Equivalent linear model for seismic damage evaluation of single-degree-of-freedom systems representing reinforced concrete structures considering cyclic degradation behavior

In this study,a novel equivalent damping ratio model that is suitable for reinforced concrete(RC)structures considering cyclic degradation behavior is developed,and a new equivalent linearization analysis method for implementing the proposed equivalent damping ratio model for use in seismic damage evaluation is presented.To this end,Ibarra’s peak-oriented model,which incorporates an energy-based degradation rule,is selected for representing hysteretic behavior of RC structure,and the optimized equivalent damping for predicting the maximum displacement response is presented by using the empirical method,in which the effect of cyclic degradation is considered.Moreover,the relationship between the hysteretic energy dissipation of the inelastic system and the elastic strain energy of the equivalent linear system is established so that the proposed equivalent linear system can be directly integrated with the Park-Ang seismic model to implement seismic damage evaluation.Due to the simplicity of the equivalent linearization method,the proposed method provides an efficient and reliable way of obtaining comprehensive insight into the seismic performance of RC structures.The verification demonstrates the validity of the proposed method.

Deterioration of equivalent thermal conductivity of granite subjected to heating-cooling treatment

Understanding the thermal conductivity of granite is critical for many geological and deep engineering applications.The heated granite was subjected to air-,water-,and liquid nitrogen(LN2-)coolings in this context.The transient hot-wire technique was used to determine the equivalent thermal conductivity(ETC)of the granite before and after treatment.The deterioration mechanism of ETC is analyzed from the meso-perspective.Finally,the numerical model is used to quantitatively study the impact of cooling rate on the microcrack propagation and heat conduction characteristics of granite.The results show that the ETC of granite is not only related to the heating temperature,but also affected by the cooling rate.The ETC of granite decreases nonlinearly with increasing heating temperature.A faster cooling rate causes a greater decrease in ETC at the same heating temperature.The higher the heating temperature,the stronger the influence of cooling rate on ETC.The main explanation for the decrease in ETC of granite is the increase in porosity and microcrack density produced by the formation and propagation of pore structure and microcracks during heating and cooling.Further analysis displays that the damage of granite at the heating stage is induced by the difference in thermal expansion and elastic properties of mineral particles.At the cooling stage,the faster cooling rate causes a higher temperature gradient,which in turn produces greater thermal stress.As a result,it not only causes new cracks in the granite,but also aggravates the damage at the heating stage,which induces a further decrease in the heat conduction performance of granite,and this scenario is more obvious at higher temperatures.

An equivalent target plate damage probability calculation mathematics model and damage evaluation method

Aiming at the requirement of damage testing and evaluation of equivalent target plate based on the explosion of intelligent ammunition, this paper proposes a novel method for damage testing and evaluation method of circumferential equivalent target plate. Leveraging the dispersion characteristics parameters of fragment, we establish a calculation model of the fragment power situation and the damage calculation model under the condition of fragment ultimate penetration equivalent target plate. The damage model of equivalent target plate involves the fragment dispersion density, the local perforation damage criterion, the tearing damage model, and the damage probability. We use the camera to obtain the image of the equivalent target plate with fragment perforation, and research the algorithm of fragment distribution position recognition and fragment perforation area calculation method on the equivalent target plate by image processing technology. Based on the obtained parameters of the breakdown position and perforation area of fragments on equivalent target plate, we apply to damage calculation model of equivalent target plate, and calculate the damage probability of each equivalent target plate, and use the combined probabilistic damage calculation method to obtain the damage evaluation results of the circumferential equivalent target plate in an intelligent ammunition explosion experiment. Through an experimental testing, we verify the feasibility and rationality of the proposed damage evaluation method by comparison, the calculation results can reflect the actual damage effect of the equivalent target plate.

An efficient approach for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations

An efficient approach is proposed for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations.The concentrated plastic hinges,described by the Bouc-Wen model,are assumed to occur at the two ends of a linear-elastic beam element.The auxiliary differential equations governing the plastic rotational displacements and their corresponding hysteretic displacements are replaced with linearized differential equations.Then,the two sets of equations of motion for the original nonlinear system can be reduced to an expanded-order equivalent linearized equation of motion for equivalent linear systems.To solve the equation of motion for equivalent linear systems,the nonstationary random vibration analysis is carried out based on the explicit time-domain method with high efficiency.Finally,the proposed treatment method for initial values of equivalent parameters is investigated in conjunction with parallel computing technology,which provides a new way of obtaining the equivalent linear systems at different time instants.Based on the explicit time-domain method,the key responses of interest of the converged equivalent linear system can be calculated through dimension reduction analysis with high efficiency.Numerical examples indicate that the proposed approach has high computational efficiency,and shows good applicability to weak nonlinear and medium-intensity nonlinear systems.

