Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell:an experimental and numerical study

The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.

Optical super-resolution effect induced by nonlinear characteristics of graphene oxide films

In this work, we focus on the optical super-resolution effect induced by strong nonlinear saturation absorption(NSA) of graphene oxide(GO) membranes. The third-order optical nonlinearities are characterized by the canonical Z-scan technique under femtosecond laser(wavelength: 800 nm, pulse width: 100 fs) excitation. Through controlling the applied femtosecond laser energy, NSA of the GO films can be tuned continuously. The GO film is placed at the focal plane as a unique amplitude filter to improve the resolution of the focused field. A multi-layer system model is proposed to present the generation of a deep sub-wavelength spot associated with the nonlinearity of GO films. Moreover, the parameter conditions to achieve the best resolution(~λ/6) are determined entirely. The demonstrated results here are useful for high density optical recoding and storage, nanolithography, and super-resolution optical imaging.

Nonlinear characteristics analyses of particle motion for predicting flow regimes

Gas-solid flow regimes have a significant impact on particle transport and separation in a fluidized bed reactor.In this study,to determine flow regime transitions in gas-solid fluidized beds,an acoustic technique was used to detect and analyze the behavior of gas and solids.Algorithm complexity,fluctuation complexity,and Shannon entropy analyses of acoustic emission signals were performed to examine non linear system characteristics,and to determine the flow regime transiti on velocities uc,uk,and ufd-Moreover,using the standard deviation of pressure signals,pressure measurements and acoustic measurements were compared.The relative deviations(RDs)between the experimental and empirical values of uk were 8.8%,13.7%,8.8%,and 30.4%for the algorithm complexity,fluctuation complexity,Shannon entropy,and pressure signal standard deviation,respectively,while the respective RDs for Ufd were 15.7%,23.9%,15.7%,and 97.8%.The RDs between the experimental and empirical values of uc were all 6.4%.The experimental values obtained from acoustic signal measurements were therefore closer to the empirical values.In summary,the integration of non-intrusive acoustic measurements,complexity analysis,and Shannon entropy analysis is suitable for identifying flow regime transitions.

Nonlinear Dynamic Characteristics of the Vectored Thruster AUV in Complex Sea Conditions

The mobility of the vectored thruster AUV in different environment is the important premise of control system design. The new type of autonomous underwater vehicle (AUV) equipped with rudders and vectored thrusters which are combined to control the course is studied. Firstly, Euler angles representation and quaternion method are applied to establish six-DOF kinematic model respectively, then Newton second law and Lagrangian approach are used to deduce the vectored thruster AUV’s nonlinear dynamic equations with six degrees of freedom (DOF) respectively in complex sea conditions based on the random wave theory according to the structural and kinetic characteristics of the vectored thruster AUV in this paper. The kinematic models and dynamic models based on different theories have the same expression and conclusion, which shows that the kinematic models and dynamic models of the vectored thruster AUV are accurate. The Runge-Kutta arithmetic is used to solve the dynamic equations, which not only can simulate the motions such as cruise and hover but also can describe the vehicle’s low-frequency and high-frequency motion. The results of computation show that the mobility of the vectored thruster AUV in interference-free environment and the integrated signals including low-frequency motion signal and high-frequency motion signal in environmental disturbance accord with practical situation, which not only solve the problem of especial singularities when the pitch angle θ = ±90° but also clears up the difficulties of computation and display of the coupled nonlinear motion equations in complex sea conditions. Moreover, the high maneuverability of the vectored thruster AUV equipped with rudders and vectored thrusters is validated, which lays a foundation for the control system design.

Effect of nonlinear translations on the pulsation of cavitation bubbles

The pulsations and translations of cavitation bubbles obey combined ordinary differential equations,and their nonlinearities are studied by the bifurcation diagram and the phase diagram in a strong ultrasonic field.Bubble pulsation can change regularly or irregularly with changing driving pressure in the time domain.The bifurcation diagrams of the pulsation versus driving pressure show that the pulsations and translations of bubbles have nonlinear characteristics,and the nonlinear translations of bubbles can disorder the pulsations for certain parameters.Disorder of the pulsation can also be caused by nonlinear pulsation itself.In addition,the phase diagrams also show that the nonlinear translations make a large contribution to the pulsations.The same result can also be obtained when the ambient radii of two bubbles are different.

