Support Stiffness Research Articles

Investigating the spall phenomena in glass filler embedded epoxy composites using laser-induced stress wave

Recently, Singh and Kitey (Experimental Mechanics, 60(7), 2020) used laser-induced stress pulse in conjugation with Michelson's interferometer to measure the spall strength of thin polymer layers. In this investigation, the method is expanded to measure the spall strength of spherical and slender glass filler-reinforced epoxy composites. A filler-reinforced epoxy layer of ∼150 μm was deposited onto a glass substrate, and a short-duration and high-magnitude stress pulse developed at the back surface of the substrate. A complex interaction between the mode-converted main compressive wave and slow-moving secondary tensile wave generated a greater magnification tensile area near the layer's free surface, causing a spall. The composite layers experienced a strain rate of ∼107/s, with the secondary wave not distinct from the interferometric data due to filler-induced multiple mode conversions. An equation correlating strain rate, impedance, and fracture toughness with spall strength was used to ascertain the composite layers' spall strength. The findings showed that stiff reinforcements improve epoxy spall strength, with milled fiber composites exhibiting greater spall strength than spherical particle cases, as corroborated by optical micrographs showing fiber-bridging across the spalled zone. The spall strength of epoxy composites with 10 % milled fibers was nearly 2.5 times greater than pure epoxy.

Quantitative Research on Roof Deformation and Temporary Support Stiffness in Deep-Mine Gob-Side Entry Retaining by Roof Cutting

The important technical process to ensure the success of gob-side entry retaining by roof cutting (GERRC) was the advanced pre-splitting blasting to cut off the mechanical connection between the roadway and working face roof. The whole-cycle roof structure evolution and stress characteristics of GERRC were analyzed. The factors affecting the roof deformation of GERRC were analyzed, and the quantitative relationship between the roof deformation of GERRC and the support stiffness was determined. The results showed that the temporary support stiffness was higher, the support position to the side of the roof cutting was closer, and the roof subsidence deformation of GERRC was smaller. It is proposed to use a single support mass with a high stiffness to control the deformation of the roof, but it also made the support mass and roof elastic potential energy aggregate. To fully utilize the matching of the support stiffness and roof subsidence, improve the stability, and control the subsidence deformation of the roof in GERRC, double-row stacking supports were adopted in the inclination of GERRC, which were used to increase the stiffness of the support system.

Study on the effect of bearing position and stiffness on the dynamic behavior of output stage of CHT system based on the cylindrical gear meshing

The internal and external rotor shafts are important components to transfer power in coaxial helicopters, and bearing supports could affect the dynamic behavior of the transmission system. In order to explore the influence of bearing support structure, bearing position and support stiffness on the dynamic behavior of the output stage of coaxial helicopter transmission (CHT) system based on the cylindrical gear meshing, a rigid-flexible coupled dynamic model is established under cantilever-cantilever support structure and cantilever-simple support structure considering the flexibility of rotor shaft based on Timoshenko beam theory, and time-varying mesh stiffness (TVMS), comprehensive meshing error are also considered. Newmark-beta numerical method was applied to calculate the dynamic response. The result indicates that the load sharing performance of gear pair using cantilever-simple support structure is better than that of cantilever-cantilever structure, but the maximum vibration displacement of bull gears is reduced apparently. Simultaneously, the bearing positions and stiffness can be adjusted to achieve better performance in load distribution and maximum vibration displacement of bull gears.

