Experimental study on failure characteristics of single-sided unloading rock under different intermediate principal stress conditions

Investigation of unloading rock failure under differentσ_(2)facilitates the control mechanism of excavation surrounding rock.This study focused on single-sided unloading tests of granite specimens under true triaxial conditions.The strength and failure characteristics were studied with micro-camera and acoustic emission(AE)monitoring.Furthermore,the choice of test path and the effect ofσ_(2)on fracture of unloading rock were discussed.Results show that the increasedσ_(2)can strengthen the stability of single-sided unloading rock.After unloading,the rock’s free surface underwent five phases,namely,inoculation,particle ejection,buckling rupture,stable failure,and unstable rockburst phases.Moreover,atσ_(2)≤30 MPa,the b value shows the following variation tendency:rising,dropping,significant fluctuation,and dropping,with dispersed damages signal.Atσ_(2)≥40 MPa,the tendency shows:a rise,a decrease,a slight fluctuation,and final drop,with concentrated damages signal.After unloading,AE energy is mainly concentrated in the micro-energy range.With the increasedσ_(2),the micro-energy ratio rises.In contrast,low,medium and large energy ratios drop gradually.The increased tensile fractures and decreased shear fractures indicate that the failure mode of the unloading rock gradually changes from tensile-shear mode to tensile-split one.The fractional dimension of the rock fragments first increases and then decreases with an inflection point at 20 MPa.The distribution of SIF on the planes changes asσ_(2)increases,resulting in strengthening and then weakening of the rock bearing capacity.

Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method

In this paper,the bifurcation properties of the vibro-impact systems with an uncertain parameter under the impulse and harmonic excitations are investigated.Firstly,by means of the orthogonal polynomial approximation(OPA)method,the nonlinear damping and stiffness are expanded into the linear combination of the state variable.The condition for the appearance of the vibro-impact phenomenon is to be transformed based on the calculation of themean value.Afterwards,the stochastic vibro-impact systemcan be turned into an equivalent high-dimensional deterministic non-smooth system.Two different Poincarésections are chosen to analyze the bifurcation properties and the impact numbers are identified for the periodic response.Consequently,the numerical results verify the effectiveness of the approximation method for analyzing the considered nonlinear system.Furthermore,the bifurcation properties of the system with an uncertain parameter are explored through the high-dimensional deterministic system.It can be found that the excitation frequency can induce period-doubling bifurcation and grazing bifurcation.Increasing the randomintensitymay result in a diffusion-based trajectory and the impact with the constraint plane,which induces the topological behavior of the non-smooth system to change drastically.It is also found that grazing bifurcation appears in advance with increasing of the random intensity.The stronger impulse force can result in the appearance of the diffusion phenomenon.

Characteristics Investigation of Single-Sided Ironless PMLSM Based on Halbach Array for Medium-Speed Maglev Train

This paper investigates characteristics of ironless permanent magnet linear synchronous motor(PMLSM)based on Halbach array used for medium-speed(200km/h)maglev train.Long primary ironless coil is laid in the middle of track and the Halbach permanent magnet array is attached to the bottom of each bogie as a source of traction,U-shape electromagnets at the both sides of the train for levitation.Two dimensional analytical model of single-sided ironless PMLSM based on Halbach array is established,using linear overlay method,the no-load air gap magnetic field is calculated firstly,winding current density distribution is obtained for calculating the characteristics of thrust and normal force against power angle,including force characteristics with equal and unequal pole pitch,the influence of steel sleeper,etc.Besides,the mathematical model for this type motor is built by 3D finite element method,the traction characteristics of medium-speed maglev under maximum speed 200km/h are calculated.The characteristics of this type motor are satisfactory owing to there is no detent force in the motor and thrust force reach maximum meanwhile normal force can be eliminated.Calculation method is verified by comparing finite element results,experimental result on a 200kW type motor further validates the accuracy of calculation and some important conclusions are obtained.

Adaptive current compensation with nonlinear disturbance observer for single-sided linear induction motor considering dynamic eddy-effect

An adaptive current compensation control for a single-sided linear induction motor(SLIM) with nonlinear disturbance observer was developed. First, to maintain t-axis secondary component flux constant with consideration of the specially dynamic eddy-effect(DEE) of the SLIM, a instantaneously tracing compensation of m-axis current component was analyzed. Second,adaptive current compensation based on Taylor-discretization algorithm was proposed. Third, an effective kind of nonlinear disturbance observer(NDOB) was employed to estimate and compensate the undesired load vibrations, then the robustness of the control system could be guaranteed. Experimental verification of the feasibility of the proposed method for an SLIM control system was performed, and it showed that the proposed adaptive compensation scheme with NDOB could significantly promote speed dynamical response and minimize speed ripple under the conditions of external load coupled vibrations and unavoidable feedback control variables measured errors, i.e., current and speed.

PERIODIC VIBRO-IMPACTS AND THEIR STABILITY OF A DUAL COMPONENT SYSTEM

The coexisting periodic impacting motions and their multiplicity of a kind of dual component systems under harmonic excitation are analytically derived. The stability condition of a periodic impacting motion is given by analyzing the propagation of small, arbitrary perturbation from that motion. In numerical simulations, the periodic impacting motions are classified according to the system states before and after an impact. The numerical results show that there exist many types of vibro-impacts and the bifurcation of periodic vibro-impacts is not smooth.

Hopf-flip bifurcation of high dimensional maps and application to vibro-impact systems

This paper addresses the problem of Hopf-flip bifurcation of high dimensional maps. Using the center manifold theorem, we obtain a three dimensional reduced map through the projection technique. The reduced map is further transformed into its normal form whose coefficients are determined by that of the original system. The dynamics of the map near the Hopf-flip bifurcation point is approximated by a so called “time-2τ^2 map” of a planar autonomous differential equation. It is shown that high dimensional maps may result in cycles of period two, tori T^1 （Hopf invariant circles）, tori 2T^1 and tori 2T^2 depending both on how the critical eigenvalues pass the unit circle and on the signs of resonant terms＇ coefficients. A two-degree-of-freedom vibro-impact system is given as an example to show how the procedure of this paper works. It reveals that through Hopf-flip bifurcations, periodic motions may lead directly to different types of motion, such as subharmonic motions, quasi-periodic motions, motions on high dimensional tori and even to chaotic motions depending both on change in direction of the parameter vector and on the nonlinear terms of the first three orders.

Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops

A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole impact process, the Poincare map of the system is constructed. Using the Poincare map and the Gram Schmidt orthonormalization, a method of calculating the spectrum of Lyapunov exponents of the above vibro-impact system is presented. Then the phase portraits of periodic and chaotic attractors for the system and the corresponding convergence diagrams of the spectrum of Lyapunov exponents are given out through the numerical simulations. To further identify the validity of the aforementioned computation method, the bifurcation diagram of the system with respect to the bifurcation parameter and the corresponding largest Lyapunov exponents are shown.

Analysis of force and energy density transferred to barrier in a single degree of freedom vibro-impact system

A mass-spring-damper linear oscillator with a limiting stop barrier is presented. Modeling non-smooth processes in mechanical engineering is a complex problem. It is especially for the systems with more than a single degree of freedom. But recent studies in dynamical systems have been applied to single degree of freedom systems. The vibrating system, consisting of an oscillator with amplitude of motion limited by a barrier, is known as a vibro-impact system. The amount of force and kinetic energy transferred to a barrier has an important application in designing of engineering systems that undergo the vibro-impact phenomenon. The results show the effect of changing restitution coefficient of a barrier on the amount of force and energy absorbed.

Multi-valued responses and dynamic stability of a nonlinear vibro-impact system with a unilateral non-zero offset barrier

In this paper, multi-valued responses and dynamic properties of a nonlinear vibro-impact system with a unilateral nonzero offset barrier are studied. Based on the Krylov-Bogoliubov averaging method and Zhuravlev non-smooth trans- formation, the frequency response, stability conditions, and the equation of backbone curve are derived. Results show that in some conditions impact system may have two or four steady-state solutions, which are interesting and not mentioned for a vibro-impact system with the existence of frequency island phenomena. Then, the classification of the steady-state solutions is discussed, and it is shown that the nontrivial steady-state solutions may lose stability by saddle node bifurcation and Hopf bifurcation. Furthermore, a criterion for avoiding the jump phenomenon is derived and verified. Lastly, it is found that the distance between the system＇s static equilibrium position and the barrier can lead to jump phenomenon under hardening type of nonlinearity stiffness.

