Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink

With its complex nonlinear dynamic behavior,the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression,and has attracted a lot of attention.In this paper,an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks(NESs)for the first time.The proposed asymmetric tristable NES(ATNES)is composed of a pair of oblique springs and a vertical spring.Then,the three stable states,symmetric and asymmetric,can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique springs.The governing equations of a linear oscillator(LO)coupled with the ATNES are derived.The approximate analytical solution to the coupled system is obtained by the harmonic balance method(HBM)and verified numerically.The vibration suppression efficiency of three types of ATNES is compared.The results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady states.In addition,compared with the symmetrical tristable NES(TNES),the ATNES can effectively control smaller structural vibrations.In other words,the ATNES can effectively solve the threshold problem of TNES failure to weak excitation.Therefore,this paper reveals the vibration reduction mechanism of the ATNES,and provides a pathway to expand the effective excitation amplitude range of the NES.

A viscoelastic metamaterial beam for integrated vibration isolation and energy harvesting

Locally resonant metamaterials have low-frequency band gaps and the capability of converging vibratory energy in the band gaps at resonant cells.It has been demonstrated by several researchers that the dissipatioin of vibratory energy within the band gap can be improved by using viscoelastic materials.This paper designs an integrated viscoelastic metamaterial for energy harvesting and vibration isolation.The viscoelastic metamaterial is achieved by a viscoelastic beam periodically arrayed with spatial ball-pendulum nonlinear energy harvesters.The nonlinear resonator with an energy harvesting function is achieved by placing a free-rolling magnetic ball in a spherical cavity with an additional induction coil.The dynamic equations of viscoelastic metamaterials under transverse excitation are established,and the energy harvesting and vibration isolation characteristics within the dispersion relation of viscoelastic metamaterials are analyzed.The results show that the vibrations of the main body of the viscoelastic metamaterial beam are significantly suppressed in the frequency range of the local resonance band gap.At the same time,the elastic waves are limited in the nonlinear resonator with an energy harvesting function,which improves the energy output.Finally,an experimental platform of viscoelastic metamaterial vibration is established for validation purposes.

Output Voltage Model and Mechanical-Magnetic Design of Magnetostrictive Vibration Energy Harvester with a Rotating Up-Frequency Structure1

A vibration energy harvester can harvest vibration energy in the environment and convert it into electrical energy to power the sensors in the Internet of Things.Human walking contains high-quality vibration energy,which serves as the energy source for vibration energy harvesters due to its abundant availability,high energy conversion efficiency,and environmental friendliness.It is difficult to harvest human walking vibration due to its low frequency.Converting the low-frequency vibration of human walking into high-frequency vibration has attracted attention.In previous studies,vibration energy harvesters typically increase frequency by raising excitation frequency or inducing free vibration.When walking frequency changes,the up-frequency method of raising the excitation frequency changes the voltage frequency,resulting in the best load resistance change and reducing the output power.The up-frequency method of inducing free vibration does not increase the external excitation frequency,which has relatively low output power.This paper designs a magnetostrictive vibration energy harvester with a rotating up-frequency structure.It consists of a rotating up-frequency structure,a magnetostrictive structure,coils,and bias magnets.The main body of the rotating up-frequency structure comprises a torsion bar and a flywheel with a dumbbell-shaped hole.The magnetostrictive structure includes four magnetostrictive metal sheets spliced by Galfenol and steel sheets.The torsion bar and flywheel interact to convert low-frequency linear vibration into rotating high-frequency excitation vibration of the flywheel.The flywheel plucks the magnetostrictive metal sheet with a high excitation frequency to generate free vibration.The vibration energy harvester increases the excitation frequency while inducing free vibration,which can effectively improve the output power.To characterize the excitation vibration and free vibration,based on the theory of Euler-Bernoulli beam theory,the vibration equation of the magnetostrictive metal sheet after being excited is given.According to the classical machine-magnetic coupling model and the Jiles-Atherton physical model,the relationship between stress and magnetization strength is derived.Combined with Faraday's law of electromagnetic induction,the distributed dynamic output voltage model is established.This model can predict the output voltage at different excitation frequencies.Based on this model,the mechanical-magnetic structural parameter optimization design is carried out.The parameters of the magnetostrictive metal sheet,the bias magnet,and the rotating up-frequency structure are determined.A comprehensive experimental system is established to test the device.The peak-to-peak voltage and output voltage signal by the proposed model are compared.The average relative deviation of the peak-to-peak voltage and the output voltage signal is 4.9%and 8.2%,respectively.The experimental results show that the output power is proportional to the excitation frequency.The optimum load resistance is always 800Ωas the excitation frequency changes,simplifying the impedance-matching process.The maximum peak-to-peak voltage of the device is 58.60 V,the maximum root mean square(RMS)voltage is 9.53 V,and the maximum RMS power is 56.20 mW.The magnetostrictive vibration energy harvester with a rotating up-frequency structure solves the problem of impedance matching,which improves the output power.The proposed distributed dynamic output voltage model can effectively predict the output characteristics.This study can provide structural and theoretical guidance for up-frequency structure vibration energy harvesters for human walking vibration.

