Equation Method Research Articles

Prediction and Analysis of Surface Residual Deformation Considering the Impact of Groundwater in Mines

With economic development and coal resource exploitation, the area of mined-out zones is expanding continuously. The traditional waste disposal methods no longer meet the current demands, making it urgent to evaluate and reuse the surface stability of these mined-out zones. Surface residual deformation is a process where voids and fissures within the mined-out zones are gradually filled and compacted, affecting the overlying rock structure. Additionally, groundwater significantly impacts the strength of the overlying rock, leading to increased subsidence. Therefore, predicting surface residual deformation while considering the effects of groundwater is crucial for forecasting surface deformation and assessing stability in mined-out zones. This study, taking into account the characteristics of subsidence zones and the impact of groundwater on the compaction of fractured rock masses, uses equivalent mining height and probability integral methods to develop a predictive model for surface residual deformation incorporating groundwater effects. Predictions for the study area show that groundwater exacerbates surface residual deformation, with various deformation values ranging from 33.8% to 51.9%. The surface stability categories are divided into stable and essentially stable regions based on the residual deformation’s impact on the working face. This model fully considers the influence of groundwater on residual deformation in mined-out zones, refining existing mining subsidence theories, addressing deformation issues caused by adverse groundwater factors, and providing a theoretical basis for predicting residual deformation and evaluating stability in mined-out zones, promoting the sustainable development of land and environmental resources in mining areas.

Spatiotemporal Eolution and Prediction of Ecosystem Service Value in Taihang Mountains Based on MCCA Land Use Scenario Simulation

Ecosystem service value （ESV） is an important indicator related to regional ecological well-being, and understanding its evolution can provide references for regional ecological civilization construction and sustainable development. The Taihang Mountains, an important ecological security barrier in North China, were taken as an example. Based on land use data from 2000 to 2020, this study revealed the changes in land use and ecosystem service value in the Taihang Mountains and conducted multi-scenario simulations of ESV in 2035. Additionally, the land use transfer matrix, improved equivalent factor method, and mixed-cell cellular automata model were used. The results showed that： ① From 2000 to 2020, the main land use types in the Taihang Mountains were cropland, forest land, and grassland. The area of cropland and grassland significantly decreased, whereas the area of forest land and construction land remained stable. The scale of land use transfer was 2.06×104 km2, with a high intensity of transfer from cropland and grassland to other areas, mainly guided by ecological construction. ② The ecosystem service functions in the Taihang Mountains were mainly dominated by regulation services, and the overall ESV showed a stable upward trend, increasing by 1.51×1010 RMB from 2000 to 2020. The spatial distribution of ESV was uneven, and the polarization phenomenon was evident, with high-value areas concentrated in the high-altitude areas in the northern and central-southern parts and low-value areas mostly located in the flat foothills and central plateaus on both sides. They were greatly influenced by human activities. ③ By 2035, compared with that in 2020, the ESV in the Taihang Mountains was projected to increase by 5.37 billion RMB in the natural growth scenario, 4.34 billion RMB in the urban development scenario, and 7.64 billion RMB in the ecological tourism scenario, mainly due to the conversion from cropland and grassland to forest land. The natural growth scenario showed a high intensity of spatial transformation of ESV, the urban development scenario experienced severe ESV loss in cropland, and the ecological tourism scenario showed a significant increase in ESV, which was an effective path for promoting green development in the Taihang Mountains. The research results can provide scientific references for the healthy management and sustainable development of the ecosystem in the Taihang Mountains.

Simulation method for dynamic characteristics of rotor-support system subjected to environmental loads

