Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode

The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified.The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated,and the four-dimensional(4D)nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method.The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed.The discussion focuses on investigating the effects of key parameters,e.g.,excitation amplitude,damping coefficient,and detuning parameters,on the resonance responses.The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system.Furthermore,the significant motions under particular excitation conditions are visualized by bifurcation diagrams,time histories,phase portraits,three-dimensional(3D)phase portraits,and Poincare maps.Finally,the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell,yielding results that are qualitatively consistent with the theoretical results.

UAV-assisted data collection for wireless sensor networks with dynamic working modes

Wireless Sensor Network(WSN)is a cornerstone of Internet of Things(IoT)and has rich application scenarios.In this work,we consider a heterogeneous WSN whose sensor nodes have a diversity in their Residual Energy(RE).In this work,to protect the sensor nodes with low RE,we investigate dynamic working modes for sensor nodes which are determined by their RE and an introduced energy threshold.Besides,we employ an Unmanned Aerial Vehicle(UAV)to collect the stored data from the heterogeneous WSN.We aim to jointly optimize the cluster head selection,energy threshold and sensor nodes’working mode to minimize the weighted sum of energy con-sumption from the WSN and UAV,subject to the data collection rate constraint.To this end,we propose an efficient search method to search for an optimal energy threshold,and develop a penalty-based successive convex approximation algorithm to select the cluster heads.Then we present a low-complexity iterative approach to solve the joint optimization problem and discuss the implementation procedure.Numerical results justify that our proposed approach is able to reduce the energy consumption of the sensor nodes with low RE significantly and also saves energy for the whole WSN.

Dynamic mode decomposition of the geomagnetic field over the last two decades

Earth’s magnetic field,which is generated in the liquid outer core through the dynamo action,undergoes changes on timescales of a few years to several million years,yet the underlying mechanisms responsible for the field variations remain to be elucidated.In this study,we apply a novel data analysis technique developed in fluid dynamics,namely the dynamic mode decomposition,to analyze the geomagnetic variations over the last two decades when continuous satellite observations are available.The dominant dynamic modes are extracted by solving an eigen-value problem,so one can identify modes with periods longer than the time span of data.Our analysis show that similar dynamic modes are extracted from the geomagnetic secular variation and secular acceleration,justifying the validity of applying the dynamic mode decomposition method to geomagnetic field.We reveal that the geomagnetic field variations are characterized by a global mode with period of 58 years,a localized mode with period of 16 years and an equatorially trapped mode with period of 8.5 years.These modes are possibly related to magnetohydrodynamic waves in the Earth’s outer core.

Mode Specificity Dynamics of Prototypical Multi-Channel H+CH_(3)OH Reaction on Globally Accurate Potential Energy Surface

The H+CH_(3) OH reaction,which plays an important role in combustion and the interstellar medium,presents a prototypical system with multiple channels.In this work,mode specific dynamics of different product channels is investigated theoretically on a recently developed reliable potential energy surface based on a large number of data points calculated at the level of UCCSD(T)-F12 a/AVTZ.It has been demonstrated that vibrational excitations of the O-H stretching motion,the torsional motion,the C-H stretching vibrations,show different infuences on the four product channels,H_(2)+CH_(3) O,H_(2)+CH_(2)OH,H_(2) O+CH_(3),and H+CH_(3) OH.This work is helpful for understanding the mode-specific dynamics and controlling the competition for complicated reactions with multiple product channels.

An Improved Coupled Dynamic Modelling for Exploring Gearbox Vibrations Considering Local Defects

Gearbox is a key part in machinery,in which gear,shaft and bearing operate together to transmit motion and power.The wide usage and high failure rate of gearbox make it attract much attention on its health monitoring and fault diagnosis.Dynamic modelling can study the mechanism under different faults and provide theoretical foundation for fault detection.However,current commonly used gear dynamic model usually neglects the influence of bearing and shaft,resulting in incomplete understanding of gearbox fault diagnosis especially under the effect of local defects on gear and shaft.To address this problem,an improved gear-shaft-bearing-housing dynamic model is proposed to reveal the vibration mechanism and responses considering shaft whirling and gear local defects.Firstly,an eighteen degree-of-freedom gearbox dynamic model is proposed,taking into account the interaction among gear,bearing and shaft.Secondly,the dynamic model is iteratively solved.Then,vibration responses are expounded and analysed considering gear spalling and shaft crack.Numerical results show that the gear mesh frequency and its harmonics have higher amplitude through the spectrum.Vibration RMS and the shaft rotating frequency increase with the spalling size and shaft crack angle in general.An experiment is designed to verify the rationality of the proposed gearbox model.Lastly,comprehensive analysis under different spalling size and shaft crack angle are analysed.Results show that when spalling size and crack angle are larger,RMS and the amplitude of shaft rotating frequency will not increase linearly.The dynamic model can accurately simulate the vibration of gear transmission system,which is helpful for gearbox fault diagnosis.

