Spring Model Research Articles

Further development of distinct lattice spring model with Finn model for liquefaction analysis

The hazards associated with sand liquefaction induced by dynamic events are significant. The study of the dynamic stability in hydraulic structures presents an interdisciplinary challenge encompassing both geotechnical engineering and engineering seismology. This study was based on an actual hydraulic engineering project. To effectively predict changes in pore pressure caused by earthquakes, we integrated the Finn constitutive equations into a distinct lattice spring model (DLSM). In this study, the code was customized to accommodate multiple materials simultaneously participating in the calculations, thus simplifying the solution to complex engineering problems. Initially, we validated the DLSM’s liquefaction equation by comparing it with the finite difference method. Subsequently, we conducted a comparative analysis of liquefaction in an engineering project of sluice using the enhanced DLSM. Our analysis indicates that untreated sand has a severe risk of trending toward liquefaction, presenting a hazard to hydraulic engineering. The incorporation of a gridded concrete framework significantly mitigated the seismic-induced pore pressure accumulation and irreversible deformations caused by vibrations. A comparative study showed that concrete retaining walls with concrete supports are more effective at reducing liquefaction hazards and minimizing irreversible deformations in engineering structures.

Implementation of DEM to calibrate contact parameters, as a novel simulation of the elastoplastic behavior of green iron pellet classified by roller screen

As green iron ore pellets exhibit elastoplastic behaviors, it is crucial to select an appropriate DEM model that accounts for these behaviors to simulate their classification in a roller screen. The most important DEM models include the Hertz-Mindlin and the hysteretic spring. In this study, for the first time, green pellet behaviors were modeled based on their actual shape (multi-spheres) under various conditions of moisture content, bentonite dosage, and iron concentrate type, using the image analysis. All parameters required to simulate the behavior of green pellets were measured through experimental tests. These properties include shape (sphericity), physical (angle of repose), and mechanical characteristics (shear modulus, yield stress, coefficient of restitution as well as static and rolling friction coefficients). Thus, the total contact parameters were adjusted based on these properties. Additionally, a comprehensive comparison was made between the Hertz-Mindlin and hysteretic spring models to accurately simulate the characteristics of the green pellets and assess the efficiency of the roller screen. Finally, it was found that the use of a realistic shape and hysteretic spring model provides a more accurate simulation of pellet classification when applying a roller screen and shows a stronger correlation with the laboratory results.

Revealing the inherent running mechanism of quadruped mammals based on a novel bionic stiffness model

In this paper, the limb of a goat is chosen as the research object, and according to mammalian anatomy, a bionic model called the quasi inverted pendulum with “J” curve spring (QIPJCS) model with nonlinear stiffness is built, and the equations of motion are derived. Based on these equations, the advantages of the QIPJCS model are illustrated from the aspect of the stable motion region by the SFA (step-to-fall analysis) numerical simulation method. These results are compared with the traditional SLIP model. Furthermore, the ARM (Apex-Return-Map) of this model is built, and the fixed points are analyzed. Finally, according to the locomotion law of goats running with gallop gaits and the analysis of the dead-point support effect, the dynamic motion mechanism of goat limbs is elucidated, and the equivalent mechanism model is built. Based on the mechanism, the dynamic mechanical analysis indicates that the joint driving torque can be minimized to conserve energy by optimizing the landing angle. The running mechanism research of quadruped mammals, which is based on the novel bionic stiffness model, provides theoretical support for the design of high-performance mechanical legs and the motion control of bionic robots.

Hybrid modeling of karstic springs: Error correction of conceptual reservoir models with machine learning

ABSTRACT Accurate spring discharge modeling and prediction is crucial for water management, helping authorities optimize use, manage variability, and prepare for droughts. Developing reliable simulation and forecasting tools is essential for effective management of groundwater resources from karstic springs. Although hybrid modeling approaches have been explored in hydrology, their application to spring discharge modeling is underexplored. Previous studies have focused on conceptual/distributed or data-driven models separately, missing the potential advantages of combining them. This creates a research gap in exploring the benefits of hybrid models for spring discharge. This study developed a hybrid model combining a conceptual GR5J model with Random Forests to simulate spring discharge from Bordeaux's largest karst aquifer. Model performance was assessed through comparison with the individual GR5J, RF, and benchmark models (weekly average of observed values). The hybrid model outperformed all models. Evaluation using actual meteorological data found the hybrid model achieved the highest accuracy by reducing GR5J simulation errors by 22%. When considering meteorological uncertainty, the hybrid model outperformed the individual GR5J, RF and benchmark models by 11, 30 and 47% respectively. The study findings suggest combining conceptual and machine learning approaches can improve spring discharge simulations, opening promising opportunities for enhanced forecasting in karst aquifers.