Resonant peak reduction of a rotor system based on gradually variable stiffness of supports with shape memory alloy springs

A novel method for reducing the resonant peak of a flexible rotor at critical speeds based on control of the gradual variable stiffness of supports (GVSS) using shape memory alloy (SMA) springs is presented in this paper. The resonance peaks of a rotor structure can be attenuated through the design of GVSS law. Firstly, the impact of GVSS on the rotor's critical speeds was analyzed, and the mechanical mechanism of vibration reduction based on GVSS was identified. Secondly, a rotor system with a single critical speed was used for simulation analysis and it was founded that the starting time to change support stiffness and the change rate were two critical factors that affect vibration reduction. Then, a further simulation was undertaken on a test rig designed with dynamic similarity of an aeroengine rotor having multiple supports and multiple critical speeds. The range of the variable stiffness with SMA springs’ supports and the control strategy of GVSS were investigated. Afterwards, the test rig was manufactured and assembled for testing and validation. To achieve rapid temperature changes for variation of the support stiffness, an innovative design utilizing the carbon fiber heating tubes and the liquid nitrogen sprays for heating and cooling of shape memory alloy springs was carried out. The test results indicate that using gradually variable stiffness of supports with SMA Springs can effectively reduce the multiple resonance peaks of a rotor, with a maximum suppression rate of 52.3 %. This verifies the feasibility of the method. It also indicates the potential for further engineering applications.

Failure Mechanism and Structural Optimization of the Primary Support Structure for Expressway Tunnel in Soft Rock: A Case Study

When the highway tunnel crosses the soft rock, the primary support structure often fails and damages because it cannot withstand the excessive surrounding rock pressure. For the Magu tunnel in Yunnan Province, which is in the upper hard and lower soft stratum, the surrounding rock deformation is large, and the primary support structure occurs spray concrete cracking, steel arch frame twisting deformation. According to the convergence constraint curve, this paper proposes to adopt the primary support optimization design scheme of "shortening the bench length + optimizing the length and arrangement of anchor rods". According to the numerical simulation results of FLAC3D, the important indexes such as deformation convergence, surrounding rock stress, anchor axial force and thickness of plastic zone in different excavation support conditions are analyzed. The conclusions are as follows: 1. The soft rock at the foot of the benches does not provide sufficient support resistance, resulting in large settlement and convergence deformation that can cause the primary support structure to fail and become damaged. 2. The length of the middle bench and the primary support strength and stiffness contribute most to the deformation. 3. The deformation control effect of the short anchor rods on the surrounding rock is relatively weak. Increasing the length of anchor can better play the role of anchor suspension enhancement and give full play to the surrounding rock's own bearing capacity. Finally, the deformation of the tunnel is under control after adopting the optimized primary support structure, which ensures the smooth construction.

Influence of wind-blown sand content on the mechanical quality state of ballast bed in sandy railways

During the operation of sandy railways, the challenge posed by wind-blown sand is a persistent issue. An in-depth study on the influence of wind-blown sand content on the macroscopic and microscopic mechanical properties of the ballast bed is of great significance for understanding the potential problems of sandy railways and proposing reasonable and adequate maintenance and repair strategies. Building upon existing research, this study proposes a new assessment indicator for sand content. Utilizing the discrete element method (DEM) and fully considering the complex interactions between ballast and sand particles, three-dimensional (3D) multi-scale analysis models of sandy ballast beds with different wind-blown sand contents are established and validated through field experiments. The effects of varying wind-blown sand content on the microscopic contact distribution and macroscopic mechanical behavior (such as resistance and support stiffness) of ballast beds are carefully analyzed. The results show that with the increase in sand content, the average contact force and coordination number between ballast particles gradually decrease, and the disparity in contact forces between different layers of the ballast bed diminishes. The longitudinal and lateral resistance of the ballast bed initially decreases and then increases, with a critical point at 10% sand content. At 15% sand content, the lateral resistance is mainly shared by the ballast shoulder. The longitudinal resistance sharing ratio is always the largest on the sleeper side, followed by that at the sleeper bottom, and the smallest on the ballast shoulder. When the sand content exceeds 10%, the contribution of sand particles to stiffness significantly increases, leading to an accelerated growth rate of the overall support stiffness of the ballast bed, which is highly detrimental to the long-term service performance of the ballast bed. In conclusion, it is recommended that maintenance and repair operations should be promptly conducted when the sand content of the ballast bed reaches or exceeds 10%.