An improved algorithm based on equivalent sound velocity profile method at large incident angle

With the development of ultra-wide coverage technology,multibeam echo-sounder(MBES)system has put forward higher requirements for localization accuracy and computational efficiency of ray tracing method.The classical equivalent sound speed profile(ESSP)method replaces the measured sound velocity profile(SVP)with a simple constant gradient SVP,reducing the computational workload of beam positioning.However,in deep-sea environment,the depth measurement error of this method rapidly increases from the central beam to the edge beam.By analyzing the positioning error of the ESSP method at edge beam,it is discovered that the positioning error increases monotonically with the incident angle,and the relationship between them could be expressed by polynomial function.Therefore,an error correction algorithm based on polynomial fitting is obtained.The simulation experiment conducted on an inclined seafloor shows that the proposed algorithm exhibits comparable efficiency to the original ESSP method,while significantly improving bathymetry accuracy by nearly eight times in the edge beam.

Analysis of secondary makeup characteristics of drill collar joint and prediction of downhole equivalent impact torque of Well SDTK1

Based on the three-dimensional elastic-plastic finite element analysis of the 8"(203.2 mm)drill collar joint,this paper studies the mechanical characteristics of the pin and box of NC56 drill collar joints under complex load conditions,as well as the downhole secondary makeup features,and calculates the downhole equivalent impact torque with the relative offset at the shoulder of internal and external threads.On the basis of verifying the correctness of the calculation results by using measured results in Well GT1,the prediction model of the downhole equivalent impact torque is formed and applied in the first extra-deep well with a depth over 10000 m in China(Well SDTK1).The results indicate that under complex loads,the stress distribution in drill collar joints is uneven,with relatively higher von Mises stress at the shoulder and the threads close to the shoulder.For 203.2 mm drill collar joints pre-tightened according to the make-up torque recommended by American Petroleum Institute standards,when the downhole equivalent impact torque exceeds 65 kN·m,the preload balance of the joint is disrupted,leading to secondary make-up of the joint.As the downhole equivalent impact torque increases,the relative offset at the shoulder of internal and external threads increases.The calculation results reveal that there exists significant downhole impact torque in Well SDTK1 with complex loading environment.It is necessary to use double shoulder collar joints to improve the impact torque resistance of the joint or optimize the operating parameters to reduce the downhole impact torque,and effectively prevent drilling tool failure.

The MDOF equivalent linear system and its applications in seismic analysis and design of framed structures

This paper reviews the applications of the multi degree-of-freedom(MDOF)equivalent linear system in seismic analysis and design of planar steel and reinforced concrete framed structures.An equivalent MDOF linear structure,analogous to the original MDOF nonlinear structure,is constructed,which has the same mass and elastic stiffness as the original structure and modal damping ratios that account for the effects of geometrical and material nonlinearities.The equivalence implies a balance between the viscous damping work of the equivalent linear structure and that of the nonlinearities in the original nonlinear structure.This work balance is established with the aid of a transfer function in the frequency domain.Thus,equivalent modal damping ratios can be explicitly determined in terms of the period and deformation levels of the structure as well as the soil types.Use of these equivalent modal damping ratios can help address a variety of seismic analysis and design problems associated with planar steel and reinforced concrete framed structures in a rational and accurate manner.These include force-based seismic design with the aid of acceleration response spectra characterized by high amounts of damping,improved direct displacement-based seismic design and the development of advanced seismic intensity measures.The equivalent modal damping ratios are also utilized in the context of linear modal analysis for the definition and construction of the MDOF response spectrum.Furthermore,the equivalent modal damping ratios are employed in a seismic retrofit method for steel-framed structures with viscous dampers.Finally,it is demonstrated that modal behavior(or strength reduction)factors can be easily constructed based on these modal damping ratios for a more rational and accurate force-based seismic design,including the determination of inelastic displacement profiles.