An improved coupled tri-stable energy harvesting system with spring stops for passive control

Motivated by enhancing the DC power output of a tri-stable energy harvester (TEH), a passive control of a coupled TEH driven by colored noise is constructed by using spring stops. The cubic trilinear spring model is utilized to describe the piecewise nonlinear impact force introduced by the spring stops. Using the stochastic averaging technique based on energy-dependent frequency, the analytical expressions of joint probability density function (PDF) and harvested power are obtained. The effects of the impact distance, impact stiffness, and colored noise on stochastic dynamics and harvesting performance are further discussed. It is found that the spring stops can change the shape of the PDF to induce stochastic bifurcation phenomena. The TEH under passive control tends to oscillate among three potential wells to effectively improve the DC output. By adjusting the appropriate impact distance and stiffness, the harvesting performance can be optimized and improved. Moreover, the numerical simulations and experimental verifications well support the theoretical analysis. Based on the experimental results, the harvested power can be enhanced by choosing the appropriate material of the stop (i.e., the spring is the optimal one among three different materials).

Investigations on toughening and self‐healing performance of plain woven composites with mendable polymer stitches

AbstractThis paper investigates toughening and self‐healing properties of plain woven composite structure with poly[ethylene‐co‐methacrylic acid] (EMAA) stitches. Firstly, the cantilever beam specimens with different stitched spacing were performed to determine inter‐laminar fracture toughness. Subsequently, the finite element models of EMAA stitched cantilever beam was established to predict the toughening effects based on nonlinear spring and cohesive zone model (CZM). The force‐displacement responds of experimental and simulation results show excellent correlation. Finally, the toughening and healing mechanism of the stitched plain woven structure were explored. Compared with the original specimen, the EMAA stitched structure shows an excellent toughening ability. After heating, the damaged structure was healed through pressure deliver mechanism to restore the interlaminar fracture toughness of the composite.Highlights Thermoplastic EMAA filaments with self‐healing properties were sewn into the woven composite. The EMAA stitched woven composite structure exhibits excellent interlaminar toughening and healing properties. Finite element model combined non‐linear spring and CZM was established to predict the toughening effects. The toughening and self‐healing mechanisms of EMAA stitched plain woven structure were revealed in detail.

Combining groundwater budget, hydrochemistry and environmental isotopes to identify the groundwater flow in carbonate aquifers located in Campania Region (Southern Italy)

Study regionCarbonate mountains of Mt. Maggiore and Mt. Tifata, Campania Region, southern-central Italy, Mediterranean basin. Study focusThe hydrogeological relationship between the carbonate massifs of Mt. Maggiore and Mt. Tifata is investigated. Archival and newly acquired data on groundwater availability, hydrochemical and isotopic data were considered. Their combined use led to the proposal of new hypotheses regarding the connection between these aquifers. The exchange of groundwater through this connection would be induced by the strong groundwater withdrawals from the well fields at Mt. Tifata; the area of possible connection was also identified. A mineralization model of some local springs showing high CO2 and TDS values is also proposed. New hydrological insights for the regionThe carbonate rocks are widely outcropping with a mountainous morphology and host important groundwater resources in the studied region. The springs related to these carbonate aquifers have excellent chemical characteristics and, for these reasons, the major aqueducts in Campania Region rely on these groundwater resources. The well fields of the Mt. Maggiore and Mt. Tifata supply part of the metropolitan area of Naples, with 3.8 million inhabitants. The quantitative evaluation of groundwater resources and the proposed groundwater circulation scheme can support a sustainable and diversified use of the resource taking into account the presence of waters already used for drinking purposes and waters with high TDS values.

Vibration transmission model of buildings based on virtual spring model and energy functional variation principle