Review of the Tuned Mass Damper Inerter(TMDI)in Energy Harvesting and Vibration Control:Designs,Analysis and Applications

Tuned mass damper inerter(TMDI)is a device that couples traditional tuned mass dampers(TMD)with an inertial device.The inertial device produces resistance proportional to the relative acceleration at its two ends through its“inertial”constant.Due to its unique mechanical properties,TMDI has received widespread attention and application in the past twenty years.As different configurations are required in different practical situations,TMDI is still active in the research on vibration control and energy harvesting in structures.This paper provides a comprehensive review of the research status of TMDI.This work first examines the generation and important vibration control characteristics of TMDI.Then,the energy harvesting performance of electromagnetic tuned mass damper inerter(EM-TMDI)is discussed.This work emphasizes the formation of a passive dynamic vibration absorber by coupling traditional TMD with inertial devices.This paper also summarizes the design and implementation of optimal vibration control and energy harvesting for TMDI.Furthermore,this paper details the applications of TMDI in the fields of bridges and building engineering.Finally,this paper summarizes the necessity of research on tuned mass-damper-inertia,the challenges faced currently,and future research directions,such as control of parameters in electromagnetic energy harvesting TMDI systems and low-cost TMDI.

Dynamic analysis of a novel multilink-spring mechanism for vibration isolation and energy harvesting

Due to technical limitations,existing vibration isolation and energy harvesting(VIEH)devices have poor performance at low frequency.This paper proposes a new multilink-spring mechanism(MLSM)that can be used to solve this problem.The VIEH performance of the MLSM under harmonic excitation and Gaussian white noise was analyzed.It was found that the MLSM has good vibration isolation performance for low-frequency isolation and the frequency band can be widened by adjusting parameters to achieve a higher energy harvesting power.By comparison with two special cases,the results show that the MLSM is basically the same as the other two oscillators in terms of vibration isolation but has better energy harvesting performance under multistable characteristics.The MLSM is expected to reduce the impact of vibration on high-precision sensitive equipment in some special sites such as subways and mines,and at the same time supply power to structural health monitoring devices.

Ab initio potential energy surface and anharmonic vibration spectrum of NF_(3)^(+)

Potential energy surfaces(PESs), vibrational frequencies, and infrared spectra are calculated for NF_(3)^(+) using ab initio calculations, based on UCCSD(T)/cc-p VTZ combined with vibrational configuration interaction(VCI). Based on an iterative algorithm, the surfaces(SURF) program adds automatic points to the lattice representation of the potential function, the one-dimensional and two-dimensional PESs are calculated after reaching a convergence threshold, finally the smooth image of the potential energy surface is fitted. The PESs accurately account for the interaction between the different modes, with the mode q_(6) symmetrical stretching vibrations having the greatest effect on the potential energy change of the whole system throughout the potential energy surface shift. The anharmonic frequencies are obtained when the VCI matrix is diagonalized. Fundamental frequencies, overtones, and combination bands of NF_(3)^(+) are calculated, which generate the degenerate phenomenon between their frequencies. Finally, the calculated anharmonic frequency is used to plot the infrared spectra.Modal antisymmetric stretching ν_(5) and symmetric stretching ν_(6) exhibit a phenomenon of large-intensity borrowing. This study can provide data to support the characterization in the laboratory.