Synchrotron X-ray diffraction studies of the internal load transfer in Ni–CrC metal matrix composites

Strengthening in metal matrix composites (MMCs) is primarily due to the load transfer from the compliant matrix to the stiff reinforcement. While internal load transfer has been studied for conventionally manufactured MMCs, the extent to which it may be affected by the preexisting defects in additively manufactured MMCs remain elusive. In this study, we performed uniaxial compression loading on cold sprayed Ni–CrC particulate-reinforced MMC. We observe significantly enhanced strength and ductility compared to the brittle behavior previously reported in tension for the same MMC. In contrast to the absence of load transfer in tension, the presence of initial defects did not preclude the internal load transfer in the composites under compressive loading. In-situ high-energy X-ray diffraction analysis revealed a relatively constant load partitioning in the elastic regime, which aligned well with predictions by the Eshelby's inclusion model. Furthermore, an internal load transfer was observed from the Ni matrix to the CrC reinforcement upon plastic deformation of the Ni matrix. Finite element modeling further confirmed this and demonstrated that localized tensile stress at the interface in the transverse direction resulted in the interfacial debonding and partial relaxation of the matrix. We also report reinforcing particle fracture upon further compression which in turn triggered the eventual failure of the MMC.

Vibration and stability of axially moving beam on multiple intermediate elastic supports with transfer matrix method

This study delves into the vibration characteristics and stability of an axially moving beam with multiple intermediate elastic supports. Initially, the motion equation of the beam is developed, setting the stage for an in-depth investigation of its free vibration characteristics through the transfer matrix method. This analysis covers the beam’s natural frequencies and critical velocity when moving at a constant velocity. Additionally, the dynamic behavior of the beam is investigated when it is subjected to constant axial movement and a concurrent traveling load. The multi-scale method is used to analyze the instability regions of the axially moving beam on multiple intermediate elastic supports as disturbance of the axial movement approaches subharmonic and sum-type combined resonances. The investigation further considers how alterations in the stiffness and configuration of the elastic supports influence the dynamic behavior and stability of the beam. Unique dynamic characteristics arise when the axially moving beam is supported by multiple elastic elements, contrasting with those observed in beams without such supports. An increase in support stiffness enhances the critical velocity at which the beam axially moves, potentially causing modal transformations of the structure prior to reaching this critical velocity, and diminishing the instability regions associated with sum-type combined resonances under disturbance velocities.

Modelling of foundation stiffness beneath intermediate support of 178 m long integral viaduct

The paper presents three methods of modelling of foundation stiffness beneath intermediate support of a 178 m long integral box girder viaduct and its impact on the values and distribution of displacements and internal forces in the pier of this support. The pier support is made of cast in situ reinforced concrete of strength class C50/60. For the analysis, three models were built in Abaqus FEA software. The first model A3D in Fig. 1 represents a complex three-dimensional model. The second L2D and the third H2D model shown in Fig. 2 represent simple two-dimensional models. The stiffness of the subgrade beneath the structure in the second and third model was modelled as spring constants calculated based on the equations given in the reference [8] model L2D and [10] model H2D. The middle range value of Young’s modulus for sand and gravel was used to calculate the subgrade stiffness parameters. In all models, a horizontal displacement in the Y direction of value 20 mm and a vertical force of value 18200 kN were applied to the top of the pier support. The horizontal displacement was caused by the thermal longitudinal expansion of the six-span viaduct deck and the braking force. The vertical force was caused by the dead, superimposed, and live loads acting on the viaduct deck. Finally, the values and distributions of displacements and internal forces in the pier support from the complex model were compared with the values in two simple models. The author focuses on the method of modelling of foundation stiffness of the pier support and its impact on the values of displacements and internal forces in the pier support. A similar structure analysed in this paper was design-checked by the author in Ireland [4].