A dynamic-mode-decomposition-based acceleration method for unsteady adjoint equations at low Reynolds numbers

The computational cost of unsteady adjoint equations remains high in adjoint-based unsteady aerodynamic op-timization.In this letter,the solution of unsteady adjoint equations is accelerated by dynamic mode decomposi-tion(DMD).The pseudo-time marching of every real-time step is approximated as an infinite-dimensional linear dynamical system.Thereafter,DMD is utilized to analyze the adjoint vectors sampled from these pseudo-time marching.First-order zero frequency mode is selected to accelerate the pseudo-time marching of unsteady adjoint equations in every real-time step.Through flow past a stationary circular cylinder and an unsteady aerodynamic shape optimization example,the efficiency of solving unsteady adjoint equations is significantly improved.Re-sults show that one hundred adjoint vectors contains enough information about the pseudo-time dynamics,and the adjoint dominant mode can be precisely predicted only by five snapshots produced from the adjoint vectors,which indicates DMD analysis for pseudo-time marching of unsteady adjoint equations is efficient.

Application of Hankel Dynamic Mode Decomposition for Wide Area Monitoring of Subsynchronous Resonance

In recent years,subsynchronous resonance(SSR)has frequently occurred in DFIG-connected series-compensated systems.For the analysis and prevention,it is of great importance to achieve wide area monitoring of the incident.This paper presents a Hankel dynamic mode decomposition(DMD)method to identify SSR parameters using synchrophasor data.The basic idea is to employ the DMD technique to explore the subspace of Hankel matrices constructed by synchrophasors.It is analytically demonstrated that the subspace of these Hankel matrices is a combination of fundamental and SSR modes.Therefore,the SSR parameters can be calculated once the modal parameter is extracted.Compared with the existing method,the presented work has better dynamic performances as it requires much less data.Thus,it is more suitable for practical cases in which the SSR characteristics are timevarying.The effectiveness and superiority of the proposed method have been verified by both simulations and field data.

Parameters Identification for Extended Debye Model of XLPE Cables Based on Sparsity-Promoting Dynamic Mode Decomposition Method

To identify the parameters of the extended Debye model of XLPE cables,and therefore evaluate the insulation performance of the samples,the sparsity-promoting dynamicmode decomposition(SPDMD)methodwas introduced,aswell the basics and processes of its applicationwere explained.The amplitude vector based on polarization current was first calculated.Based on the non-zero elements of the vector,the number of branches and parameters including the coefficients and time constants of each branch of the extended Debye model were derived.Further research on parameter identification of XLPE cables at different aging stages based on the SPDMD method was carried out to verify the practicability of the method.Compared with the traditional differential method,the simulation and experiment indicated that the SPDMD method can effectively avoid problems such as the relaxation peak being unobvious,and possessing more accuracy during the parameter identification.And due to the polarization current being less affected by the measurement noise than the depolarization current,the SPDMD identification results based on the polarization current spectral line proved to be better at reflecting the response characteristics of the dielectric.In addition,the time domain polarization current test results can be converted into the frequency domain,and then used to obtain the dielectric loss factor spectrum of the insulation.The integral of the dielectric loss factor on a frequency domain can effectively evaluate the insulation condition of the XLPE cable.

A novel dynamic terminal sliding mode control of uncertain nonlinear systems

A new dynamic terminal sliding mode control （DTSMC） technique is proposed for a class of single-input and single-output （SISO） uncertain nonlinear systems. The dynamic terminal sliding mode controller is formulated based on Lyapunov theory such that the existence of the sliding phase of the closed-loop control system can be guaranteed, chattering phenomenon caused by the switching control action can be eliminated, and high precision performance is realized. Moreover, by designing terminal equation, the output tracking error converges to zero in finite time, the reaching phase of DSMC is eliminated and global robustness is obtained. The simulation results for an inverted pendulum are given to demonstrate the properties of the proposed method.

Stability analysis for flow past a cylinder via lattice Boltzmann method and dynamic mode decomposition

A combination of the lattice Boltzmann method and the most recently developed dynamic mode decomposition is proposed for stability analysis. The simulations are performed on a graphical processing unit. Stability of the flow past a cylinder at supercritical state, Re = 50, is studied by the combination for both the exponential growing and the limit cycle regimes. The Ritz values, energy spectrum, and modes for both regimes are presented and compared with the Koopman eigenvalues. For harmonic-like periodic flow in the limit cycle, global analysis from the combination gives the same results as those from the Koopman analysis. For transient flow as in the exponential growth regime, the combination can provide more reasonable results. It is demonstrated that the combination of the lattice Boltzmann method and the dynamic mode decomposition is powerful and can be used for stability analysis for more complex flows.