Unlocking multidirectional and broadband wind energy harvesting with triboelectric nanogenerator and vortex-induced vibration of sphere

A unique oscillating wind-driven triboelectric nanogenerator(OWTENG)based on the sphere's vortex-induced vibration(VIV)behavior is proposed in this study,which can harvest wind energy across a multitude of horizontal directions.With the Euler-Lagrange method,the coupled governing equations of the OWTENG are established and subsequently validated by experimental tests.The vibrational properties and output performance of the OWTENG for varying wind speeds are analyzed,demonstrating its effectiveness in capturing wind energy across a broad range of wind speeds(from 2.20 m/s to 8.84 m/s),and the OWTENG achieves its peak output power of 106.3μW at a wind speed of 5.72 m/s.Furthermore,the OWTENG maintains a steady output power across various wind directions within the speed range of 2.20 m/s to 7.63 m/s.Nevertheless,when the wind speed exceeds 7.63 m/s,the vibrational characteristics of the sphere shift based on the wind direction,leading to fluctuations in the OWTENG's output power.This research presents an innovative approach for designing vibrational triboelectric nanogenerators,offering valuable insights into harvesting wind energy from diverse directions and speeds.

Accurate studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of halogen molecule

This paper obtains accurate vibrational spectroscopic constants and full vibrational energy spectrum by the al- gebraic method （AM） for some electronic states of halogen diatomic molecules. Motivated by the recent success of obtaining the dissociation energies of Li2 molecule by using a new analytical formula, it further extends the formula to study the dissociation energies of halogen diatomic molecules. The results show that the AM spectrum and the theoretical dissociation energies agree well with RKR data and experimental data respectively.

Improved Calculation of Vibrational Energy Levels in F2 Molecule using the RKR Method

The potential energy curves of the ground state X2∑＋g of the fluorine molecule have been accurately reconstructed employing the Ryderg-Klein-Rees （RKR） method extrapolated by a Hulburt and Hirschfeler potential function for longer internuclear distances. Solving the corresponding radial one-dimensional Schr？dinger equation of nuclear motion yields 22 bound vibrational levels above v=0. The comparison of these theoretical levels with the experimental data yields a mean absolute deviation of about 7.6 cm^-1 over the 23 levels. The highest vibrational level energy obtained using this method is 13308.16 cm？1 and the relative deviation compared with the experimental datum of 13408.49 cm^-1 is only 0.74%. The value from our method is much closer and more accurate than the value obtained by the quantum mechanical ab initio method by Bytautas. The reported agreement of the vibrational levels and dissociation energy with experiment is contingent upon the potential energy curve of the F2 ground state.

Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting

A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule （GDQR） method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.

Low-frequency and broadband vibration energy harvester driven by mechanical impact based on layer-separated piezoelectric beam

Vibration energy harvesting is to transform the ambient mechanical energy to electricity. How to reduce the resonance frequency and improve the conversion efficiency is very important. In this paper, a layer-separated piezoelectric cantilever beam is proposed for the vibration energy harvester(VEH) for low-frequency and wide-bandwidth operation, which can transform the mechanical impact energy to electric energy. First,the electromechanical coupling equation is obtained by the Euler-Bernoulli beam theory.Based on the average method, the approximate analytical solution is derived and the voltage response is obtained. Furthermore, the physical prototype is fabricated, and the vibration experiment is conducted to validate the theoretical principle. The experimental results show that the maximum power of 0.445 μW of the layer-separated VEH is about3.11 times higher than that of the non-impact harvester when the excitation acceleration is 0.2 g. The operating frequency bandwidth can be widened by increasing the stiffness of the fundamental layer and decreasing the gap distance of the system. But the increasing of operating frequency bandwidth comes at the cost of reducing peak voltage. The theoretical simulation and the experimental results demonstrate good agreement which indicates that the proposed impact-driving VEH device has advantages for low-frequency and wide-bandwidth. The high performance provides great prospect to scavenge the vibration energy in environment.