In recent years, the “metro depot + over-track buildings” development model has witnessed rapid growth in China, driven by its advantages of high land utilization and investment return rate. However, the issue of vibration and noise caused by trains entering and exiting the depot has become a major impediment to its sustainable development. To predict the vibration of over-track buildings induced by trains, this paper presented a vibration transmission model of buildings based on the virtual spring model and the energy functional variation principle. The model was then applied to an actual engineering project at a metro depot in Guangzhou, China, and its accuracy was validated by comparing the results with finite element analysis and field measurements. Additionally, the vibration transmission characteristics of the over-track building were studied. The results indicated that the vibration transmission model of buildings presented in this paper aligns well with the results obtained through finite element analysis and field measurements. This approach eliminates the need to disassemble structural members, and the introduced virtual spring model effectively simulates non-ideal connections and boundary conditions. Consequently, it offers convenient structural connection and boundary condition settings, as well as high computational efficiency. Due to the edge effects on the top floor of the buildings, vibration waves in the higher floors experience a combination of reflected and incident waves, resulting in slow attenuation and, in some cases, amplification of vibrations as they propagate from the middle floors to the top floor. The vibration of the over-track building is closely related to the natural vibration characteristics of the floor and the frequency spectrum characteristics of the vibration source. When the natural frequency of a building's floor aligns with the main frequency of the vibration source, significant vibration amplification occurs due to local resonance.

Transverse surface wave in non-planar layered nearly incompressible elastic structure having imperfect contact

The prime motive of the present work is to bring out the emphatic impacts of planar boundary and non-planar boundary as well as imperfectness of the interface on the displacement components and phase velocity of Love-type wave (LTW) propagating in the layered structure. The layered structure essentially incorporates two dissimilar nearly incompressible elastic materials bonded imperfectly to each other having non-planar boundaries at the free surface and at the common interface. A linear spring model has been adopted to describe the imperfect bonding at the interface. The solution methodology features the applicability of variable separable technique along with Taylor’s series expansion that leads to establish dispersion relation and displacement components of LTW. The displacement components and phase velocity of LTW have been numerically computed, and their dependence on wave number have been graphically manifested. As a special case of the study, the dispersion relations for incompressible and isotropic elastic layered structures have been deduced. A comparative analysis between compressible, nearly incompressible and incompressible layered structures comprised of Neo–Hookean material, and isotropic layered structure has been performed to trace out the impact of imperfect bonding parameter on the phase velocity of LTW. The established result of dispersion relation for the considered geometrical structure, as a particular deduction, concur well with the result present in the literature.

Research on impact vibration response of hinged fluid-conveying pipe with bilateral gap constraints

Factors such as loose supports or barriers over the fluid-conveying pipe may cause bilateral gap constraints. Flow-induced vibration will occur during pumping, which leads to collision between the pipe and the constraints. A piecewise linear spring model with large stiffness is employed to simulate the collision process between the pipe and the constraints, and numerical simulation is carried out for the collision of hinged fluid-conveying pipe with the bilateral gap constraints. The dynamic characteristics of hinged fluid-conveying pipe with pulsating internal flow excitation and bilateral gap constraints during impact vibration are studied. Influences of various parameters including frequency, average flow rate of the pulsed internal flow excitation, position of the bilateral constraints, and gap dimensions on the system are investigated. Three paths are found for the pipe system entering chaotic window from stable periodic motion: entering chaotic window after the occurrence of period-double bifurcation, transitioning into chaotic window after developing almost periodic motion, and jumping into chaotic window directly. If the distance between two constraints is closer, the pipe between the constraints will be subject to stronger constraints during the collision process, which can cause the system to enter chaos easily. Many dynamic phenomena have been observed, such as a sliding bifurcation when periodic incomplete chattering-impact developing periodic complete chattering-impact, strong centrosymmetric properties in the bifurcation diagram and the Poincaré map at the mid-point of the pipe, jumping between stable periods, period-double vibration response, inverse period-double vibration response, grazing motion, and viscous motion.

Dynamic Response of the Tunnel Lining with a Circumferential Crack Subjected to a Harmonic Point Load

Cracks are one of the most common diseases of tunnel lining, and the structural dynamic response can be used to assess the health of a tunnel. Hence, this paper investigates the dynamic response of shield tunnel lining with a partly circumferential crack. The shield tunnel lining is regarded as a thin cylindrical shell and analyzed independently. The research methodology integrates the wave propagation method, the local flexibility matrix, the line spring model and the wave superposition principle. The results show that the position and depth of a partly circumferential crack can influence the natural frequency of the shield tunnel lining. Under the fixed-position load, as the distance from the monitoring point to the crack increases, the difference in displacement response amplitude between the undamaged and cracked linings diminishes. Moreover, deepening cracks enlarge the magnitude of amplitude differences. When the load approaches the crack, the radial amplitude difference first increases and then decreases as the monitor moves away from the crack. This finding helps determine the required monitor position. The displacement response of the selected monitor indicates that the closer the load position is to the crack, the larger the amplitude difference. The results aid in identifying the crack position and selecting corresponding load and monitor locations.

