The energy response of LaBr_(3)(Ce),LaBr_(3)(Ce,Sr),and NaI(Tl)crystals for GECAM

The GECAM series of satellites utilizes LaBr_(3)(Ce),LaBr_(3)(Ce,Sr),and NaI(Tl)crystals as sensitive materials for gamma-ray detectors(GRDs).To investigate the nonlinearity in the detection of low-energy gamma rays and address the errors in the calibration of the E-C relationship,comprehensive tests and comparative studies of the three aforementioned crystals were conducted using Compton electrons,radioactive sources,and mono-energetic X-rays.The nonlinearity test results of the Compton electrons and X-rays demonstrated substantial differences,with all three crystals presenting a higher nonlinearity for X/-rays than for Compton electrons.Despite the LaBr_(3)(Ce)and LaBr_(3)(Ce,Sr)crystals having higher absolute light yields,they exhibited a noticeable nonlinear decrease in the light yield,especially at energies below 400 keV.The NaI(Tl)crystal demonstrated an"excess"light output in the 6-200 keV range,reaching a maximum"excess"of 9.2%at 30 keV in the X-ray testing and up to 15.5%at 14 keV during Compton electron testing,indicating a significant advantage in the detection of low-energy gamma rays.Furthermore,we explored the underlying causes of the observed nonlinearity in these crystals.This study not only elucidates the detector responses of GECAM,but also initiates a comprehensive investigation of the nonlinearity of domestically produced lanthanum bromide and sodium iodide crystals.

Nonlinear current response and electric quantum oscillations in the Dirac semimetal Cd_(3)As_(2)

Chiral anomaly is a distinct quantum anomaly associated with chiral fermions in Dirac or Weyl semimetals.The use of negative magnetoresistance(negative MR)as a signature for this anomaly remains contentious,as trivial mechanisms such as current jetting and weak localization can also induce negative MR.In this study,we report a novel nonlinear behavior of the chiral anomaly in the longitudinal direction,which we observed by applying parallel current and magnetic field to the Dirac semimetal Cd_(3)A_(s_(2)).This nonlinear characteristic peaks at an intermediate magnetic field of approximately5 T,displaying a resistance-increasing property concomitant with strengthening of the current source.Through angledependence experiments,we were able to rule out trivial factors,such as thermal effects,geometric artifacts,and anisotropy.Furthermore,additional electric quantum oscillations were observed when the direct current(DC)was applied as high as300μA.Such an unusual phenomenon is ascribed to the formation of quantized levels due to Bloch oscillation in the high DC regime,suggesting that an oscillatory density distribution may arise as the electric field increases.The non-Ohmic electric quantum oscillations open a new avenue for exploring chiral anomaly and other nontrivial topological properties,which is also one of the salient features of nonequilibrium steady states in condensed matter physics.

Tool Condition Monitoring Based on Nonlinear Output Frequency Response Functions and Multivariate Control Chart

Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significant damage to workpieces and reduce manufacturing costs.Recently,an innovative TCM approach based on sensor data modelling and model frequency analysis has been proposed.Different from traditional signal feature-based monitoring,the data from sensors are utilized to build a dynamic process model.Then,the nonlinear output frequency response functions,a concept which extends the linear system frequency response function to the nonlinear case,over the frequency range of the tooth passing frequency of the machining process are extracted to reveal tool health conditions.In order to extend the novel sensor data modelling and model frequency analysis to unsupervised condition monitoring of cutting tools,in the present study,a multivariate control chart is proposed for TCM based on the frequency domain properties of machining processes derived from the innovative sensor data modelling and model frequency analysis.The feature dimension is reduced by principal component analysis first.Then the moving average strategy is exploited to generate monitoring variables and overcome the effects of noises.The milling experiments of titanium alloys are conducted to verify the effectiveness of the proposed approach in detecting excessive flank wear of solid carbide end mills.The results demonstrate the advantages of the new approach over conventional TCM techniques and its potential in industrial applications.

Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions

A novel vibration isolation device called the nonlinear energy sink(NES)with NiTiNOL-steel wire ropes(NiTi-ST)is applied to a whole-spacecraft system.The NiTi-ST is used to describe the damping of the NES,which is coupled with the modified Bouc-Wen model of hysteresis.The NES with NiTi-ST vibration reduction principle uses the irreversibility of targeted energy transfer(TET)to concentrate the energy locally on the nonlinear oscillator,and then dissipates it through damping in the NES with NiTi-ST.The generalized vibration transmissibility,obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions(NOFRFs),is first used as the evaluation index to analyze the whole-spacecraft system in the future.An optimization analysis of the impact of system responses is performed using different parameters of NES with NiTi-ST based on the transmissibility of NOFRFs.Finally,the effects of vibration suppression by varying the parameters of NiTi-ST are analyzed from the perspective of energy absorption.The results indicate that NES with NiTi-ST can reduce excessive vibration of the whole-spacecraft system,without changing its natural frequency.Moreover,the NES with NiTi-ST can be directly used in practical engineering applications.

GLOBAL ASYMPTOTICAL PROPERTIES FOR A DIFFUSED HBV INFECTION MODEL WITH CTL IMMUNE RESPONSE AND NONLINEAR INCIDENCE

This article proposes a diffused hepatitis B virus （HBV） model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.

Accuracy of three-dimensional seismic ground response analysis in time domain using nonlinear numerical simulations

To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the Open Sees simulation platform. The standard mesh of a three-dimensional soil column was suggested to be satisfied with the specified maximum frequency. The layered soil column was divided into multiple sub-soils with a different viscous damping matrix according to the shear velocities as the soil properties were significantly different. It was necessary to use a combination of other one-dimensional or three-dimensional nonlinear seismic ground analysis programs to confirm the applicability of nonlinear seismic ground motion response analysis procedures in soft soil or for strong earthquakes. The accuracy of the three-dimensional soil column finite element method was verified by dynamic centrifuge model testing under different peak accelerations of the earthquake. As a result, nonlinear seismic ground motion response analysis procedures were improved in this study. The accuracy and efficiency of the three-dimensional seismic ground response analysis can be adapted to the requirements of engineering practice.

ANALYSIS OF NONLINEAR DYNAMIC RESPONSE FOR VISCOELASTIC COMPOSITE PLATE WITH TRANSVERSE MATRIX CRACKS

Based on the Schapery three-dimensional viscoelastic constitutive relationship with growing damage, a damage model with transverse matrix cracks for the unidirectional ?bre rein- forced viscoelastic composite plates is developed. By using Karman theory, the nonlinear dynamic governing equations of the viscoelastic composite plates under transverse periodic loading are es- tablished. By applying the ?nite di?erence method in spatial domain and the Newton-Newmark method in time domain, and using the iterative procedure, the integral-partial di?erential gov- erning equations are solved. Some examples are given and the results are compared with available data.

Heave-Roll-Pitch Coupled Nonlinear Internal Resonance Response of a Spar Platform Considering Wave and Vortex Exciting Loads

Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model.In fact,in addition to the heave and pitch which are in one plane,the nonlinear unstable motion will also occur in roll.From the results of the experiments,the unstable roll motion plays a dominant role in the motion of a spar platform which is much stronger than that of pitch.The objective of this paper is to study 3-DOF coupling response performance of spar platform under wave and vortex-induced force.The nonlinear coupled equations in heave,roll and pitch are established by considering time-varying wet surface and coupling.The first order steady-state response is solved by multi-scales method when the incident wave frequency approaches the heave natural frequency.Numerical integration of the motion equations has been performed to verify the first-order perturbation solution.The results are confirmed by model test.There is a saturation phenomenon associated with heave mode in 3-DOF systems and all extra energy is transferred to roll and pitch.It is observed that sub-harmonic response occurs in roll and pitch when the wave force exceeds a certain value.The energy distribution in roll and pitch is determined by the initial value and damping characteristics of roll and pitch.The energy transfers from heave to pitch and then transfers from pitch to roll.Due to the influence of the low-frequency vortex-excited force,the response of roll is more complicated than that of pitch.