New text classification algorithm based on interdependence and equivalent radius

To improve the traditional classifying methods, such as vector space model （VSM）-based methods with highly complicated computation and poor scalability, a new classifying method （ called IER） is presented based on two new concepts： interdependence and equivalent radius. In IER, the attribute is selected according to the value of interdependence, and the classifying rule is based on equivalent radius and center of gravity. The algorithm analysis shows that IER is good at classifying a large number of samples with higher scalability and lower computation complexity. After several experiments in classifying Chinese texts, the conclusion is drawn that IER outperforms k-nearest neighbor （kNN） and classifcation based on the center of classes （CCC） methods, so IER can be used online to automatically classify a large number of samples while keeping higher precision and recall.

ROUTING AND WAVELENGTH ASSIGNMENT ALGORITHMS BASED ON EQUIVALENT NETWORKS

In this paper, a Wavelength Division Multiplexing (WDM) network model based on the equivalent networks is described, and wavelength-dependent equivalent arc, equivalent networks, equivalent multicast tree and some other terms are presented. Based on this model and relevant Routing and Wavelength Assign- ment (RWA) strategy, a unicast RWA algorithm and a multicast RWA algorithm are presented. The wave- length-dependent equivalent arc expresses the schedule of local RWA and the equivalent network expresses the whole topology of WDM optical networks, so the two algorithms are of the flexibility in RWA and the optimi- zation of the whole problem. The theoretic analysis and simulation results show the two algorithms are of the stronger capability and the lower complexity than the other existing algorithms for RWA problem, and the complexity of the two algorithms are only related to the scale of the equivalent networks. Finally, we prove the two algorithms’ feasibility and the one-by-one corresponding relation between the equivalent multicast tree and original multicast tree, and point out the superiorities and drawbacks of the two algorithms respectively.

Subsidence prediction method based on equivalent mining height theory for solid backfilling mining

Based on the characteristics of strata movement of solid backfilling mining technology, the surface subsidence prediction method based on the equivalent mining height theory was proposed, and the parameters selection guideline of this method was also described. While comparing the parameters of caving mining with equivalent height, the subsidence efficient can be calculated according to the mining height and bulk factor of sagging zone and fracture zone, the tangent of main influence angle of solid backfilling mining is reduced by 0.2-0.5（while it cannot be less than 1.0）. For sake of safety, offset of the inflection point is set to zero, and other parameters, such as horizontal movement coefficient and main propagation angle are equal to the corresponding parameters of caving mining with equivalent height. In the last part, a case study of solid backfilling mining subsidence prediction was described. The results show the applicability of this method and the difference of the maximum subsidence point between the prediction and the observation is less than 5%.

Effect of gas bubble on cell voltage oscillations based on equivalent circuit simulation in aluminum electrolysis cell

A method to investigate the effect of gas bubble on cell voltage oscillations was established. The whole aluminum electrolysis cell was treated as a resistance circuit, and the dynamic simulation of the cell equivalent circuit was modeled with Matlab/Simulink simulation software. The time-series signals of cell voltage and anode current were obtained under different bubble conditions, and analyzed by spectral and statistical analysis methods. The simulation results show that higher bubble release frequency has a significant effect on the cell voltage oscillations. When the bubble coverage of one anode block exceeds 80%, the cell voltage may exceed its normal fluctuation amplitude. The simulation also proves that the anode effect detected by computer in actual production is mainly the whole cell anode effect.

Equivalent Circuit Analysis of an RF Integrated Inductor with Ferrite Thin-Film

An equivalent circuit for a novel RF integrated inductor with ferrite thin-film is derived. The enhancement of the magnetic ferrite thin-film on the inductance （L） and quality factor （Q） of the inductor is analyzed. Circuit element parameters are extracted from RF measurements. Compared with the reference air-core inductor without magnetic film, L and Q of the ferrite thin-film inductor are 17% and 40% higher at 2GHz,respectively. Both the equivalent circuit analysis and test results demonstrate significant enhancement of the performance of RF integration inductors by ferrite thin-film integration.

Small-Signal Equivalent Circuit Modeling of a Photodetector Chip

A small-signal equivalent circuit model and the ted. The equivalent lumped circuit, which takes the main extraction techniques for photodetector chips are presen- factors that limit a photodetector＇s RF performance into consideration,is first determined based on the device＇s physical structure. The photodetector＇s S parameters are then on-wafer measured, and the measured raw data are processed with further calibration. A genetic algorithm is used to fit the measured data, thereby allowing us to calculate each parameter value of the model. Experimental resuits show that the modeled parameters are well matched to the measurements in a frequency range from 130MHz to 20GHz, and the proposed method is proved feasible. This model can give an exact description of the photodetector chip＇s high frequency performance,which enables an effective circuit-level prediction for photodetector and optoelectronic integrated circuits.