Dynamical mode decomposition of Gurney flap wake flow

The present work uses dynamic mode decomposition(DMD) to analyze wake flow of NACA0015 airfoil with Gurney flap.The physics of DMD is first introduced.Then the PIV-measured wake flow velocity field is decomposed into dynamical modes.The vortex shedding pattern behind the trailing edge and its high-order harmonics have been captured with abundant information such as frequency,wavelength and convection speed.It is observed that high-order dynamic modes convect faster than low-order modes;moreover the wavelength of the dynamic modes scales with the corresponding frequency in power law.

Fast Model-based Design of High Performance Permanent Magnet Machine for Next Generation Electric Propulsion for Urban Aerial Vehicle Application

Model order reduction(MOR)is considered as a good alternative to reduce the computational scale for electro-magnetic problems.The aim of this work is to introduce the use of dynamic mode decomposition(DMD)as a promising tool for MOR to analyze its effectiveness in creating a fast model-based design platform for the permanent magnet motor design for ur-ban aerial vehicles(UAVs).Using a singular value decomposition(SVD)based DMD,the design process is constructed and verified against different scenarios.

Mode decomposition of a noise suppressed mixing layer

Noise is generated in a two-dimensional mixing layer due to the growing of instability waves and vortex pairings. The adjoint-based control methodology has shown to be a robust tool to suppress noise radiation. The mode decomposition algorithms such as the compressible version of proper orthogonal decomposition （POD） and dynamic mode decomposition （DMD） are employed to analyze the spatial/spatial-temporal coherent structures for a consecutive data sets of the controlled mixing layer and its uncontrolled counterpart. The analyses of POD indicate that the y-direction body force control mainly modify the most energetic spatial structures, and increase the uniformity of the flow. The analyses of DMD show us prevalent frequencies and corresponding mode structures, and the stability characteristics of each mode can be obtained from DMD-spectrum. The spectral signatures illustrate that a lot of neutral/slightly damping modes emerging in uncontrolled flow within the frequency range （w 〈 0.4） are suppressed due to control, relevant spatial-temporal structures are also varied, which is coincident with the change of far-field noise spectra. From the view of mode decomposition, the action of control redistribute the energy for frequency components of ~ 〈 0.4 by weakening nonlinearities and regularizing corresponding dynamic structures in streamwise direction, and thus suppress the noise radiation. Moreover, the POD- and DMD-analysis in this study demon- strate that DMD can serve as an important supplement for POD in analyzing a time-resolved physical process.

A SIMULATION STUDY ON DYNAMIC-SAMPLING-MODE FOR FLUORESCENCE MOLECULAR TOMOGRAPHY

Fluorescence tomography can obtain a sufficient dataset and optimal three-dimensional imageswhen projections are captured over 360◦ by CCD camera. Herein a non-stop dynamic samplingmode for fluorescence tomography is proposed in an attempt to improve the optical measurementspeed of the traditional imaging system and stability of the object to be imaged. A series ofsimulations are carried out to evaluate the accuracy of dataset acquired from the dynamicsampling mode. Reconstruction with the corresponding data obtained in the dynamic-modeprocess is also performed with the phantom. The results demonstrate the feasibility of suchan imaging mode when the angular velocity is set to the appropriate value, thus laying thefoundation for real experiments to verify the superiority in performance of this new imagingmode over the traditional one.

Dynamic failure mode and energy-based identification method for a counter-bedding rock slope with weak intercalated layers

The dynamic failure mode and energybased identification method for a counter-bedding rock slope with weak intercalated layers are discussed in this paper using large scale shaking table test and the Hilbert-Huang Transform(HHT) marginal spectrum.The results show that variations in the peak values of marginal spectra can clearly indicate the process of dynamic damage development inside the model slope.The identification results of marginal spectra closely coincide with the monitoring results of slope face displacement in the test.When subjected to the earthquake excitation with 0.1 g and 0.2 g amplitudes,no seismic damage is observed in the model slope,while the peak values of marginal spectra increase linearly with increasing slope height.In the case of 0.3 g seismic excitation,dynamic damage occurs near the slope crest and some rock blocks fall off the slope crest.When the seismic excitation reaches 0.4 g,the dynamic damage inside the model slope extends to the part with relative height of 0.295-0.6,and minor horizontal cracks occur in the middle part of the model slope.When the seismic excitation reaches 0.6 g,the damage further extends to the slope toe,and the damage inside the model slope extends to the part with relative height below 0.295,and the upper part(near the relative height of 0.8) slides outwards.Longitudinal fissures appear in the slope face,which connect with horizontal cracks,the weak intercalated layers at middle slope height are extruded out and the slope crest breaks up.The marginal spectrum identification results demonstrate that the dynamic damage near the slope face is minor as compared with that inside the model slope.The dynamic failure mode of counter-bedding rock slope with weak intercalated layers is extrusion and sliding at the middle rock strata.The research results of this paper are meaningful for the further understanding of the dynamic failure mode of counter-bedding rock slope with weak intercalated layers.