An improved finite element method was proposed to investigate the dynamic characteristics of rotor system with environmental loads (temperature and aerodynamic forces) in aeroengines. According to the axial temperature distribution within shaft elements, the polynomials were established for physical properties of material. The derivation for coefficient matrices under thermal loads, and the tensile stiffness matrix considering axial aerodynamic forces were completed, based on the Timoshenko beam theory. A high-pressure rotor was simulated with operating temperature 200∼600∘C, and the magnitude of aerodynamic force is 105N. Furthermore, a squeezed film damper (SFD) was adopted to this rotor-support system, its steady responses were solved by the equivalent coefficient method, and the Newmark-HHT method was utilized to solve the transient responses. The results indicate that the first two critical speeds are reduced by 1.85 % and 2.07 %, which is mainly caused by thermal loads. The rising temperature leads to lower elastic modulus, higher Poisson's ratio and expansion ratio. With the amount of a mass unbalance being 500 g·mm located at the 1st-stage compressor disk (CD1): the 1st resonance peaks at CD1 and turbine disk (TD) increase by 4.56 % and 4.98 %, respectively, and the 2nd resonance peaks at CD1 and TD rise 5.88 % and 5.00 %, separately. Owing to SFD damping, the first two resonance peaks at CD1 and TD decrease by 69 % and 51 %, respectively. Compared to 40 °C, the first two resonance peaks at CD1 increase by 88 % and 55 % at the oil temperature 100 °C. The oil-film damping deteriorates significantly due to the lower oil viscosity in higher temperature. When operating near the first-order critical speed, the transient responses of rotor perform as simple harmonics, circular precession trajectory, dominant rotational frequency, and periodic motions. Overall, the dynamic characteristics of rotor-SFD-support systems exposed to environmental loads can be predicted by the proposed simulation method.

Assessment of damage prediction models for composite laminates under single and repeated low-velocity impacts

The aim is to explore the influence of damage initiation criteria and evolution methods on the damage prediction for composite laminates under single and repeated low-velocity impacts. A 3D finite element model is established to analyze the impact behavior of laminate, and a damage analysis process including the initiation determination, progressive evolution, and constitutive relationship is designed. Hashin criterion based on tensile strain for matrix is modified by an empirical assumption method. Besides, the quantitative evolution of damage area during impact is studied, which provides a new perspective for elucidating the damage mechanism. The numerical model is first validated against the available experimental data. The influence of initiation criteria and evolution methods on damage prediction is then performed in two-phase research. The first phase discusses the prediction capabilities of different combinations under single impact. In the second phase, a method for removing residual vibrations under repeated impacts is proposed. The differences caused by the removal and non-removal of residual vibrations are analyzed, and the sensitivity of these differences to various combinations is discussed. Results show that the numerical prediction agrees well with the experiment in dynamic mechanical response curve. Combining Hashin-Strain criterion with linear equivalent strain method and Puck criterion with exponential equivalent displacement method yields optimal results. Moreover, the sensitivity to differences caused by the residual vibrations effects is related to the initiation criterion, and the evolution method.

The relationship between singular value decomposition orthogonal space vector and sound field reconstruction in equivalent source method

In acoustic holography, the equivalent source method represents a typical ill-posed inverse problem, characterized by the significant impact of measurement errors on the sought solution. To minimize the interference of noise with the sought solution, we analyze the relationship between orthogonal space vectors obtained through singular value decomposition and acoustic field reconstruction. The research findings indicate that the primary information of the acoustic field exhibits strong correlation with a small number of space vectors, while noise information demonstrates random correlation with all space vectors. Therefore, we retain the space vectors with higher correlation to the acoustic field while filtering out redundant ones, thereby stabilizing and accurately reconstructing the acoustic field. Numerical analysis of the acoustic field reconstruction demonstrates that compared to regularization methods such as Tikhonov and truncated singular value decomposition (TSVD), this approach achieves higher computational accuracy. Furthermore, the text combines practical examples to further explain the reasons behind the superior accuracy of this method.

Estimation of random incidence sound transmission loss of panels based on normal incidence sound transmission loss measurements

The performance of building sound insulation is an important parameter for evaluating the quality of construction projects. So far, the sound insulation performance testing of building walls requires the installation of large-dimensioned wall samples in specialized sound insulation laboratories, which is time-consuming and costly. If small-dimensioned components of the wall panels can be applied and quickly tested at the project site, it could significantly improve efficiency and reduce costs. To address this issue, this paper investigates a method for estimating the random incidence sound transmission loss of wall panels based on the measurement of the normal incidence sound transmission loss of corresponding small samples. Initially, the sound transmission loss of single-layer and composite structures is theoretically analyzed based on the theories of Equivalent Single Layer method and Layer-Wise method. Subsequently, the random incidence sound transmission loss is estimated by the normal incidence sound transmission loss. The methodology for estimating the random incidence sound transmission loss of wall panels proposed in this study offers both a practical approach and theoretical support for the rapid assessment of the sound insulation performance of building walls. This study is of great significance for improving the quality of construction projects and inspection efficiency.