COMPACT FOUR-COMPONENT 2-D FDFD METHOD WITH EQUIVALENT SURFACE IMPEDANCE BOUNDARY CONDITION FOR MULTILAYER METAL-COATED WAVEGUIDE

A compact four-component two-dimensional （2-D） finite-difference frequency domain （FDFD） method with the equivalent surface impedance boundary condition is used to analyze the dispersion characteristics of multilayer metal-coated waveguides. According to the equivalent surface impedance boundary condition,the relationship between transverse field components on the boundary can be easily depicted. Once the eigen equation is solved,the propagation constant can be obtained as the eigen value for a given frequency. Results of the proposed method agaree well with those of high frequency structure simulator（HFSS）.

An equivalent finite element method to kinetics analysis of complex mechanism

The Finite Element Method was combined with the results from considerable analysis, producing a new kinetics analysis method of EFEM for a mechanism in truss, geared system, and assembled system. The equivalent principle and the motive differential equation of the system were derived by using an equivalent element, a virtual inertia matrix, and a systematic force matrix. The element’s mass matrix expression in the two dimensional and three dimensional mechanisms of the equivalent element was determined. The equivalent mass matrixes fashion of the Jacobin matrix, generalized coordinate matrix, and equivalent forces matrix were also determined. It was validated by two examples that the new method was normal, simple and direct, and had a higher efficiency than alternative methods; this is regardless of whether traditional methods are used with differential equations and calculated by using a computer.

THEORETIC RESEARCH ON ROBUSTIFIED LEAST SQUARES ESTIMATOR BASED ON EQUIVALENT VARIANCE-COVARIANCE

Depending on analyzing the abuse of equivalent weights,a set of self-contained theory system on robust estimation based on equivalent variance-covariance is established,which includes ρ function, φ function,equivalent variance-covariance function,influence function and breakdown point.And an example is given to verify that the robust models proposed in this paper are reliable and correct.

Equivalent bending stiffness of simply supported preflex beam bridge with variable cross-section

In order to understand mechanical characters and find out a calculating method for preflex beams used in particular bridge engineering projects, two types of simply supported preflex beams with variable crosssection, preflex beam with alterative web depth and preflex beam with aherative steel flange thickness, are dis- cussed on how to achieve the equivalent moment of inertia and Young＇ s modulus. Additionally, methods of cal- culating the equivalent bending stiffness and post-cracking deflection are proposed. Results of the experiments on 6 beams agree well with the theoretical analysis, which proves the correctness of the proposed formulas.

Equivalent Cake Filtration Model

Cake filtration has been widely used in many chemical processes with more non-Newtonian, highly viscous and compressible materials involved. Neither traditional nor modem filtration theory can be applied in practice ＂Equivalent cake filtration model＂ is a recently developed mathematical model to describe cake filtration for both Newtonian and non-Newtonian fluids, in either steady or unsteady filtration stages. This model has two strengths： （1） It can be used to determine equivalent capillary radii and predict filtration quality based on the properties of solid/liquid system and operation parameters; and （2） to calculate cake specific resistance and its variations with time at various cake thickness locations.

Abstraction of Small Signal Equivalent Circuit Parameters of Enhancement-Mode InGaP/AlGaAs/InGaAs PHEMT

An extraction method of the component parameter values of an enhancement-mode InGaP/AIGaAs/In-GaAs PHEMT small signal equivalent circuit is presented,and these component parameter values are extracted by using the EEHEMT1 model of IC-CAP software. The extraction results are verified by ADS software,and the DC I-V curves and S parameters simulated by ADS are basically accordant with those of the test results. These results indicate that the EEHEMT1 model can be used for extracting the component parameters of an enhancement-mode PHEMT.

Equivalent Doping Transformation Method for Predicting Breakdown Voltage and Peak Field at Breakdown of Epitaxial-Diffused Punch-Through Junction

Based on a new semi empirical analytical method, namely equivalent doping transformation, the breakdown voltage and the peak field of the epitaxial diffused punch through junction have been obtained. The basic principle of this method is introduced and a set of breakdown voltage and peak field plots are provided for the optimum design of the low voltage power devices. It shows that the analytical results coincide with the previous numerical simulation well.