Nonlinear magneto-electric response of a giant magnetostrictive/piezoelectric composite cylinder

In this study, we investigate the nonlinear cou- pling magneto-electric （ME） effect of a giant magnetostric- tive/piezoelectric composite cylinder. The nonlinear consti- tutive relations of the ME material are taken into account, and the influences of the nonlinear material properties on the ME effect are investigated for the static and dynamic cases, respectively. The influences of different constraint conditions on the ME effect are discussed. In the dynamic case considering nonlinear material properties, the double frequency ME response （The response frequency is twice the applied magnetic frequency） is obtained and discussed, which can be used to explain the experiment phenomenon in which the input signal with frequency f is converted to the output signal with 2f in ME laminated structures. Some calculations on nonlinear ME effect are conducted. The obtained results indicate that the nonlinear material properties affect not only the magnitude of the ME effect in the static case but also the ME response frequency in the dynamic case

Probabilistic analysis for the response of nonlinear base isolation system under the ground excitation induced by high dam flood discharge

According to theoretical analysis, a general characteristic of the ground vibration induced by high dam flood discharge is that the dominant frequency ranges over several narrow frequency bands, which is verified by observations from the Xiangjiaba Hydropower Station. Nonlinear base isolation is used to reduce the structure vibration under ground excitation and the advantage of the isolation application is that the low-frequency resonance problem does not need to be considered due to its excitation characteristics, which significantly facilitate the isolation design. In order to obtain the response probabilistic distribution of a nonlinear system, the state space split technique is modified. As only a few degrees of freedom are subjected to the random noise, the probabilistic distribution of the response without involving stochastic excitation is represented by the δ function. Then, the sampling property of the δ function is employed to reduce the dimension of the Fokker-Planck-Kolmogorov （FPK） equation and the low-dimensional FPK equation is solvable with existing methods. Numerical results indicate that the proposed approach is effective and accurate. Moreover, the response probabilistic distributions are more reasonable and scientific than the peak responses calculated by conventional time and frequency domain methods.

Orthogonal expansion of ground motion and PDEM-based seismic response analysis of nonlinear structures

This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.

A time-domain nonlinear effective-stress non-Masing approach of ground response analysis of Guwahati city, India

The response of subsoil strata subjected to seismic excitations plays an important role in governing the response of the overlying superstructures at any site. Ground response analysis(GRA) helps to assess the influence of soil characteristics on the propagating seismic stress waves from the bedrock level to the ground surface during an earthquake. For the northeastern region of India, located in the highest seismic zone in the country, conducting an extensive GRA study is of prime importance. Conventionally, most of the GRA studies are carried out using the equivalent linear method, which, being a simplistic approach, cannot capture the nonlinear behavior of soil during seismic shaking. This paper presents the outcomes of a one-dimensional effective stress based nonlinear GRA conducted for Guwahati city(located in northeast India) incorporating the non-Masing load/unload/reload characteristics. The various ground response parameters evaluated from this study help in assessing the ground shaking, soil amplification, and site responses expected in this region. 2D contour maps, which are representative of the distribution of some of these parameters throughout Guwahati city, are also developed. The results presented herein can serve as guidelines for the design of foundations and superstructures in this region.

Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.

Effective AC response of a nonlinear spherical coated composite

An effective nonlinear response of a nonlinear composite with spherical coated inclusions randomly embedded in a host medium under the action of an external AC electric field, Ea= E1 sin（wt） ＋ E3 sin（3wt）, is investigated using a perturbation method. The local potentials of the composite at higher harmonics are given both in the region of local inclusion particles and in the local host region under the external AC electric field. All effective nonlinear responses of the composite and the relationship between the effective nonlinear responses at the fundamental frequency and third harmonics are also studied for spherical coated inclusion in a dilute limit.

Nonlinear Modeling and Identification of Structural Joint by Response Control Vibration Test

Components of mechanical product are assembled by structural joints,such as bolting,riveting,welding,etc.Structural joints introduce nonlinearity to some engineering structures,and the nonlinearity need to be modeled precisely.To meet serious quality requirements,it is necessary to detect and identify nonlinearity of mechanical products for structural optimization.Modal test to acquire a dynamic response has been applied for decades,which provides reliable results for finite element(FE)model updating.Here response control vibration test for identification of nonlinearity is presented.A nonlinear system can be regarded as linearity for particular steady state response,and classical linear analysis tool is applicable to extract modal data for particular response.First,its applicability is illustrated by some numerical simulations.Subsequently,it is implemented on experimental setup with structural joints by shaking table.The stiffness and damping function dependent of relative displacement are fitted to describe its inherent nonlinearity.The spring and damping forces are identified by harmonic balance method(HBM)to predict output response.Based on the identified results,the procedure is recommended that it allows a reliable measurement of nonlinearity with a certain accuracy.

