In this paper, we have developed a solver based on the message-passing interface (MPI) to enable rapid large-scale simulation of generic metastructures composed of bi- or multi-stable elements. The ...in-house solver has been thoroughly validated against a commercial numerical solver (Abaqus) and the well-established serial codes from the previous studies. We can achieve up to 4th-order solution accuracy with fully explicit Runge-Kutta (RK) methods, exceeding what many commercial structural analysis tools provide. With our parallel code dedicated to solving specific problem types, the absolute computational speed can be improved by three orders of magnitude, enabling the investigation of a large parameter space. More importantly, the in-house implementation enables an effective distribution of the computational load following the intrinsic structural periodicity, thus achieving efficient parallel scalability. To demonstrate our code's capability to handle massively large problems previously unattainable with existing solvers, we investigate the amplitude-dependent energy transmissibility of bi-stable metabeams and the stability of the transition wave's propagation speed. The achieved numerical and computational performance gains drastically expand the accessible analysis domains of general nonlinear metamaterial and metastructure architectures, thus opening up the potential to uncover new dynamics and enable practical implementations.
Program Title:NM̂3 (Nonlinear MetaMaterials MPI) solver
CPC Library link to program files:https://doi.org/10.17632/8f4n99jccf.1
Developer's repository link:https://github.com/wonnie87/NMCube
Licensing provisions: MIT
Programming language: Fortran
Nature of problem:NM̂3 enables massively parallel simulations of strongly nonlinear metamaterials and metastructures, including 1D multi-stable lattice with coupled pendula (discrete sine-Gordon model), 1D lattice with quartic on-site potentials (discrete ϕ-4 model), and metabeam with a bi-stable microstructure.
Solution method: Up to the 4th-order explicit Runge-Kutta (RK) methods are implemented in NM̂3. The Newmark-β (implicit) method with constant average acceleration is also available if unconditional numerical stability is desired.
Additional comments including restrictions and unusual features: Running NM̂3 requires installation of Python (with NumPy library), MPI, and HDF5. A Python script is used to generate input files. The code use MPI system calls to allow a massive parallelization among the compute processes. The code uses HDF5 file format for data storage.
•Fast analyses of general metastructures composed of multi-stable elements.•Extended numerical accuracy with fully explicit Runge-Kutta methods.•Wallclock time reduction by three orders of magnitude.•Improved parallel scalability offered by the inherent structural periodicity.•Large-scale simulation of metastructures with strong nonlinearities.
•Bistable and tristable mechanisms significantly improve efficiency of the point absorbers.•A multi-stable point absorber has a higher frequency bandwidth.•Robustness of the multi-stable wave energy ...device increases with respect to the damping detuning.
Here, we show that a nonlinear multi-stable system, composed of a nonlinear restoring mechanism and a linear damper-like generator, can significantly enhance the absorption efficiency of a heaving wave energy converter. This efficiency increase can be as large as few times higher than a wave energy absorber with a classical power take off system composed of a linear spring and a linear generator. Through a quantitative analysis, we also show that a nonlinear multi-stable system broadens the frequency bandwidth of the wave absorber, as well as, the bandwidth of the power take off’s damping coefficient. We propose a simple mechanical system that has the required multi-stable response upon which the investigation of this paper is based. Methodology developed and the results obtained here can be readily extended to other types of wave energy converters with one or multi degrees of freedom.
•This study is to present a novel multi-stable energy harvesting system by adjusting the geometric parameters of linear springs.•The increase of steady state can enhance the expected value of the ...mean square current and mean harvested power.•The proposed multi-stable system can improve the power capture performance of energy harvesting from higher-energy interwell motion.
Scavenging energy from external vibration with low-frequencies and low-level intensities has always been a huge challenge for the energy harvesting. To remedy this key issue, this study is to present a novel multi-stable electromagnetic transduction energy harvesting system by adjusting the geometric parameters of linear springs. Here, we prove that the multi-stable energy harvesting system composed of a nonlinear restoring mechanism can significantly improve the efficiency of the energy converter. The electromechanical model is set up, and the corresponding equations are derived by the Extended Averaging Method and Fokker–Planck equation analysis. The response under harmonic excitation exhibits that, compared to a mono-stable and a bi-stable system, with a tri-stable or a quad-stable system, we can achieve a higher-energy interwell motion with large-amplitude periodic oscillation, leading to significant increases of the harvested current and power. Moreover, improved the expected value of the mean square current and mean harvested power can also be attained under the Gaussian white noise with a small intensity. The results show that the proposed multi-stable system is a feasible design that can improve the power capture performance of energy harvesting from low-level excitations.