Effects of Unbalance Location on Dynamic Characteristics of High-speed Gasoline Engine Turbocharger with Floating Ring Bearings

For the high-speed gasoline engine turbocharger rotor, due to the heterogeneity of multiple parts material, manufacturing and assembly errors, running wear in impeller and uneven carbon of turbine, the random unbalance usually can be developed which will induce excessive rotor vibration, and even lead to nonlinear vibration accidents. However, the investigation of unbalance location on the nonlinear high-speed turbocharger rotordynamic characteristics is less. In order to discuss the rotor unbalance location effects of turbocharger with nonlinear floating ring bearings（FRBs）, the realistic turbocharger of gasoline engine is taken as a research object. The rotordynamic equations of motion under the condition of unbalance are derived by applied unbalance force and nonlinear oil film force of FRBs. The FE model of turbocharger rotor-bearing system is modeled which includes the unbalance excitation and nonlinear FRBs. Under the conditions of four different applied locations of unbalance, the nonlinear transient analyses are performed based on the rotor FEM. The differences of dynamic behavior are obvious to the turbocharger rotor systems for four conditions, and the bifurcation phenomena are different. From the results of waterfall and transient response analysis, the speed for the appearance of fractional frequency is not identical and the amplitude magnitude is different from the different unbalance locations, and the non-synchronous vibration does not occur in the turbocharger and the amplitude is relative stable and minimum under the condition 4. The turbocharger vibration and non-synchronous components could be reduced or suppressed by controlling the applied location of unbalance, which is helpful for the dynamic design, fault diagnosis and vibration control of the high-speed gasoline engine turbochargers.

Effects of Floating Ring Bearing Manufacturing Tolerance Clearances on the Dynamic Characteristics for Turbocharger

The inner and outer oil film dynamic characteristic coefficients of floating ring bearings（FRBs） change due to the manufacturing tolerance of the floating ring, journal and intermediate, which leads to high-speed turbocharger＇s vibration too large and even causes nonlinear vibration accident. However, the investigation of floating ring bearing manufacturing tolerance clearance on the rotordynamic characteristics is less at present. In order to study the influence law of inner and outer clearance on turbocharger vibration, the rotor dynamic motion equations of turbocharger supported in FRBs are derived by analyzing the size relations between floating ring, journal and intermediate for the inner and outer oil film clearances, the time transient response analysis for combination of FRBs clearance are developed. A realistic turbocharger is taken as a research object, the FE model of the turbocharger with FRBs is modeled. Under the conditions of four kinds of limit state bearing clearances for inner and outer oil film, the nonlinear transient analyses are performed based on the established FE dynamic models of the nonlinear rotor-FRBs system applied incentive combinations of gravity and unbalance force, respectively. From the waterfall, the simulation results show that the speed for the appearance of fractional frequency is not identical and the amplitude magnitude is different under the four kinds of bearing manufacturing tolerance limit clearances, and fractional frequency does not appear in the turbocharger and the amplitude is minimum under the ODMin/IDMax bearing manufacturing tolerance clearances. The turbocharger vibration is reduced by controlling the manufacturing tolerance clearance combinations of FRBs, which is helpful for the dynamic design and production-manufacturing of high-speed turbocharger.

Investigation on dynamic characteristics of a rod fastening rotor-bearing coupling system with fixed-point rubbing

The aim of this paper is to gain insight into the nonlinear vibration feature of a dynamic model of a gas turbine.First,a rod fastening rotor-bearing coupling model with fixed-point rubbing is proposed,where the fractal theory and the finite element method are utilized.For contact analysis,a novel contact force model is introduced in this paper.Meanwhile,the Coulomb model is adopted to expound the friction characteristics.Second,the governing equations of motion of the rotor system are numerically solved,and the nonlinear dynamic characteristics are analyzed in terms of the bifurcation diagram,Poincarémap,and time history.Third,the potential effects provided by contact degree of joint interface,distribution position,and amount of contact layer are discussed in detail.Finally,the contrast analysis between the integral rotor and the rod fastening rotor is conducted under the condition of fixed-point rubbing.

Vibration Characteristics of Rotor System with Loose Disc Caused by the Insufficient Interference Force

The rotating parts looseness is one of the common failures in rotating machinery.The current researches of looseness fault mainly focus on non-rotating components.However,the looseness fault of disc-shaft system,which is the main work part in the rotor system,is almost ignored.Here,a dynamic model of the rotor system with loose disc caused by the insufficient interference force is proposed based on the contact model of disc-shaft system with the microscopic surface topography,the vibration characteristics of the system are analyzed and discussed by the number simulation,and verified by the experiment.The results show that the speed of the shaft,the contact stiffness,the clearance between the disc and shaft,the damping of the disc and the rotational damping have an influence on the rotation state of the disc.When the rotation speed of the disc and the shaft are same,the collision frequency is mainly composed of one frequency multiplication component and very weak high frequency multiplication components.When the rotation speed of the disc and the shaft is close,the vibration of the disc occurs a beat vibration phenomenon in the horizontal direction.Simultaneously,a periodical similar beat vibration phenomenon also occurs in the waveform of the disc-shaft displacement difference.The collision frequency is mainly composed of a low frequency and a weak high frequency component.When the rotation speed of the disc and the shaft has great difference,the collision frequency is mainly composed of one frequency multiplication,a few weak high frequency multiplication components and a few low frequency multiplication component.With the reduction of the relative speed of the disc,the trajectory of the disc changes from circle-shape to inner eight-shape,and then to circle-shape.In the inner eight-shape,the inner ring first gradually becomes smaller and then gradually becomes larger,and the outer ring is still getting smaller.The obtained research results in this paper has important theoretical value for the diagnosis of the rotor system with the loose disc.

Characteristic fractional step finite difference method for nonlinear section coupled system

For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of coarse and fine partitions. Some tech- niques, such as calculus of variations, energy method, twofold-quadratic interpolation of product type, multiplicative commutation law of difference operators, decomposition of high order difference operators, and prior estimates, are used in theoretical analysis. Optimal order estimates in 12 norm are derived to show accuracy of the second order approximation solutions. These methods have been used to simulate the problems of migration-accumulation of oil resources.

The effect of initial geometric imperfection on the nonlinear resonance of functionally graded carbon nanotube-reinforced composite rectangular plates

The purpose of the present study is to examine the impact of initial geometric imperfection on the nonlinear dynamical characteristics of functionally graded carbon nanotube-reinforced composite(FG-CNTRC) rectangular plates under a harmonic excitation transverse load. The considered plate is assumed to be made of matrix and single-walled carbon nanotubes(SWCNTs). The rule of mixture is employed to calculate the effective material properties of the plate. Within the framework of the parabolic shear deformation plate theory with taking the influence of transverse shear deformation and rotary inertia into account, Hamilton’s principle is utilized to derive the geometrically nonlinear mathematical formulation including the governing equations and corresponding boundary conditions of initially imperfect FG-CNTRC plates. Afterwards, with the aid of an efficient multistep numerical solution methodology, the frequency-amplitude and forcing-amplitude curves of initially imperfect FG-CNTRC rectangular plates with various edge conditions are provided, demonstrating the influence of initial imperfection,geometrical parameters, and edge conditions. It is displayed that an increase in the initial geometric imperfection intensifies the softening-type behavior of system, while no softening behavior can be found in the frequency-amplitude curve of a perfect plate.

Nonlinear magneto-mechanical-thermo coupling characteristic analysis for transport behaviors of carriers in composite multiferroic piezoelectric semiconductor nanoplates with surface effect

In this paper,to better reveal the surface effect and the screening effect as well as the nonlinear multi-field coupling characteristic of the multifunctional piezoelectric semiconductor(PS)nanodevice,and to further improve its working performance,a magneto-mechanical-thermo coupling theoretical model is theoretically established for the extensional analysis of a three-layered magneto-electro-semiconductor coupling laminated nanoplate with the surface effect.Next,by using the current theoretical model,some numerical analyses and discussion about the surface effect,the corresponding critical thickness of the nanoplate,and the distributions of the physical fields(including the electron concentration perturbation,the electric potential,the electric field,the average electric displacement,the effective polarization charge density,and the total charge density)under different initial state electron concentrations,as well as their active manipulation via some external magnetic field,pre-stress,and temperature stimuli,are performed.Utilizing the nonlinear multi-field coupling effect induced by inevitable external stimuli in the device operating environment,this paper not only provides theoretical support for understanding the size-dependent tuning/controlling of carrier transport as well as its screening effect,but also assists the design of a series of multiferroic PS nanodevices.