The influence of existing piles on station settlement during the construction of a tunnel undercrossing under existing stations

In the construction of tunnels under existing stations, it is necessary to control their settlement. When there is a pile foundation in the existing station, the pile cutting has a significant impact on the settlement of the existing station. To determine the influence of existing piles on the settlement of subway stations, a reasonable pile-cutting time is proposed. Based on the Chengdu Metro Line 9 underpassing the existing Line 1 hatchery station, the settlement law of the tunnel underpassing the existing Line 1 station is analysed via a numerical simulation. Furthermore, the deformation and stress characteristics of the existing piles, pipe roofs, and tunnel linings and the supporting effect on the existing station are discussed. It is concluded that the cutting of existing piles causes a change in the tunnel bearing system, thus resulting in a certain deformation of the station. The influence of different pile cutting times on the settlement of the existing station is then analysed, and it is clarified that the tunnel support stiffness is significantly enhanced after the construction of the secondary lining. At this time, the settlement of the existing pile station is significantly reduced. Finally, through a field investigation, the effect of surface grouting, pipe shed, and multilayer lining on the settlement control of the existing station while the existing pile foundation exists is determined. This research can provide a reference for the settlement control and foundation underpinning of existing stations at ultra-small distances in underground excavation tunnels.

Study on prestress distribution and structural performance of heptagonal six-five-strut alternated cable dome with inner hole

The cable dome structure is a highly efficient prestressed space structure with reasonable force, attractive shape, and large spanning capacity. It is increasingly widely used in stadiums, exhibition halls, terminals, and other large-scale public buildings and the roof structure of various transport hub projects. To solve the problem of weak overall structural stability of the traditional cable dome structure, a new type of prestressed space structure is proposed - heptagonal six-five-strut alternated cable dome with an inner hole. The composition of the structural system was given and a theoretical study of the distribution of structural prestress was carried out; based on the symmetry and periodicity conditions, the initial prestress distribution of the structure was accurately calculated using the node balance method, and the formulae for the geometric parameters of the structural cable-strut were derived; the numerical model was established by using the finite element software ANSYS 2022 R1, and the force characteristics of the structure under full-span uniform load, half span uniform live load, wind load, and temperature were studied. The effects of structural prestress, overall shape, and support stiffness, totaling three categories and six parameters, on the structural mechanical performance of the internal force of the member, node displacement, and support reaction force were analysed in detail and the sensitivity of the parameters is assessed quantitatively, accordingly, the values of the main design parameters such as thick-span ratio are given as suggestions. The analysis results show that the new structural system has a high load-carrying capacity and deformation resistance, and its proposal provides a new scheme and new ideas for the selection and design of the cable dome.

Research on a Calculation Method for the Horizontal Displacement of the Retaining Structure of Deep Foundation Pits

The precise calculation and effective control of the horizontal displacement of deep foundation pit retaining structures are critical for foundation pit support design and construction. Based on stress–strain linear elastomer theory and considering the deformation coordination between an enclosure wall and its internal support member, a formula for the redundant restraint force acting on the retaining wall was derived through the unit load method and the principle of elastic superposition. Moreover, a method for calculating the horizontal displacement of the retaining structure of a deep foundation pit was formulated, which is convenient for engineering applications. The method can also be used to calculate the horizontal displacement of cantilevered and anchored retaining structures when the loading conditions of the deep foundation pit and the relevant parameters of the enclosure structure are known. A case study was conducted on a standard section with an excavation width H of 19.3 m and an excavation depth h of 17.8 m. The structural parameters of the enclosure wall, along with the elastic support stiffness coefficient and soil layer parameters of the pit, were inputted into a MATLAB calculation code. Then, four internal support constraint forces Fi and the calculated values for the horizontal displacement of the enclosure wall were obtained after running the code. The calculated curve closely matched the curve of values measured in the field. The horizontal displacements of the top of the wall of several cement–soil gravity enclosure structures mentioned in the literature were also calculated. The results of these calculations were then compared with the measured data and corresponding data from the literature. The examples provided clear evidence demonstrating that the proposed method is highly reliable for calculating the horizontal displacement of deep foundation pit enclosure structures.