Stochastic responses of Duffing–Van der Pol vibro-impact system under additive colored noise excitation

A response analysis procedure is developed for a vibro-impact system excited by colored noise. The non-smooth transformation is used to convert the vibro-impact system into a new system without impact term. With the help of the modified quasi-conservative averaging, the total energy of the new system can be approximated as a Markov process, and the stationary probability density function （PDF） of the total energy is derived. The response PDFs of the original system are obtained using the analytical solution of the stationary PDF of the total energy. The validity of the theoretical results is tested through comparison with the corresponding simulation results. Moreover, stochastic bifurcations are also explored.

Dynamical behaviour of a controlled vibro-impact system

In this paper, we give a controlled two-degree-of-freedom （TDOF） vibro-impact system based on the damping control law, and then investigate the dynamical behaviour of this system. According to numerical simulation, we find that this control scheme can suppress chaos to periodic orbit successfully. Furthermore, the feasibility and the robustness of the controller are confirmed, separately. We also find that this scheme cannot only suppress chaos, but also generate chaos in this system.

Optimization for vibro-impact nonlinear energy sink under randomexcitation

As a promising vibration control device, the vibro-impact nonlinear energy sink (VI-NES) gathered extensively attention in recent years. However, general optimization procedures have not been available forthe design of VI-NES subjected to random excitations. To this end, this paper constitutes a research effortto address this gap. Specifically, the approximate analytical solution of the system stochastic responseis obtained in conjunction with non-smooth conversion and stochastic averaging methodology. Takingadvantages of this approximate solution, the variance of the system is defined and easily minimized tocalculate the optimal parameters for VI-NES. In addition, the results computed by this way fairly correlatewith direct numeric simulations.

COEXISTING PERIODIC ORBITS IN VIBRO-IMPACTING DYNAMICAL SYSTEMS

A method is presented to seek for coexisting periodic orbits which may be stable or unstable in piecewise-linear vibro-impacting systems. The conditions for coexistence of single impact periodic orbits are derived, and in particular, it is investigated in details how to assure that no other impacts will happen in an evolution period of a single impact periodic motion. Furthermore, some criteria for nonexistence of single impact periodic orbits with specific periods are also established. Finally, the stability of coexisting periodic orbits is discussed, and the corresponding computation formula is given. Examples of numerical simulation are in good agreement with the theoretic analysis.

Resonance response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random parametric excitation

The resonant response of a single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to a narrow-band random parametric excitation is investigated. The narrow-band random excitation used here is a bounded random noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, thereby permitting the applications of random averaging over ＂fast＂ variables. The averaged equations are solved exactly and an algebraic equation of the amplitude of the response is obtained for the ease without random disorder. The methods of linearization and moment are used to obtain the formula of the mean-square amplitude approximately for the case with random disorder. The effects of damping, detuning, restitution factor, nonlinear intensity, frequency and magnitude of random excitations are analysed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak response amplitudes will reduce at large damping or large nonlinear intensity and will increase with large amplitude or frequency of the random excitations. The phenomenon of stochastic jump is observed, that is, the steady-state response of the system will jump from a trivial solution to a large non-trivial one when the amplitude of the random excitation exceeds some threshold value, or will jump from a large non-trivial solution to a trivial one when the intensity of the random disorder of the random excitation exceeds some threshold value.

Stationary response of colored noise excited vibro-impact system

The generalized cell mapping(GCM) method is used to obtain the stationary response of a single-degree-of-freedom.Vibro-impact system under a colored noise excitation. In order to show the advantage of the GCM method, the stochastic averaging method is also presented. Both of the two methods are tested through concrete examples and verified by the direct numerical simulation. It is shown that the GCM method can well predict the stationary response of this noise-perturbed system no matter whether the noise is wide-band or narrow-band, while the stochastic averaging method is valid only for the wide-band noise.

Low-field, high-gradient NMR shows diffusion contrast consistent with localization or motional averaging of water near surfaces