A Further Study on an Extended Nonlinear Ocean-Atmosphere Coupled Hydrodynamic Characteristic System and the Abrupt Feature of ENSO Events

An extended ocean-atmosphere coupled characteristic system including thermodynamic physical processes in ocean mixed layer is formulated in order to describe SST explicitly and remove possible limitation of ocean-atmosphere coupling assumption in hydrodynamic ENSO models. It is revealed that there is a kind of abrupt nonlinear characteristic behaviour, which relates to rapid onset and intermittency of El Nino events, on the second order slow time scale due to the nonlinear interaction between a linear unstable low-frequency primary eigen component of ocean-atmosphere coupled Kelvin wave and its higher order harmonic components under a strong ocean-atmosphere coupling background. And, on the other hand, there is a kind of finite amplitude nonlinear characteristic behaviour on the second order slow time scale due to the nonlinear interaction between the linear unstable primary eigen component and its higher order harmonic components under a weak ocean-atmosphere coupling background in this model system.

Bubble acoustical scattering cross section under multi-frequency acoustic excitation

The acoustical scattering cross section is usually employed to evaluate the scattering ability of the bubbles when they are excited by the incident acoustic waves. This parameter is strongly related to many important applications of performance prediction for search sonar or underwater telemetry, acoustical oceanography, acoustic cavitation, volcanology, and medical and industrial ultrasound. In the present paper, both the analytical and numerical analysis results of the acoustical scattering cross section of a single bubble under multi-frequency excitation are obtained. The nonlinear characteristics（e.g.,harmonics, subharmonics, and ultraharmonics） of the scattering cross section curve under multi-frequency excitation are investigated compared with single-frequency excitation. The influence of several paramount parameters（e.g., bubble equilibrium radius, acoustic pressure amplitude, and acoustic frequencies） in the multi-frequency system on the predictions of scattering cross section is discussed. It is shown that the combination resonances become significant in the multi-frequency system when the acoustic power is big enough, and the acoustical scattering cross section is promoted significantly within a much broader range of bubble sizes and acoustic frequencies due to the generation of more resonances.

Roles of voltage in semi-insulating GaAs photoconductive semiconductor switch

An experimental study of leakage current is presented in a semi-insulating（SI） Ga As photoconductive semiconductor switch（PCSS） with voltages up to 5.8 kV（average field is 19.3 kV/cm）. The leakage current increases nonlinearly with the bias voltage increasing from 1.2×10^-9 A to 3.6×10^-5A. Furthermore, the dark resistance, which is characterized as a function of electric field, does not monotonically decrease with the field but displays several distinct regimes. By eliminating the field-dependent drift velocity, the free-electron density n is extracted from the current, and then the critical field for each region of n（E） characteristic of PCSS is obtained. It must be the electric field that provides the free electron with sufficient energy to activate the carrier in the trapped state via multiple physical mechanisms, such as impurity ionization, fielddependent EL2 capture, and impact ionization of donor centers EL10 and EL2. The critical fields calculated from the activation energy of these physical processes accord well with the experimental results. Moreover, agreement between the fitting curve and experimental data of J（E）, further confirms that the dark-state characteristics are related to these field-dependent processes. The effects of voltage on SI-Ga As PCSS may give us an insight into its physical mechanism.

Argument on the magnitude-frequency relation

The complexity of seismicity and the relation of magnitude and frequency are discussed in this paper on the basis of nonlinear dynamics and multifractal theory. We argue that seismic active systems normally have multifractal characteristics, either for the spatial-temporal distribution or the intensity distribution of events. In the view of multifractal theory the nonlinear characteristics of the magnitude-frequency relation are discussed and the formulation is revised. Also, one example of the variance of bq estimated based on the recent New Zealand catalogue is enumerated.