A study on the difference in noise reduction between rear and side microphone on CPX measurement method through sound absorption frequency analysis

The road noise evaluation method in Korea is based on the 'noise vibration process test standard' by the Ministry of Environment. In this evaluation method, the noise felt at the sound-receiving point is measured as LAeq. Recently, in order to clarify the noise measurement standards for low-noise pavements, an international standard (ISO11819-2, CPX method) was first introduced in the Porous Pavement Guidelines of the Ministry of Land, Infrastructure and Transport. According to ISO, CPX measurement method adopts side microphones as mandatory, and the rear microphone as optional. Due to the difference in location noise level is different, causing confusion in the road noise evaluation method. Researchers have published several studies in the past that the rear microphone is highly correlated with the equivalent noise level method based on the Korean standard. As a follow-up study to the above results, this study examines the characteristics and causes of the frequency spectrum of the rear and side microphones in the case of dense asphalt pavement and porous asphalt pavement and derives the results through frequency analysis of the sound absorption coefficient test to determine and to contribute improving reliability and institutional rationalization of the CPX measurement method.

A novel method measuring orifice conductance and testing time-of-flight mass spectrometer for water vapor–binary gas

Abstract The miniature time-of-flight mass spectrometer (TOF-MS) is a crucial instrument for detecting water ice in Chinese Lunar Exploration Program (CLEP), so it is necessary to compare its detection results for pure water vapor and water vapor-binary gas (such as H2O-N2, H2O-CH4, and H2O-Ar) to evaluate its water detection performance. The throughput must be calculated using the measured conductance to test the miniature TOF-MS. According to the VΔp method, the pΔt method, whose uncertainty is less than 14.2%, is proposed to measure orifice conductance for water vapor-binary gas, and an apparatus was developed based on those two methods. The orifice conductance of four kinds of pure gases (N2, H2O, CH4, and Ar) was measured using those two methods separately, and the measurement results allowed to calculate the conductance of the water vapor-binary gas through the Equivalent Single Gas method. The conductance of the water vapor-binary gas was measured using the pΔt method, and the difference between the calculated and measured results is less than 7%. Hence, the measured conductance allows the miniature TOF-MS to be tested for the water vapor-binary gas. As throughput is from 10-9 to 10-6 Pa m3 s-1, the difference between the test signals of water vapor-binary gas and pure water vapor is less than 40%.

Particle damping equivalent method based on force chain for high frequency vibration reduction: Mechanism analysis and experimental verification

A particle damping equivalent method based on force chain is newly proposed for simulating the behavior of particle damper (PD) with higher accuracy. Compared with other existing equivalent methods, this method considers the contact between particles and evaluates the particle motion state. Firstly, the particle damping equivalent method based on the theory of force chain and contact model is proposed, and the simulation process of the equivalent method is described. Then, this equivalent method is adopted to simulate the high frequency vibration of pipe installed with PD using SAP2000 software. The simulated vibration response exhibits excellent agreement with experimental results, validating the effectiveness of the proposed equivalent method. Finally, based on the calculation results, it is observed that the particle motion state of the PD in the experiment is quasi-static. This further shows that the particle chain in the damper under high frequency vibration can ignore the wave propagation behavior, which aligns with the assumption of the particle contact model.

An equivalent source method for acoustic problems with thermoviscous effects.