Nonlinear dynamic fractional sliding mode control to the motor of mining locomotive

The harsh operating environment and complex operating conditions of the mine electric locomotive affect the control performance of the locomotive traction motor.In order to improve the speed control performance of electric locomotive traction motors,a dynamic fractional-order sliding mode control(DFOSMC)algorithm considering uncertain factors was proposed.A load torque sliding mode observer was designed for the complex load disturbance of the traction motor,and its observations were integrated into the DFOSMC controller to overcome the influence of load disturbance.Finally,the stability of the designed controller was proved by Lyapunov's theorem.Besides,the control performance of DFOSMC controller was compared with integer-order sliding mode controller and fractional-order sliding mode controller through simulation experiments.Compared with integer-order sliding mode and fractional-order sliding mode controllers,the dynamic and static performance of the DFOSMC controller with load observation is better,and it has stronger anti-interference ability.The DFOSMC controller effectively improves the control performance of the traction motor of the mining locomotive.

NANOSCALE CUTTING OF MONOCRYSTALLINE SILICON USING MOLECULAR DYNAMICS SIMULATION

It has been found that the brittle material, monocrystalline silicon, can be machined in ductile mode in nanoscale cutting when the tool cutting edge radius is reduced to nanoscale and the undeformed chip thickness is smaller than the tool edge radius. In order to better understand the mechanism of ductile mode cutting of silicon, the molecular dynamics （MD） method is employed to simulate the nanoscale cutting of monocrystalline silicon. The simulated variation of the cutting forces with the tool cutting edge radius is compared with the cutting force results from experimental cutting tests and they show a good agreement. The results also indicate that there is silicon phase transformation from monocrystalline to amorphous in the chip formation zone that can be used to explain the cause of ductile mode cutting. Moreover, from the simulated stress results, the two necessary conditions of ductile mode cutting, the tool cutting edge radius are reduced to nanoscale and the undeformed chip thickness should be smaller than the tool cutting edge radius, have been explained.

Dynamic modeling and simulation for the flexible spacecraft with dynamic stiffening

A rigid flexible coupling physical model which can represent a flexible spacecraft is investigated in this paper. By applying the mechanics theory in a non-inertial coordinate system,the rigid flexible coupling dynamic model with dynamic stiffening is established via the subsystemmodeling framework. It is clearly elucidated for the first time that,dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beamand the transverse vibration deformation of the beam. The modeling approach in this paper successfully avoids problems which are caused by other popular modeling methods nowadays： the derivation process is too complex by using only one dynamic principle; a clearly theoretical explanation for dynamic stiffening can＇t be provided. First,the continuous dynamic models of the flexible beamand the central rigid body are established via structural dynamics and angular momentumtheory respectively. Then,based on the conclusions of orthogonalization about the normal constrained modes,the finite dimensional dynamic model suitable for controller design is obtained. The numerical simulation validations showthat： dynamic stiffening is successfully incorporated into the dynamic characteristics of the first-order model established in this paper,which can indicate the dynamic responses of the rigid flexible coupling system with large overall motion accurately,and has a clear modeling mechanism,concise expressions and a good convergence.

Constructing reduced model for complex physical systems via interpolation and neural networks

The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD)and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approximate thenonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation beforeapproximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic modedecomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, anovel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid oferror data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy.Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.

Dynamic mode decomposition and reconstruction of transient cavitating flows around a Clark-Y hydrofoil

The transient cavitating flow around the Clark-Y hydrofoil is numerically investigated by the dynamic mode decomposition with criterion.Based on the ranking dominant modes,frequencies of the first four modes are in good accordance with those obtained by fast Fourier transform.Furthermore,the cavitating flow field is reconstructed by the first four modes,and the dominant flow features are well captured with the reconstructed error below 12%when compared to the simulated flow field.This paper offers a reference for observing and reconstructing the flow fields,and gives a novel insight into the transient cavitating flow features.