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.

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.

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.

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.

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 flight stability of a bumblebee in forward flight

The longitudinal dynamic flight stability of a bumblebee in forward flight is studied. The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are employed for solving the equations of motion. The primary findings are as the following. The forward flight of the bumblebee is not dynamically stable due to the existence of one （or two） unstable or approximately neutrally stable natural modes of motion. At hovering to medium flight speed [flight speed Ue = （0-3.5）m s^-1; advance ratio J = 0-0.44], the flight is weakly unstable or approximately neutrally stable; at high speed （Ue = 4.5 m s^-1; J = 0.57）, the flight becomes strongly unstable （initial disturbance double its value in only 3.5 wingbeats）.

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.

Dynamic Stability Analysis of Linear Time-varying Systems via an Extended Modal Identification Approach

The problem of linear time-varying（LTV） system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the ＂frozen-time＂ assumption are not able to determine the dynamic stability of LTV systems. Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stabilitypreserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system＇s stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam exper- imental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides anew way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.

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.

Field structure at mode Ⅲ dynamically propagating crack tip in elastic-viscoplastic materials

An elastic-viscoplastic mechanics model is used to investigate asymptotically the mode Ⅲ dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at the crack tip possess the same power-law singularity under a linear-hardening condition. The singularity exponent is uniquely determined by the viscosity coefficient of the material. Numerical results indicate that the motion parameter of the crack propagating speed has little effect on the zone structure at the crack tip. The hardening coefficient dominates the structure of the crack-tip field. However, the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at the crack tip while it does have certain influence on the crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. The corresponding perfectly-plastic solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero.

Dynamic Control of Defective Gap Mode Through Defect Location

A one dimensional model is developed for defective gap mode（DGM）with two types of boundary conditions：conducting mesh and conducting sleeve.For a periodically modulated system without defect,the normalized width of spectral gaps equals to the modulation factor,which is consistent with previous studies.For a periodic system with local defects introduced by the boundary conditions,it shows that the conducting-mesh-induced DGM is always well confined by spectral gaps while the conducting-sleeve-induced DGM is not.The defect location can be a useful tool to dynamically control the frequency and spatial periodicity of DGM inside spectral gaps.This controllability can be potentially applied to the interaction between gap eigenmodes and energetic particles in fusion plasmas,and optical microcavities and waveguides in photonic crystals.

External blast flow field evolution and response mechanism of single-layer reticulated dome structure

Single-layer reticulated dome structure are commonly high-profile building in the public and can be attractive targets for terrorist bombings,so the public can benefit from enhanced safety with a stronger understanding of the behavior of single-layer reticulated dome structure under explosion.This paper investigates the fluid-structure interaction process and the dynamic response performance of the singlelayer reticulated dome under external blast load.Both experimental and numerical results shown that structural deformation is remarkably delayed compared with the velocity of blast wave,which advises the dynamic response of large-span reticulated dome structure has a negligible effect on the blast wave propagation under explosion.Four failure modes are identified by comparing the plastic development of each ring and the residual spatial geometric of the structure,i.e.,minor vibration,local depression,severe damage,and overall collapse.The plastic deformation energy and the displacement potential energy of the structure are the main consumers of the blast energy.In addition,the stress performance of the vertex member and the deep plastic ratio of the whole structure can serve as qualitative indicators to distinguish different failure modes.

Numerical analysis of the correlation between fluid dynamic modes and hydrodynamic noise in flows around a three-dimensional circular cylinder

The flow around a circular cylinder for Re=1000 is characterized by flow separation and Karman vortex street.The typical flow features can be captured to study the correlation between fluid fields and sound fields.In this paper,the three-dimensional circular cylinder is taken as the research object,and the probes of surface fluctuating pressure and far field sound pressure are arranged every 10°.The directional diagram and the coherence of fluctuating pressure and sound pressure are analyzed.The relationship between the flow mode and hydrodynamic noise is studied by using dynamic mode decomposition(DMD).The characteristics of the dipole and quadrupole sound source term of a long span cylinder are studied.The results show that at the angles between 30°–120°and 190°–350°,the fluctuating pressure contributes more to the generation of dipole sounds.The quadrupole sound source shows three-dimensional effects,which is more obvious in a cylinder with large spanwise length.

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.