This paper presents an equivalent source method (ESM) for analyzing sound propagation in small-scale acoustic structures with thermoviscous effects. The formulations that describe the thermal, viscous, and acoustic modes for thermoviscous acoustic problems are introduced. The concept of ESM is then applied to solve these formulations, resulting in an efficient numerical computation and implementation procedure. Based on two different strategies, the obtained ESM formulations are coupled at the boundary using the isothermal, non-slip, and null-divergence conditions. The coupling based on the first strategy is efficient for solving thermoviscous acoustic problems with few matrices required. However, this procedure faces the evaluation of the tangential derivatives of the boundary velocity. Coupling the ESM formulations directly for each component of the total particle velocity at the boundary has no such problem, which leads to the second strategy. However, it entails a larger memory usage compared to the former. Additionally, the coupled finite element method (FEM)-ESM formulations based on the above strategies are developed for acoustic-structural interaction. The validity of the presented ESM formulations is demonstrated through benchmark examples, and that of the coupled FEM-ESM formulation is illustrated by the numerical analysis of a simplified microphone.

Broadband and robust vibration reduction in lattice-core sandwich beam with 3D-printed QZS resonators

The demand for lightweight lattice-core sandwich structures that exhibit superior mechanical and dynamic properties is widespread in many devices. This paper presents a lattice-core sandwich beam (LSB) with an embedded array of quasi-zero-stiffness (QZS) resonators, referred to as Q-LSB. This research distinguishes itself from existing studies on metamaterial structures with QZS resonators by investigating the nonlinear stiffness of QZS resonators and the damping of a soft three-dimensional (3D) printing material. The objective is to achieve efficient and robust vibration reduction beyond the band gap of its linear counterpart. We investigate the beam vibration using both experimental and numerical methods. The experimental results demonstrate that the resonators can entail significant vibration reduction in a wide frequency range, covering the first three eigenmodes of the host LSB. Furthermore, the reduction effect improves as the excitation level increases within the tested excitation range, highlighting the structure’s robustness against the excitation amplitude. A numerical model based on a dynamically equivalent homogenization method and the finite element method is established and experimentally validated. Subsequently, the numerical parametric results reveal that the broadband vibration reduction is due to the damping effect, while the robust vibration reduction effect is attributed to the nonlinear stiffness of the resonators.

Modeling of output characteristics of giant magnetostrictive transducer considering temperature and eddy currents

Due to the high conductivity and low permeability of giant magnetostrictive materials (GMMs), eddy currents and temperature rise caused by these materials are unavoidable. These factors will significantly impact the output efficiency and reliability of giant magnetostrictive transducers (GMTs). It is essential to conduct precise evaluations of the output characteristics in various temperature settings to effectively design and optimize the transducer. However, to reduce the eddy current loss of GMMs, a radial slit is introduced. The intricate geometry also contributes to the complexity of analysis. According to the practical engineering requirements, this paper initially established a testing system for GMM characteristic and analyzed the mechanism between material temperature and output characteristics. Second, improvements have been made to the equivalent circuit method. Research has been conducted on the influence of temperature and eddy currents on the electrical and mechanical equivalent circuits, leading to the creation of a comprehensive equivalent circuit model for GMTs. Finally, a testing platform has been set up to assess the temperature-output characteristics of the transducer. The impedance and displacement characteristics of a GMT were examined to validate the proposed model. The test results demonstrated that within the 20 – 100 °C range, the discrepancy between the model and the measured impedance is under 1%, and the displacement amplitude error is less than 5%, thus confirming the precision of the proposed model.

A visible transparent infrared microwave compatible stealth metasurface with low infrared emissivity

Abstract This article proposes a visible transparent infrared microwave-compatible stealth metasurface with low infrared emissivity, aiming to integrate visible transparency, low infrared radiation, and broadband microwave absorption. The entire structure consists of a dual layer of infrared shielding layer (IRSL) and microwave absorption layer (MAL). Among them, IRSL adopts a frequency selective surface (FSS) structure with high-duty cycle dielectric-metal-dielectric (DMD) to obtain low infrared emissivity and high microwave transmittance. MAL combines the equivalent circuit method (ECM) and particle swarm optimization algorithm (PSO) to design a circular ring metasurface for broadband microwave absorption. To achieve better absorption performance, a transition layer (TL) is introduced to improve impedance matching between IRSL and MAL. Meanwhile, the use of transparent materials throughout the entire structure has the characteristic of visible transparency. In summary, this article proposes a multiband compatible stealth metasurface design method that can meet the stealth requirements of modern battlefields.