Deformation constrained support-structure optimization for laser powder bed fusion

Support structures act as primary conduits for heat flow in laser powder bed fusion (LPBF). Frame supports, as opposed to block-type supports, have proven to be a good choice for LPBF, with no metal powder entrapment and ease of removal. In this paper, we use a multi-load formulation, where different loads at different instances of time are used for frame support optimization, to constrain the structural deformation of the part during printing. Parts and supports are analyzed in tandem at the end of each layer build, to account for the role of support stiffness in the overall part deformation. The proposed framework prevents recoater collision, and controls the geometric accuracy of the part, by optimizing the size of frame supports. Numerical results for the optimal volume of manufacturable frame support are reported for geometries with varying overhang characteristics.

Modelling and testing of the dynamic support stiffness of assembled bearings in motorized spindles

Modelling and testing of the dynamic support stiffness of assembled bearings in motorized spindles

Processing parameter effect, formation mechanism and inhibition method of micro-hole exit defects in rotary ultrasonic pecking drilling of SiCf/SiC composites

High brittleness and anisotropy of ceramic matrix composites lead to great challenges for micro-hole machining. Micro-holes with large depth-to-diameter ratio (10:1) of SiCf/SiC composites were machined by rotary ultrasonic pecking drilling process. Based on the mechanical theory and structural characteristics of SiCf/SiC, a critical thrust force model was established. The effects of processing parameters on machining accuracy and machining quality of micro-hole exits were analyzed and parameters were optimized. The formation mechanism of exit defects includes interfacial debonding, fiber bending and matrix fracture. A method based on the surface morphology to inhibit exit defects by increasing the support stiffness of the material was proposed, under which the exit roundness all reached IT8 level and chipping factors decreased by 53 %–67 %, and only a small amount of chipping and micro-cracks was at the exit. The proactive control of micro-hole exit defects was realized, and a better machining quality was obtained.

Experiences Using MEMS Accelerometers on Railway Bearers at Switches and Crossings to Obtain Displacement—Awkward Situations

A sleeper, or more generally a “bearer”, moves vertically under a passing train load. The extent of this motion depends on the static and dynamic load of the train, the train speed, and the support conditions at the bearer and its neighbours. Excessive motion, typically from voiding see-sawing, low support stiffness or possibly excessive stiffness, or even too little stiffness, are all of interest to maintainers. Typically, problems arise around transition zones, switches and crossings, but plain track with poor support can also be a problem. Within the last decade, low-cost micro-electro-mechanical system (MEMS) accelerometers have been used to capture the time history of vertical motion for use in condition monitoring. Existing condition monitoring systems often overlook or sometimes even ignore the possibility of problematic data, which seem to be common in monitored locations. It is essential to understand whether such “bad” data require further attention. Three problematic sites are presented, focussing on examples where the acceleration was higher than expected or the computed displacement was not as expected. Potential causes include wheel defects, hammering of the ballast by a hanging bearer, or high acceleration at some structural resonant frequency. The present paper aims to show the challenges of using MEMS accelerometers to collect data for condition monitoring and offers insights into the sort of problematic data that may be collected from real sites.

Experimental study and numerical simulation of the impact of under-sleeper pads on the dynamic and static mechanical behavior of heavy-haul railway ballast track

AbstractLaying the under-sleeper pad (USP) is one of the effective measures commonly used to delay ballast degradation and reduce maintenance workload. To explore the impact of application of the USP on the dynamic and static mechanical behavior of the ballast track in the heavy-haul railway system, numerical simulation models of the ballast bed with USP and without USP are presented in this paper by using the discrete element method (DEM)—multi-flexible body dynamic (MFBD) coupling analysis method. The ballast bed support stiffness test and dynamic displacement tests were carried out on the actual operation of a heavy-haul railway line to verify the validity of the models. The results show that using the USP results in a 43.01% reduction in the ballast bed support stiffness and achieves a more uniform distribution of track loads on the sleepers. It effectively reduces the load borne by the sleeper directly under the wheel load, with a 7.89% reduction in the pressure on the sleeper. Furthermore, the laying of the USP changes the lateral resistance sharing ratio of the ballast bed, significantly reducing the stress level of the ballast bed under train loads, with an average stress reduction of 42.19 kPa. It also reduces the plastic displacement of ballast particles and lowers the peak value of rotational angular velocity by about 50% to 70%, which is conducive to slowing down ballast bed settlement deformation and reducing maintenance costs. In summary, laying the USP has a potential value in enhancing the stability and extending the lifespan of the ballast bed in heavy-haul railway systems.