A mass spring model applied for simulation and characterization of behavior of composite structures

A mass spring model applied for simulation and characterization of behavior of composite structures

Experimental investigation and numerical modeling of effect of specimen size on microwave-induced fracturing of diorite

The effect of specimen size on microwave-induced fracturing of rocks has not been well understood. In this study, the experimental tests using open-ended microwave and numerical simulations coupling COMSOL Multiphysics and four-dimensional lattice spring model (4D-LSM) were carried out to investigate the evolution process of microwave-induced cracks, and to elucidate the mechanisms responsible for size-dependent microwave-induced fracturing. The experiments show that with the increase of the specimen dimension, the number of microwave-induced cracks is almost constant, and the total crack length first increases and then decreases, while the maximum crack width and maximum crack depth decrease gradually. A comparison of the experimental and numerical temperature characteristics as well as cracking characteristics indicates that the models established in this study are reasonable in the simulation of the rock fracturing behaviours. The numerical results show that the crack initiation time increases logarithmically with the increase of the specimen dimension. For the small-sized specimens, the microwave-induced cracks started from the outer boundary of the specimen and propagated toward to specimen center and into the depth. For the medium-sized and large-sized specimens, the microwave-induced cracks initiated near the outer boundary of the antenna aperture, and then propagated toward to the center of the specimen and the outer boundary of the specimen. The main reason for the size-dependent of fracturing behavior is that the local fracture energy will dramatically decrease when the crack is approaching the specimen boundary.

Effect of Oil Acoustic Properties on Film Thickness Measurement by Ultrasound Using Spring and Resonance Models

The principle of reflection of ultrasonic waves at lubricated interfaces has been widely studied in recent years using different models. In this work, two different models (the spring model and the resonance model) were used to verify the influence of the acoustic properties of four different lubricating oils. A simple three-layer configuration was used, where carefully prepared, well-controlled gaps between stainless steel plates were established to accommodate a drop of oil. Optical measurements showed that the gaps formed were: gap 1 = 11 µm, gap 2 = 85 µm, gap 3 = 100 µm, and gap 4 = 170 µm. The smaller gap (11 µm) was found to be in the limit measurement range using the spring model for the sensor used in this work (14 MHz), whereas the resonance method was used for the thicker gaps. For the resonance model, the use of the phase spectra helped the identification of the resonance frequencies. The results showed good agreement between the measured thicknesses and the nominal gap values. There was little effect of the acoustic properties of the oils on the measured values, with the largest discrepancies found for the oil with the highest speed of sound (PAO4). This new way to characterize oil properties in a thin gap, where the material and geometry of the contact are fully characterized, enables us to compare different measurement methods and understand their sensitivity when testing similar materials of the same class of lubricants, as small deviations are crucial in real-life applications.

Three-dimensional elastic properties of open-cell porous structures: Analytic and finite element modelling

The current paper introduces a three-dimensional micromechanical model of open-cell cellular solid materials and presents the homogenization of the model to an orthotropic continuum. An orthotropic microstructural beam model was created and tested under pure stretch and pure angular distortion to identify the dominant deformation modes by mapping the contributions of normal-, bending- and torsional stiffness to the total strain energy. In the case of unidirectional tension, the deformation mode was dependent primarily on the proportion of normal- and bending stiffnesses, except for the cases with similarly small bending- and torsional stiffness values, where the contribution of torsion was significant. In the case of the pure angular distortion, the key deformation mode was defined by the ratio of bending- and torsional stiffness values, except for the case of large normal- and torsional stiffness values, which resulted in normal-deformation-driven behaviour.The homogenization of the micromodel was conducted by creating an equivalent spring model, by means of which the equivalent elastic modulus values for the main directions of orthotropy have been derived as functions of the geometric and elastic properties of the beams. With the aid of the equivalent spring models, the relative density dependence of Young’s modulus and shear modulus have been examined. The typical second-degree relationship was found to become inaccurate in the range of lower porosity. In the case of increasing relative density values, the exponent of the elastic modulus function decreased while the exponent of the shear modulus increased.