Theoretical modeling and parameter identification of balanced armature loudspeakers.

Theoretical modeling and parameter identification are essential for optimizing loudspeaker performance and enabling active control. Although relevant theories for moving-coil loudspeakers are well-developed, accurate theoretical modeling and parameter identification methods for balanced armature loudspeakers (BALs) are scant. This study proposes a model using the equivalent circuit method (ECM) for BALs, with consideration of the armature-suspension coupling as well as the non-piston vibration of the diaphragm. Based on the proposed ECM model, a time-domain identification algorithm utilizing measured voltage, current, and displacement data is established to identify the necessary parameters. Employing the theoretical model and proposed identification method, the model parameters of two different BALs are measured. Comparisons between experimental and numerical results demonstrate the accuracy and effectiveness of the proposed model and identification method in predicting impedance, displacement, and sound pressure responses.

An equivalent model of horizontal vibratory finishing process: Model construction and analysis based on similarity theory

The manufacturing cost of parts and experimental equipment seriously limits the development of experimental research on mass finishing. To tackle this issue, an equivalent model construction method was proposed based on similarity theory. First, the similarity criterion of relevant physical quantities in horizontal vibratory finishing was determined, and the calculation formula of the distortion coefficient was derived to correct the prediction results. Second, the effects of vibration parameters on the characteristics and similarities of particle velocity and normal force were analyzed by DEM simulation. Finally, the validity of the equivalent model was proved by PIV and force tests. The results show that the equivalent model can be used to reflect the variation of the actual model and anticipate the particle velocity and normal force. And the prediction accuracy can reach 99.56 % and 97.46 %, respectively. The research results provide a new efficient and low-cost method for researching the mass finishing process.

Fatigue Crack Propagation Life of Metallic Materials Under Random Loading: A Coupling Analysis Method in the Frequency Domain

ABSTRACTThis paper proposes an equivalent spectrum method to predict the fatigue crack propagation (FCP) life of metallic materials subjected to random loading. To adequately account for the coupling effects between crack propagation and the random response of structures, a coupling analysis model is introduced. The stress intensity factor (SIF) can be estimated based on the power spectral density (PSD) of an equivalent displacement. Random vibration fatigue tests were conducted to evaluate the proposed model on aluminum alloy specimens. Results indicate significant variations in natural frequency with crack length. The predicted results are compared with the experimental values, demonstrating satisfactory prediction accuracy of the proposed coupling analysis model. This model enables the assessment of coupling effects between crack length and random response, facilitating more precise predictions of FCP life in metallic materials and guiding the expanded application of damage tolerance criteria in structural engineering.

Simulation and fabrication of a 20 kHz single-beam transducer

Abstract With the vigorous development of underwater acoustic technology in China, underwater acoustic transducers are constantly moving towards broadband, low-frequency, and high-power directions. How to obtain piezoelectric transducers with lower frequencies is still a research direction that scholars from various countries are striving to study. This article mainly studies and manufactures a 20 kHz single-beam piezoelectric transducer, using the classic Tonpilz transducer structure. Firstly, the Tonpilz transducer is theoretically analyzed using the classical equivalent circuit method. Secondly, the transducer is analyzed using ANSYS finite element analysis software to study the influence of piezoelectric ceramics on the frequency of the transducer, and the size of the piezoelectric ceramics is optimized to determine the size of the piezoelectric ceramic structure of the transducer. The working frequency of the transducer was calculated using software, and it was determined that the working frequency was approximately 20 kHz.