Load-sharing Characteristic of Multiple Pinions Driving in Tunneling Boring Machine

The failure of the key parts, such as gears, in cutter head driving system of tunneling boring machine has not been properly solved under the interaction of driving motors asynchronously and wave tunneling torque load. A dynamic model of multi-gear driving system is established considering the inertia effects of driving mechanism and cutter head as well as the bending-torsional coupling. By taking into account the nonlinear coupling factors between ring gear and multiple pinions, the influence for meshing angle by bending-torsional coupling and the dynamic load-sharing characteristic of multiple pinions driving are analyzed. Load-sharing coefficients at different rotating cutter head speeds and input torques are presented. Numerical results indicate that the load-sharing coefficients can reach up to 1.2-1.3. A simulated experimental platform of the multiple pinions driving is carried out and the torque distributions under the step load in driving shaft of pinions are measured. The imbalance of torque distribution of pinions is verified and the load-sharing coefficients in each pinion can reach 1.262. The results of simulation and test are similar, which shows the correctness of theoretical model. A loop coupling control method is put forward based on current torque master slave control method. The imbalance of the multiple pinions driving in cutter head driving system of tunneling boring machine can be greatly decreased and the load-sharing coefficients can be reduced to 1.051 by using the loop coupling control method. The proposed research provides an effective solution to the imbalance of torque distribution and synchronous control method for multiple pinions driving of TBM.

Realization of high-performance tri-layer graphene saturable absorber mirror fabricated via a one-step transfer process

Graphene,as a saturable absorber(SA),has attracted much attention for its application in ultrashort pulse fiber lasers due to its ultrafast interband carrier relaxation and ultra-broadband wavelength operation.Nevertheless,during the stacking process of monolayer graphene layer,the induced nonuniform contact at the interface of graphene layers deteriorate the device performance.Herein,we report the fabrication of graphene saturable absorber mirrors(SAMs)via a one-step transfer process and the realization of the much enlarged modulation depth and the much reduced nonsaturable loss with tri-layer graphene(TLG)than single-layer graphene(SLG)due to the improved uniform contact at the interface.Moreover,the operation of 1550 nm mode-locked Er-doped fiber laser with the TLG SAM exhibits excellent output characteristics of the maximum output power of 9.9 mW,a slope efficiency of 2.4%and a pulse width of 714 fs.Our findings are expected to pave the way toward high-performance ultrashort pulse fiber lasers based on graphene SAs.

Dynamic Analysis Model of Embedded Fluid Elastomeric Damper for Bearingless Rotor

According to the structural characteristics of embedded fluid elastomeric damper and dynamic modeling method of bearingless rotor(BR)system,a time-domain dynamic model based on multilayer elastomeric theory and fluid dynamic equations is developed.The parameters contained in the analysis model are identified by dynamic experiment data of embedded fluid elastomeric damper.The dynamic characteristics curves calculated through dynamic model are compared with those derived from experimental data.The consistent results illustrate that the model can describe the nonlinear relationship between stress and strain of embedded fluid elastomeric damper under different displacement amplitude and frequency.Due to the validity and reliability of the dynamic analysis model,it can be used in aeroelastic characteristics calculation of BR with embedded fluid elastomeric damper for helicopters.

Linear polarization holography

Polarization holography is a newly researched field,that has gained traction with the development of tensor theory.It primarily focuses on the interaction between polarization waves and photosensitive materials.The extraordinary capabil-ities in modulating the amplitude,phase,and polarization of light have resulted in several new applications,such as holo-graphic storage technology,multichannel polarization multiplexing,vector beams,and optical functional devices.In this paper,fundamental research on polarization holography with linear polarized wave,a component of the theory of polariz-ation holography,has been reviewed.Primarily,the effect of various polarization changes on the linear and nonlinear po-larization characteristics of reconstructed wave under continuous exposure and during holographic recording and recon-struction have been focused upon.The polarization modulation realized using these polarization characteristics exhibits unusual functionalities,rendering polarization holography as an attractive research topic in many fields of applications.This paper aims to provide readers with new insights and broaden the application of polarization holography in more sci-entific and technological research fields.