Deformation features of high-pressure rotary pile reinforced strata by discrete lattice spring modeling (DLSM)

Deformation features of high-pressure rotary pile reinforced strata by discrete lattice spring modeling (DLSM)

A GFDM based computational model for the analysis of tunnels under gravitational loadings

Based on an impedance relation, a new computational model is developed for the analysis of tunnels under gravitational loading. The shape of tunnel is arbitrary. The impedance matrix, representing the soil resistance, is evaluated through integration of the equations of elasticity by generalized finite difference method (GFDM). The rigidity matrix of tunnel ring is constructed by using two types of elements: plate and shell elements. The equations of these elements are evaluated through integration of the equations of higher order plate and shell theories again by GFDM. These element equations accommodate not only axial and bending deformations, but, also shear deformations in the ring. In the study, the rotational joint deformation is simulated through the use of rotational spring model and the slippage is considered by modifying the impedance matrix so that the tangential soil resistance force between the ring and soil medium vanishes. Some numerical results are presented, in nondimensional forms, for circular and square tunnels where the following three cases are considered for circular tunnels: a) the soil medium is infinite, the change in σv (vertical (in situ) compressional stress) in the vicinity of tunnel is disregarded b) the soil medium is infinite, the change in σv is taken into account c) the soil medium is halfspace (HS). In connection with the case of (a), a comparison is presented for the ring flexibility curves of radial displacement and section forces of circular ring with those reported in literature. In view of the interpretations of the results and comparisons, we think, the proposed model may be used reliably in the analysis of tunnels.

Topology optimization for rigid and compliant hybrid mechanisms

This paper proposes a topology optimization method integrating the variable trajectory constraints to design rigid and compliant hybrid mechanisms. The variable trajectory constraints are distributed in the design domain and are uniformly modeled by nonlinear spring model. Each of the variable trajectory constraints has an active or inactive state and different states map various mechanical properties of the nonlinear springs. The nonlinear relation between force and displacement of the spring is formulated. A new group of design variables denoting the states of the springs is introduced into the traditional density-based topology optimization model. The design variables representing the element density of the continuum structure and the states of the variable trajectory constraints are uniformly penalized to avoid intermediate values in order to obtain a physically realizable mechanism. Sensitivity analysis is performed by the adjoint equation method. To demonstrate the versatility and the generality of the proposed method, the typical numerical examples including linear, spline and circular trajectory constraints were implemented. The numerical comparisons between the nonlinear spring model and the actual trajectory constraints verify the accuracy. The proposed method expands the application of topology optimization and can be extensively employed to design the mechanisms integrating both the compliant members and rigid parts.

Free vibration of cracked FGM Mindlin plate in fluid

The free vibration of cracked functionally graded material (FGM) plate in fluid is investigated in this paper. The material components are supposed following the power law and formulated by the Voigt model. The Mindlin plate theory (MPT) including the shear deformation effect is established and the physical neutral plane is adopted to simplify the derivation due to the in-plane displacements of this plane assumed as zero. A massless linear rotational spring model (LRSM) is established to simulate the through-width surface crack. The hydrodynamic pressure at the fluid-plate interface is derived by the potential flow theory, and is regarded as the added mass of cracked FGM plate during the analyses of fluid-plate coupled vibration. The derivation and discretization of vibrational equations for cracked FGM plates in fluid are respectively achieved though the Hamilton’s principle and differential quadrature (DQ) method. The frequencies and mode shapes are iteratively calculated with these values of the vacuum case. The influences of immersed depth, fluid density, gradient index, crack depth, crack location, length-to-width ratio, length-to-thickness ratio, and boundaries on vibration characteristics are conducted in the section of numerical results. The present vibration analyses of cracked structures can be applicable to avoid structural resonance and failure.

Relationships between functional temporomandibular joint space and disc morphology, position, and condylar osseous condition in patients with temporomandibular disorder.

To investigate the correlations between joint space and temporomandibular joint (TMJ) components and the compressive states of the disc and condyle subsequent to joint space changes. A total of 240 TMJs were categorized according to disc morphology, disc position, and condylar osseous condition. The two-dimensional (2D) and three-dimensional (3D) measurements were compared. The functional joint space (FJS) and disc areas on closed- and open-mouth images (DA-C and DA-O) were also calculated, and the joint space was measured in five directions. Different groups of TMJ components were compared. A spring model was used to simulate the effect of condylar displacement on the disc and condyle. Disc morphology was strongly correlated with its position. The measurements were equivalent between 2D and 3D methods. DA-C and FJS differed significantly between groups. The DA-C to FJS ratio differed between the Class 2 and Class 3 groups and between disc displacement groups with and without reduction. Altered disc morphology and position were correlated with significant changes in joint space in the 60°, 90°, and 120° directions. Despite minor discrepancies among condylar osseous conditions, reduced joint space was correlated with bone destruction at the corresponding site. The spring model stimulation revealed that condylar displacement caused elevated stresses on the disc and condyle. Condylar displacement causes joint space alterations while exerting compressive pressure on both the disc and condyle. Proper condylar positioning within the fossa is recommended to ensure sufficient articular disc accommodation.