Deformation of Existing Shield Tunnel Adjacent to Deep Excavations: Simulation and Monitoring Analysis

Deep excavations near subway tunnels can induce deformation, necessitating a comprehensive investigation into causal factors and mitigation strategies. Field measurements were conducted to assess both vertical and horizontal displacements of existing tunnels near a deep excavation in Shenzhen. Utilizing a validated three-dimensional finite element model that considers structure−strata interactions, this study analyzes tunnel displacements, ground movements, diaphragm wall impacts and the sensitivity of enclosure structure parameters. The results indicate that tunnel deformation correlates with enclosure structure deformation, particularly near the center of the pit. Moreover, shallow soil excavation significantly affects the vertical displacement of shallow-buried tunnels. However, the design parameters of the existing enclosure structures inadequately limit tunnel displacement. Therefore, it is crucial to intensify vertical displacement monitoring in shallow tunnels during early excavation stages and to enhance horizontal displacement monitoring during later phases. Implementing measures such as optimizing central support design or retaining soil at the pit bottom helps control maximum horizontal displacement. While support stiffness plays a greater role than retaining wall thickness, its impact on deep excavation projects is limited.

Development of transition schemes and optimization measures between normal slab track and ladder-type sleeper track

Severe vibrations and deterioration of track system are often observed due to the sudden change in support stiffness between normal slab track (NST) and damping track. To improve the dynamic performance of both the train and track system when a train runs on the transition zone between the NST and the damping track, we focused on the ladder-type sleeper track (LS track) and developed several optimized transition schemes. Firstly, a train-LS track coupled dynamics mode is developed, and it was verified using field testing. Afterward, using the dynamic responses of train and track systems in the transition zone between the NST and the resilient-fastener slab track (RFS track) as a reference, the shortcomings of the traditional transition scheme are identified, and the optimal transition scheme is developed by comparison of the proposed multiple schemes. Finally, the device for suppressing track vibration (DSTV) is installed on the longitudinal sleeper to alleviate the vibration of the LS track and improve the overall stability of the vehicle and track system during the transition zone. The results indicate that the optimal transition scheme proposed in this study lead to significant improvements in the dynamic performance of both the vehicle and LS track.

Numerical simulation analysis of sleeper damage under dynamic load based on discrete element method

To analyze the damage development of concrete sleepers during railway operation, the discrete element method and the parallel bond degradation model are introduced into the damage analysis of concrete sleepers for the first time. The cracking resistance and dynamic characteristics of the sleeper model are verified by comparing the existing literature. The influence of load and the stiffness of the bottom support on the damage development of the sleeper is considered and the following conclusions are drawn: with the increase in the load amplitude, the damage of the sleeper will increase nonlinearly; under the conditions of the same time and the same load amplitude, the number of cracks of the sleeper will increase with the increase of load frequency, and increase exponentially with the number of loads. Different support stiffness at the bottom of the sleeper will change the dynamic characteristics of the sleeper under load, thus changing the damage development of the sleeper. For the sleeper with full support at the bottom, when the support stiffness at the bottom is low, the center of the sleeper is more likely to be damaged. When the support stiffness at the bottom of the sleeper is large, hanging the center of the sleeper about 1/3 of the length of the sleeper can reduce the damage to the center of the sleeper. The research results show that this method can be applied to the study of sleeper damage and provide a new idea for the structural damage of sleepers.