In order to better capture energy from natural water flow, we designed a novel captive energy model using wake induced vibration (WIV) combined with multi-stable theory. The model consists of an ...upstream stationary square cylinder and a downstream vibrating circular cylinder. The multi-stable characteristics are achieved by controlling the horizontal distance (l) and vertical distance (d) between the tip magnet of the vibrating cylinder and the stationary magnets. We simulate the capture energy characteristics of the harvester for different stable conditions at 0.1 m/s-0.8 m/s (i.e., 1990 ≤ Reynolds number ≤ 15,923) using the computational fluid dynamics (CFD) method. The simulation results show that when fixing l = 0.020, d = 0.016 and d = 0.017 are bi-stable systems, and at the same time, it will be trapped in a potential well at a flow velocity of 0.1 m/s, resulting in a lower amplitude and vibration frequency. When d is fixed at 0.017 m, l = 0.021 and l = 0.022 are tri-stable systems with a wider flow velocity interval corresponding to its high amplitude. Different magnet positions affect the phase between the lift coefficients and displacements of the bluff body. At flow velocities from 0.1 m/s to 0.4 m/s, the energy harvesting effect of the with-magnet system is better than that of the non-magnet system.
Multi-stable WIV energy harvesting system with the introduction of magnetism. Different stable conditions can be constructed by changing the position of the bottom magnets. Display omitted
•The introduction of magnetism into the energy harvester resulted in a significant change in the amplitude and frequency.•There are differences in the vibration characteristics of the cylinder under different stable conditions.•The performance of the with-magnet system is better than without-magnet system in the low flow rate range (U = 0.1–0.3 m/s).
Abstract
Nonlinear mono-stable and multi-stable piezoelectric energy harvesters have attracted a lot of attention owing to their broadband frequency spectra and excellent energy harvesting ...performance. Herein, two types of nonlinear mono-stable, bi-stable, tri-stable, and quad-stable piezoelectric energy harvesters using cantilever structure and magnetic interaction are compared and analyzed. Based on the magnetizing current method, the magnetic force equations are obtained. Calculation results demonstrate that the stability of these harvesters is dependent on the equivalent linear elastic force and the vertical magnetic force. The equilibrium point occurs when the equivalent linear elastic force equals to the vertical magnetic force. The relationship between the number of stable equilibrium points
E
S
and the number of the intersections of the two force curves
N
I
is that
E
S
= (
N
I
+ 1)/2. Experiments are carried out to verify the equivalent linear elastic force, vertical magnetic force, and the number of stable equilibrium points of the fabricated prototypes. The experimental results are consistent with the calculated results, which verifies the correctness of the stability mechanism. Moreover, it is found that the stability mechanism is also applicable to the harvesters with more stable equilibrium points, such as penta-stable and hexa-stable harvesters. This work reveals the stability mechanism of nonlinear mono-stable and multi-stable energy harvesters using cantilever structure and magnetic interaction, and provides technical methods for the design of multi-stable energy harvesters.
The mean first-passage time (MFPT) and the weak signal detection method of stochastic resonance (SR) on multi-stable nonlinear system under color correlated noise are studied. Using the uniform color ...noise approximation method, the Fokker-Planck equation of the system is obtained, and the steady-state probability density function of the multi-stable system driven by the multiplicative noise and additive noise is derived. On the basis of this, the formula of MFPT is derived, and the influence of parameters on the MFPT is analyzed. The problem of weak signal detection under color noise background is studied based on multi-stable SR. The results of simulation and experiment show that the method can effectively extract the frequency feature of weak signal in the background of color noise.
•Forcing item has been taken as a variable parameter to investigate its effect on the dynamics of bursting.•Several types of bursters are presented and their occurrence mechanism is ...discussed.•Bifurcation parameters will affect the occurrence and oscillating of bursting like a ‘switch’ in multiple scroll chaotic systems.