Land Use Optimization from the Perspective of Multiple Stakeholder Groups: A Case Study in Yongsheng County, Yunnan Province, China

With China’s rapid economic development in recent years, enhancing the sense of well-being among citizens has become a critical objective. However, the interests of various stakeholder groups are often overlooked in decision-making surrounding land use. In this study, Yongsheng County, Yunnan Province serves as a case study for land use scenario simulations. The equivalent factor method is combined with Participatory Rural Appraisal (PRA) to investigate the relationship between ecosystem multifunctionality (EMF) and the equity index of multiple stakeholder groups in various land use scenarios. We also explore whether an optimal combination of land use types exists. The results indicate that (1) The current ecosystem service value in Yongsheng County is primarily driven by climate regulation and biodiversity conservation, with a relatively high functional value index but a comparatively low equity index; (2) Different stakeholder groups mainly prioritize food production and ecosystem services impacting food production, such as water resource provision and climate regulation; (3) A land use allocation pattern of 20% farmland, 4% water bodies, 21% mixed forest, 20% coniferous forest, and 35% grassland appears to provide the optimal EMF index while simultaneously achieving the optimal equity index across stakeholder groups. This research may offer valuable insights for optimizing land use planning while taking into account the well-being of diverse stakeholder groups. It also may have practical implications for the formulation of innovative land use management strategies.

The Validity-Reliability Study of Turkish Version of Electronical Symptom Screening Tool (8-18) in SSPedi-Pediatric Patients with Cancer

Objective: The first step in symptom management is symptom screening which is necessary to keep the symptom under control. This study aimed to determine the validity and reliability of the Turkish version of the Electronic Symptom Screening Tool in Pediatrics for children aged 8-18 (SSPedi 8-18) with cancer. Methods: The research was conducted between September 2020 and June 2021. The sample in our study consists of 80 children (8-18 years) with cancer. For content validity, the scale was first translated into Turkish and then adapted using Davis’ correspondence analysis technique. The construct validity of the scale was assessed using the Barlett test and Kaiser-Mayer Olkin. For the scale’s reliability, Cronbach Alpha Reliability Coefficient, Equivalent Forms Method, bisection method and Item Total Score Correlation Coefficient correlation tests were analyzed. Before starting the study, ethics committee approval and written permits from institutions and individuals were obtained. Results: The content validity index was found between 0.93 and 1. The reliability of the scale of the equivalent form method was r:0.57, and bisection method was r:0.85 and the Cronbach internal consistency coefficient of scale=0.86. The correlation coefficient between the items and the total score was greater than r=0.20. The Kaiser-Meyer-Olkin coefficient was 0.82. The χ2 value (Bartlett test) was statistically significant (p= .001). Conclusion: The SSPedi 8-18 is a reliable and valid tool that can be used to assess the symptoms of Turkish children with cancer. Nurses’ use of the scale while providing nursing care to children diagnosed with cancer and their families will guide them in objectively determining symptoms, understanding the relationship between symptoms, and managing symptoms.

Bond behavior between bundled steel-FRP composite bars and grouted corrugated duct

The utilization of steel-fiber reinforced polymer (FRP) composite bars (SFCBs) reinforcement in precast concrete structures offers numerous benefits, including controllable post-yield stiffness and reduced residual displacement. Employing bundled reinforcement can improve construction efficiency. This study presents direct pull-out tests conducted on SFCBs embedded in grouted corrugated ducts. The results show that bond strength decreases with both the number of bars in a bundle (nb) and the actual embedded length (la). The bond strength of single bar SF-1b-3d with 3d embedded length is 24.21 MPa, while that of 2-bar bundled SF-2b-3d and 3-bar bundled SF-3b-3d is 17.41 MPa and 12.61 MPa, respectively. Additionally, the error in predicting the bond strength between bundled SFCBs and grouted corrugated duct using the equivalent diameter method is found to be less than 8.4%. Utilizing the mBPE constitutive model, an analytical hardening-slip model with a linear slip field assumption accurately predicts the full-range behavior, bond stress distribution, and SFCB's axial stress distribution. Furthermore, the effects of different parameters on yield slip sy, ultimate slip su, and critical anchorage length Ltr are investigated by considering different local bond-slip constitutive models (varying peak bond strength τm and its corresponding slip sm and ascending section coefficient (α) as variables. The yield slip sy varies from 0.1 mm to 1.3 mm, while the ultimate slip su can reach a maximum of 35.0 mm. Furthermore, the validity of existing models for evaluating the anchorage length of single SFCB and bundled SFCBs grouted in corrugated duct connections is discussed, and a formula to estimate the critical anchorage length of bundled SFCBs and grout considering the number of bars within one bundle (nb) is proposed.