Chatter Suppression with Ultrasonic Elliptical Vibration Based on Energy Principle

A new method is proposed to suppress chatter, in which the ultrasonic elliptical vibration is added on the cutting tool edge. It results in the fact that the rake face of tool is separated from the chip and the direction of the frictional force between the rake face and the chip is reversed in each cycle of elliptical vibration cutting. The experimental investigations show that the chatter can be suppressed effectively by adding ultrasonic elliptical vibration on the cutting tool edge. In order to make clear the reason of chatter suppression, the mechanism of chatter suppression is analyzed theoretically from the viewpoint of energy.

Modeling and power performance improvement of a piezoelectric energy harvester for low-frequency vibration environment

A novel oscillator structure, bimorph piezoelectric cantilever beam with two-stepped variable thicknesses,is proposed to improve the energy harvestingperformance of the vibration energy harvester (VEH) under low-frequency vibration environment. Firstly, the piezoelectric cantilever is segmented to obtain the energy functions based on the Euler-Bernoulli beam assumptions, and the Galerkin approach is utilized to discretize the energy functions. Applying boundary conditions and continuity conditions enforced at separation locations, the electromechanical coupled governing equations for the piezoelectric energy harvesterareintroduced by means of the Lagrange equations. Furthermore, the steady state response expressions are obtained for harmonic base excitations at arbitrary frequencies. Numerical results are computed and the effects ofthe lengths-ratio, thicknesses-ratio,end thicknessand load resistance on the output voltage, harvested power and power density are discussed. Moreover, to verify thecorrectness ofanalytical results, the finite element method (FEM)simulationis also conducted to analyze performance of the proposed VEH, where a good agreement is presented. All the results show thatthe present oscillator structureis moreefficient than the conventional uniform beam structure, specifically, for vibration energy harvesting in low-frequency environment.

Energy harvester array using piezoelectric circular diaphragm for rail vibration

Generating electric energy from mechanical vibration using a piezoelectric circular membrane array is presented in this paper.The electrical characteristics of the functional array consisted of three plates with varies tip masses are examined under dynamic conditions.With an optimal load resistor of 11 k,an output power of 21.4 m W was generated from the array in parallel connection at 150 Hz under a pre-stress of 0.8 N and a vibration acceleration of9.8 m/s2.Moreover,the broadband energy harvesting using this array still can be realized with different tip masses.Three obvious output power peaks can be obtained in a frequency spectra of 110 Hz to 260 Hz.The results show that using a piezoelectric circular diaphragm array can increase significantly the output of energy compared with the use of a single plate.And by optimizing combination of tip masses with piezoelectric elements in array,the frequency range can be tuned to meet the broadband vibration.This array may possibly be exploited to design the energy harvesting for practical applications such as future high speed rail.

Intermolecular Vibrational Energy Transfers in Melts and Solutions

Resonant and nonresonant intermolecular vibrational energy transfers in Gdm- SCN/KSCN=1/1, GdmSCN/KS^13CN=1/1 and GdmSCN/KS^13C^15N=1/1 mixed crystals in melts and in aqueous solutions are studied with the two dimensional infrared spectroscopy. The energy transfers in the samples are slower with a larger energy donor/acceptor gap, independent of the Raman spectra. The energy gap dependences of the nonresonant energy transfers cannot be described by the phonon compensation mechanism. Instead, the experi- mental energy gap dependences can be quantitatively described by the dephasing mechanism. Temperature dependences of resonant and nonresonant energy transfer rates in the melts are also consistent with the prediction of the dephasing mechanism. The series of results suggest that the dephasing mechanism can be dominant not only in solutions, but also in melts （pure liquids without solvents）, only if the molecular motions （translations and rotations） are much faster than the nonresonant energy transfer processes.

