaotic snapthrough, the intermittency between the multiple periods snapthrough and the chaotic snapthrough, the multiple periods snapthrough and the chaotic snapthrough are elaborated by the Time history diagram, the Phase diagram and the Poincare map. The dynamic regimes are graphically presented delivering the stability zone for the dynamic responses and the optimal region for the energy harvesting. The RMS power output and the Max voltage output are checked to be the value judgements. Due to the softening nonlinear effect and the hysteresis, the conspicuous biases between the forward and reverse frequency sweeps are found to exist illustrating that the limit cycle oscillations expand the bandwidth of the double-well regimes during the reverse frequency sweep. From the perspective of the energy harvesting capacity, the limit cycle oscillations are demonstrated to be optimal, the double-well responses generally outperform the single-well responses concerning the off-resonance and the single-well responses concerning the primary resonance around the reduced modal frequency may outperform the double-well responses except the limit cycle oscillations. The load resistance is crucial to the power generation performance and needs optimizing with the change of the external excitation. The load resistance, the external excitation amplitude and frequency are interrelated and can be optimized simultaneously for the maximum power generation efficiency.

Experimental investigation on acoustic emission in fretting friction and wear of bolted joints

Fretting between bolted interfaces may change the dynamic characteristics of structures under vibration loading. The acoustic emission (AE) technique has been successfully used to investigate friction and wear mechanisms between different kinds of contact pairs. This paper experimentally investigates the AE signals of a bolted joint structure during friction and long-time fretting wear to explore the relationship between AE characteristics and interface fretting behaviors. A test apparatus dedicated to the study of fretting behaviors of bolted joints together with an AE acquisition system is used to carry out the experimental tests. Relative displacement, tangential friction force and the related AE waveform features are obtained simultaneously to better relate acoustic emission signals with hysteresis loops. The effects of external excitation amplitude and fretting wear cycles are investigated. The frequency signatures of the individual burst acoustic emission event under different excitation amplitudes and wear stages are analyzed. Results show that AE events mainly occur in the micro-slip and the gross-slip regime, and AE technique is more sensitive to the transition point from micro-slip to gross-slip regime. As the external excitation amplitude increases, the value of most AE parameters is gradually increased. As the fretting wear cycles increase, evolutions of bolt preload, frictional coefficients, and AE parameters first show a significant change and then become asymptotically stable. Furthermore, the frequency intensity and range will increase with the increase of excitation amplitude and decrease with the wear cycles.

Effects of longitudinal excitation on liquid hydrogen sloshing in spacecraft storage tanks under microgravity conditions

Based on the real physical model and operating environment of the spacecraft tank, the numerical model of the tank is established and the sloshing behavior of liquid hydrogen in the tank under different longitudinal excitations is studied in this work. The Realizable k- ε model is used to predict the fluid turbulence, and the mixture model is used to analyze the phase transitions and flows. The harmonic external excitation is loaded by the user-defined function (UDF). Based on the CFD sloshing model verified through comparison with experimental results, the influences of different longitudinal external excitation frequencies and amplitudes on the liquid hydrogen volume fraction in the tank are firstly analyzed. On this basis, including pressure and other physical quantities of the monitoring points and whole internal fluid domain during the sloshing simulation process are studied quantitatively. In addition, the relationship between the carrier amplitude of the sloshing curves and the external excitation amplitude is discussed. The simulation results show that in microgravity environment, compared with large amplitude excitation, high-frequency longitudinal harmonic excitation has a significant effect on the variation of physical parameters in the tank, which may become a negative factor for the safety of liquid hydrogen storage and supply systems. Meanwhile, the traditional baffle design has a limited influence on the liquid hydrogen motion under the high-frequency longitudinal excitation which may occur during the spacecraft changing load process. The results provide valuable information for the understanding of sloshing behavior and safety evaluation of the tank under longitudinal excitation.

Dynamic characteristic analysis of beam structures with nonlinear elastic foundations and boundaries

The research of structures with elastic foundations has attracted extensive attention and many dynamic modeling and analysis methods for beam structures with elastic foundations have been proposed in current mainstream research. However, the low-dimension and high-accuracy models are more in line with the requirements of engineering practice. Hence, this paper aims to establish a novel nonlinear dynamic model of beam structures with nonlinear elastic foundations and boundaries. The global modes are first obtained by using the global mode method, and the forced vibration response analysis of the beam structures is subsequently carried out by developing a corresponding solving procedure. Thereafter, case studies are conducted on a cantilever beam with nonlinear elastic foundations and boundaries to validate the established nonlinear dynamic model. The consistency of the results obtained by the established model and finite element analysis demonstrates the accuracy of the established model. Finally, the effects of elastic foundations, boundaries, external excitation amplitude and nonlinear coupling terms on the dynamic characteristics of the cantilever beam structure are analyzed through the comparative case studies.

P-bifurcation phenomena of the non-smooth modified rayleigh-duffing oscillator under the combined action of harmonic excitation and noise perturbation

In this paper, the stochastic dynamics of a modified Rayleigh-Duffing oscillator with Coulomb frictional damping and elastic impact is investigated under combined harmonic and noise excitations. On the premise of retaining the non-smooth properties, a non-smooth steady-state probability density response numerical calculation method is introduced by taking advantage of Markov process. Utilizing this method, the stochastic P-bifurcation phenomena of oscillators without and with externally excitation are discussed in detail by inscribing changes in the topology of the steady-state probability density function. It is displayed that certain nonlinear damping coefficient and external excitation amplitude change the structure of the response, and that both the friction coefficient and the elastic coefficient of the contact surface induce stochastic P-bifurcation phenomena in systems without and with harmonic excitation, respectively. This study reveals the effect of non-smooth factors on the stability of the Rayleigh-Duffing oscillator.

On the Stability of the van der Pol-Mathieu-Duffing Oscillator under the Effect of Fast Harmonic Excitation

This paper aims to examine the nonlinear dynamics of a van der Pol-Mathieu-Duffing oscillator under the effect of fast harmonic excitation. The governing equations of motion describing the harmonically forced oscillations of the van der-Pol-Mathieu-Duffing oscillator are expressed in terms of the second-order nonhomogeneous nonlinear ordinary differential equation with suitable initial conditions. This paper uses Krylov-Bogoliubov averaging technique for the stability analysis of the system. The frequency response curves under the effect of external excitation, damping, and nonlinearity are obtained at various resonances. Additionally, the stable and unstable regions were identified. It turns out that the damping reduces the amplitude of oscillations and squeezes the instability regions, whereas the stability region grew with the increase in the amplitude of external excitation.