Nuclear magnetic resonance(NMR)measurements of water diffusion have been extensively used to probe microstructure in porous materials,such as biological tissue,however primarily using pulsed gradient spin echo(PGSE)methods.Low-field single-sided NMR systems have built-in static gradients(SG)much stronger than typical PGSE maximum gradient strengths,which allows for the signal attenuation at extremely high b-values to be explored.Here,we perform SG spin echo(SGSE)and SG stimulated echo(SGSTE)diffusion measurements on biological cells,tissues,and gels.Measurements on fixed and live neonatal mouse spinal cord,lobster ventral nerve cord,and starved yeast cells all show multiexponential signal attenuation on a scale of b with significant signal fractions observed at b×Do>1 with b as high as 400 ms/um2.These persistent signal fractions trend with surface-to-volume ratios for these systems,as expected from porous media theory.An exception found for the case of fixed vs.live spinal cords was attributed to faster exchange or permeability in live spinal cords than in fixed spinal cords on the millisecond timescale.Data suggests the existence of multiple exchange processes in neural tissue,which may be relevant to the modeling of time-dependent diffusion in gray matter.The observed multi-exponential attenuation is from protons on water and not macromolecules because it remains proportional to the normalized signal when a specimen is washed with D20.The signal that persists to b×Do>1 is also drastically reduced after delipidation,indicating that it originates from lipid membranes that restrict water diffusion.The multiexponential or stretched exponential character of the signal attenuation at b×Do>1 appears mono-exponential when viewed on a scale of(b×Do)/3,suggesting it may originate from localization or motional averaging of water near membranes on sub-micron length scales.To try to disambiguate these two contributions,signal attenuation curves were compared at varying temperatures.While the curves align when normalizing them using the localization length scale,they separate on a motional averaging length scale.This supports localization as the source of non-Gaussian displacements,but this interpretation is still provisional due to the possible confounds of heterogeneity,exchange,and relaxation.Measurements on two types of gel phantoms designed to mimic extracellular matrix.one with charged functional groups synthesized from polyacrylic acid(PAC)and another with uncharged functional groups synthesized from polyacrylamide(PAM),both exhibit signal at b×Do>1,potentially due to water interacting with macromolecules.These preliminary finding motivate future research into contrast and attenuation mechanisms in tissue with low-field,high-gradient NMR。

带刚性限位的双层隔振系统的离散随机模型

研究由多刚体组成的带刚性限位的双层隔振系统,对其冲击后受到周期性外激励和低强度噪声扰动共同作用下可能会产生的碰撞进行了分析.基于单向约束多体动力学理论,导出了此隔振系统的最大Poincar啨映射,建立了其冲击后的零次近似随机离散模型和一次近似随机离散模型.通过对一MTU公司的柴油机隔振系统冲击作用后振动响应的调查指出,由于可能发生间歇性碰撞,该系统呈现复杂的非线性特性.零次近似模型和一次近似模型有较大的区别,低强度的噪声也会对系统产生较大的影响.得到的结果对如何正确设计带刚性限位的双层隔振系统提供了理论参考依据.

单边核磁共振传感器研究及其应用

单边核磁共振(single-sided NMR)传感器具有体积小、造价低和结构开放等特点,特别适用于大型样品的现场无损检测,具有广阔的应用前景.该文介绍了一种均匀度较高的单边核磁共振传感器,在10 mm×10 mm的水平目标区域内,静态磁场均匀度为338×10–6,在垂直方向上静态磁场具有4.6 T/m的恒定梯度.结合该磁场分布的梯度特性,提出了一种基于快速傅里叶变换和带通滤波处理的回波信号处理方法,可提取薄层样品的核磁共振信号,从而实现对样品纵深方向的高分辨率一维测量(分辨率达到50?m).最后使用该传感器对复合绝缘子高分子聚合物、液体的扩散行为,以及植物叶片的枯萎过程进行了测量.展现了该方法在高分子材料分析、液体测量以及农业应用方面的潜力.

QUASI-PERIODIC AND CHAOTIC BEHAVIOUR OF A TWO-DEGREE-OF-FREEDOM IMPACT SYSTEM IN A STRONG RESONANCE CASE

A two-degree-of-freedom system contacting a single stop isconsidered. Quasi-periodic and chaotic behavior of the system in astrong resonance case is investigated by theoretical analysis andnumerical simulation.

RESEARCH IN STABILITY OF PERIODIC MOTION,BIFURCATION AND CHAOS IN A VIBRATORY SYSTEM WITH A CLEARANCE

A two-degrees-of-freedom vibratory system with a clearance or gap is under con- sideration based on the Poincaré map.Stability and local bifurcation of the period-one double- impact symmetrical motion of the system are analyzed by using the equation of map.The routes from periodic impact motions to chaos,via pitchfork bifurcation,period-doubling bifurcation and grazing bifurcation,are studied by numerical simulation.Under suitable system parameter con- ditions,Neimark-Sacker bifurcations associated with periodic impact motion can occur in the two-degrees-of-freedom vibro-impact system.