Influence of explosion parameters on wavelet packet frequency band energy distribution of blast vibration

Blast vibration analysis is one of the important foundations for studying the control technology of blast vibration damage. According to blast vibration live data that have been collected and the characteristics of short-time non-stationary random signals, the wavelet packet energy spectrum analysis for blast vibration signal has made by wavelet packet analysis technology and the signals were measured under different explosion parameters （the maximal section dose, the distance of blast source to measuring point and the section number of millisecond detonator）. The results show that more than 95% frequency band energy of the signals sl-s8 concentrates at 0-200 Hz and the main vibration frequency bands of the signals sl-s8 are 70.313-125, 46.875-93.75, 15.625-93.75, 0-62.5, 42.969-125, 15.625-82.031, 7.813-62.5 and 0-62.5 Hz. Energy distributions for different frequency bands of blast vibration signal are obtained and the characteristics of energy distributions for blast vibration signal measured under different explosion parameters are analyzed. From blast vibration signal energy, the decreasing law of blast seismic waves measured under different explosion parameters was studied and the wavelet packet analysis is an effective means for studying seismic effect induced by blast.

Analysis on Output Power for Multi-direction Piezoelectric Vibration Energy Harvester

To predict the performance of multi-direction piezoelectric vibration energy harvester,an equation for calculating its output power is obtained based on elastic mechanics theory and piezoelectricity theory.Experiments are performed to verify theoretical analysis.When the excitation direction is along Y direction,a maximal output power about 0.139 mW can be harvested at a resistive load of 65kΩ and an excitation frequency of 136 Hz.Theoretical analysis agrees well with experimental results.Furthermore,the performance of multi-direction vibration energy harvester is experimentally tested.The results show that the multi-direction vibration energy harvester can harvest perfect energy as the excitation direction changes in XY plane,YZ plane,XZ plane and body diagonal plane of the harvester.

Pendulum systems for harvesting vibration energy from railroad tracks and sleepers during the passage of a high-speed train: A feasibility evaluation

We evaluate the feasibility of recovering energy from the vibrations of track and sleepers,during passage of a high-speed train,by means of a pendulum harvester.A simple mathematical model of the parametric pendulum is employed to obtain numerical predictions,while measured data of vibration tests during the passage of a Thalys high-speed train are considered as input forcing.Since a sustained rotation is the most energetic motion of a pendulum,the possibility of achieving such state is evaluated,taking into account the influence of initial conditions,damping and other factors.Numerical simulations show that rotating pendulum harvesters with sufficiently low viscous damping could be able to generate a usable average power on the order of 5–6 W per unit.Considering a modular arrangement of devices,such energy is enough to feed variety of rail-side equipment,as wireless sensors or warning light systems.However,a suitable choice of initial conditions could be a difficult task,leading to the need of a control action.

Free torsional vibration of cracked nanobeams incorporating surface energy effects

This paper investigates surface energy effects, including the surface shear modulus, the surface stress, and the surface density, on the free torsional vibration of nanobeams with a circumferential crack and various boundary conditions. To formulate the problem, the surface elasticity theory is used. The cracked nanobeam is modeled by dividing it into two parts connected by a torsional linear spring in which its stiffness is related to the crack severity. Governing equations and corresponding boundary conditions are derived with the aid of Hamilton＇s principle. Then, natural frequencies are obtained analytically, and the influence of the crack severity and position, the surface energy, the boundary conditions, the mode number, and the dimensions of nanobeam on the free torsional vibration of nanobeams is studied in detail. Results of the present study reveal that the surface energy has completely different effects on the free torsionl vibration of cracked nanobeams compared with its effects on the free transverse vibration of cracked nanobeams.

Inversion Vibrational Energy Levels of PH3^＋（^～X^2A″2） Calculated by a New Two-dimension Variational Method

A new 2-D variational method is proposed to calculate the vibrational energy levels of the symmetric P-H stretching vibration （vl） and the symmetric umbrella vibration （inversion vibration） （v2） of PH3^＋（^～X^2A″2） that has the tunneling effect. Because the symmetric internal Cartesian coordinates were employed in the calculations, the kinetic energy operator is very simple and the inversion vibrational mode is well characterized. In comparison with the often used I-D model to calculate the inversion vibrational energy levels, this 2-D method does not require an assmnption of reduced mass, and the interactions between the vl and v2 vibrational modes are taken into consideration. The calculated vibrational energy levels of PH3^＋ are the first reported 2-D calculation, and the average deviation to the experimental data is less than 3 cm^-1 for the first seven inversion vibrational energy levels. This method has also been applied to calculate the vibrational energy levels of NH3. The application to NH3 is less successful, which shows some limitations of the method compared with a full dimension computation.