In this paper, we investigate the emergence of bursting dynamics with complex waveforms and their relation to periodic behavior in typical Van der pol-Duffing equation with fifth order polynomial stiffness nonlinearity, when the external force changes slowly with the variation of time. We exploit bifurcation characteristics of the fast subsystem using the slowly changing periodic excitation as a bifurcation parameter to show how the bursting oscillations are created in this model. We also identify that some regimes of bursting patterns are related to codimension two bifurcation type over a wide range of parameters. A subsequent two-parameter continuation reveals a transition in the bursting behavior from fold/fold hysteresis cycle to sup-Hopf/sup-Hopf or limit point cycle/sub-Hopf bursting type. Furthermore, the effects of external forcing item on bursting oscillations are investigated. For instance, the time interval between two adjacent spikes of bursting oscillations is dependent on the forcing frequency. Some numerical simulations are included to illustrate the validity of our study.
The classical tri-stable stochastic resonance (CTSR) has the weakness of output saturation, which restricts the ability to enhance weak signal detection. To overcome the limitation of output ...saturation, a piecewise unsaturated multi-stable stochastic resonance (PUMSR) method is proposed. Due to the presence of trichotomous noise in practical application, this paper explores the PUMSR under a trichotomous noise environment. The performance of PUMSR is evaluated by means of an index, mean signal-to-noise ratio increase (MSNRI). In order to meet the adiabatic approximation conditions, the signal is secondary sampled and a genetic algorithm (GA) is implemented to optimize the system parameters. Simulation experiments demonstrate that the proposed PUMSR system is superior to the CTSR system in terms of its ability to extract signals at multi-frequency. The PUMSR is then applied to the diagnosis of bearing faults. It is further proved that the PUMSR system has good performance in bearing fault diagnosis and has great feasibility in real engineering application.
•A multi-stable stochastic resonance system driven by Lévy noise is investigated.•The effects of system parameters on SNR-GM are discussed.•The comparisons of SNR-GM performance between multi-stable, ...bistable and monostable systems have been studied.
In this paper, the stochastic resonance (SR) of a multi-stable system driven by Lévy noise is investigated by the mean signal-to-noise ratio gain (SNR-GM). The characteristics for resonant output of multi-stable system, governed by the system parameters (a and c), the noise amplification factor D of Lévy noise are investigated under different values of stability index α and asymmetry parameter β of Lévy noise. The results reveal that the parameter α is closer to 1, the amplitude of SNR-GM versus system parameter a (or c) is larger. The interval of SR presents a trend that the curve of SNR-GM shifts to the right with the increase of α especially when α > 1. In addition, the SNR-GM for different values of system parameter a (or c) exhibits a tendency to move to the left with the increase of system parameter c (or a). Finally, the simulation results prove that the proposed multi-stable model has better advantage than bistable system and monostable system in signal enhancement and SNR-GM performance.
Nonlinear multi-stable piezoelectric energy harvesters show broadband frequency spectra and excellent energy harvesting performance, owing to their high output power related to inter-well ...transitions. However, existing quad-stable piezoelectric energy harvesters contain too many structural parameters, which makes the systems clumsy, and increases the difficulties of dynamic analysis and structural optimization. Herein, a nonlinear quad-stable piezoelectric energy harvester, with only one external magnet, is proposed based on the magnetic force characteristics between a ring magnet and a rectangular magnet. Under selected structural parameters, as the magnet spacing increases, the stability characteristic of the harvester changes from quad-stability to bi-stability, and then to mono-stability. The transformation of the stability characteristic results from the changes in the variation rate of the vertical magnetic force. Subsequently, under the filtered Gaussian white noise within the frequency range of 0–120 Hz, the energy harvesting performance of the harvester is simulated by the classic fourth-order Runge-Kutta method. Simulation results show that the performance of the harvester under the quad-stable structural parameters is better than that under the bi-stable structural parameters, independent of whether the excitation acceleration is small or large. This result is related to the potential well characteristics under the quad-stable and bi-stable structural parameters. More specifically, the potential well depths under the quad-stable and bi-stable structural parameters are almost the same, but the distance between the two outer potential wells under the quad-stable structural parameters is larger than that under the bi-stable structural parameters. Finally, a fabricated prototype is used to measure the experimental performance of the harvester. The experimental data and the estimated data share the same trend. This study provides a new conception and technical method for the design, optimization, and application of quad-stable piezoelectric energy harvesters.
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