The role of soil in structure response of a building damaged by the 26 December 2018 earthquake in Italy

Local soil conditions can significantly modify the seismic motion expected on the soil surface.In most cases,the indications concerning the influence of the underlying soil provided by the in-force European and Italian Building Codes underestimate the real seismic amplification effects.For this reason,numerical analyses of the local seismic response(LSR)have been encouraged to estimate the soil filtering effects.These analyses are generally performed in free-field conditions,ignoring the presence of superstructures and,therefore,the effects of dynamic soil-structure interaction(DSSI).Moreover,many studies on DSSI are characterised by a sophisticated modelling of the structure and an approximate modelling of the soil(using springs and dashpots at the foundation level);while others are characterised by a sophisticated modelling of the soil and an approximate modelling of the structure(considered as a simple linear elastic structure or a single degree of freedom system).This paper presents a set of finite element method(FEM)analyses on a fully-coupled soil-structure system for a reinforced concrete building located in Fleri(Catania,Italy).The building,designed for gravity loads only,was severely damaged during the 26 December 2018 earthquake.The soil was modelled considering an equivalent visco-elastic behaviour,while the structure was modelled assuming both the visco-elastic and visco-inelastic behaviours.The comparison made between the results of the FEM analyses and the observed damage is valuable.

Effectof Film Force Nonlinearity on Unbalance Responseof a Jeffcot RotorJournal Bearing System

The effect of oil film force nonlinearity on unbalance response of Jeffcot rotor elliptical bearing system is studied. Linear analysis is done by linearizing the bearing oil film dynamic forces and expressing them with stiffness and damping constants. Nonlinear dynamic simulation is done by taking the nonlinearity of bearing oil film dynamic force into full consideration, with the latter being expressed by a special database which is generated beforehand, and based on non stationary Reynolds equation and Reynolds boundary condition of film rupture. The linear and nonlinear unbalance responses of a Jeffcot rotor supported on a pair of elliptical bearings is studied. The resulting dynamic characteristics and rotor and journal whirling orbits are compared. While good consistancy between nonlinear and linear predictions is found under very small unbalance, significant or even drastic differences are found whenever the unbalance is not small, indicating the necessity of including the nonlinearity of oil film dynamic forces, especially when response to large unbalance is to be predicted.

Effect of nonlinear soil-structure interaction on seismic response of low-rise SMRF buildings

The nonlinear behavior of a soil-foundation system may alter the seismic response of a structure by providing additional flexibility to the system and dissipating hysteretic energy at the soil-foundation interface. However, the current design practice is still reluctant to consider the nonlinearity of the soil-foundation system, primarily due to lack of reliable modeling techniques. This study is motivated towards evaluating the effect of nonlinear soil-structure interaction （SSI） on the seismic responses of low-rise steel moment resisting frame （SMRF） structures. In order to achieve this, a Winkler- based approach is adopted, where the soil beneath the foundation is assumed to be a system of closely-spaced, independent, nonlinear spring elements. Static pushover analysis and nonlinear dynamic analyses are performed on a 3-story SMRF building and the performance of the structure is evaluated through a variety of force and displacement demand parameters. It is observed that incorporation of nonlinear SSI leads to an increase in story displacement demand and a significant reduction in base moment, base shear and inter-story drift demands, indicating the importance of its consideration towards achieving an economic, yet safe seismic design.

STEADY-STATE RESPONSES AND THEIR STABILITY OF NONLINEAR VIBRATION OF AN AXIALLY ACCELERATING STRING

The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.

Nonlinear dynamic response of beam and its application in nanomechanical resonator

Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application. Two categories of the tension-dominant and curvaturedominant nonlinearities are analyzed. The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach. The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity, its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects. However, for the nanomechanical resonator of the curvature-dominant nonlinearity, its dynamic nonlinearity is only dependent on axial loading. Compared with the tension-dominant nonlinearity, the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity