Variable Cross-section Research Articles

The Deformation of a Liquid Metal Droplet Under Continuous Acceleration in a Variable Cross-Section Groove

This paper constructs a numerical simulation model for the deformation of droplets in a variable cross-section groove of a liquid droplet MEMS switch under different directions, amplitudes, frequencies, and waveforms of acceleration. The numerical simulation utilizes the level set method to monitor the deformation surface boundary of the metal droplets. The simulation outcomes manifest that when the negative impact acceleration on the X-axis is 12.9 m/s2, the negative impact acceleration on the Y-axis is 90 m/s2, the negative impact acceleration on the Z-axis is 34.5 m/s2, and the metal droplet interfaces with the metal electrode. The droplet deformation under the effect of a sine wave acceleration signal in the X and Y directions is lower than that under impact acceleration, while in the Z direction, the deformation is higher than that under impact acceleration. The deformation of metal droplets under square wave acceleration is more pronounced than that under sinusoidal wave acceleration. The deformation escalates with the augmentation in square wave amplitude and dwindles with the reduction in square wave acceleration frequency. Furthermore, there exists a phase difference between the deformation curve of the metal droplet and the continuous acceleration signal curve, and the phase difference is dependent of the material properties of the metal droplet. This work elucidates the deformation of the liquid-metal droplets under continuous acceleration and furnishes the foundation for the continuous operation design of MEMS droplet switches.

Investigation on coupling vibration characteristics of asymmetric rails with variable cross-sections based on modal separation

In railway turnouts, asymmetric switch rails with variable cross-sections are designed for wheel load transitions. However, the dynamic characteristics of these specially shaped switch rails are not yet fully understood. This paper investigates the vibration characteristics of switch rails through theoretical simulations, on-site admittance tests, and operational deflection shape (ODS) measurements. The study reveals that the modes of the switch rail involve multi-directional coupling vibrations, making the mode types indiscernible through direct observation. To address this, a modal separation method is proposed, based on the calculation of modal mass. The vertical vibration of the switch rail can be categorized into three types: torsional mode, vertical bending mode, and reverse torsion mode of the rail head and base above 600 Hz. As the position approaches the switch rail point, the degree of cross-sectional asymmetry increases, which consequently intensifies torsional vibration. Cross-sectional asymmetry is identified as the primary factor causing the coupling of bending-torsional vibrations, while variable cross-sections contribute to mode shape asymmetry and the gradual alteration of natural frequency along the rail.

A non-destructive measurement method for axial force using torque in connecting bar with joint bearing ends

ABSTRACT The measurement of axial force in connecting bar is widely used in scenarios such as condition monitoring, motion controlling and fatigue analysing of mechanisms. By measuring the torque applied to the bar, this paper proposes an innovative method for non-destructive obtaining axial force in connecting bar with joint bearing ends. A mechanical analysis of joint bearing is conducted, and a theoretical model of axial force and torque is established. An experimental setup for measuring axial force and torque is constructed, and then the theoretical model is refined. The bar axial force and torque formula is calibrated at different torsional speeds, and the method correctness and reliability are verified experimentally. In summary, in a non-destructive way, this method is innovative and practical, addressing issues like inaccuracies in measuring bars with variable cross-section, even unknown material and inside structure, achieving relatively accurate measurement of axial force in connecting bar without damage.

Crashworthiness and stiffness improvement of a variable cross-section hollow BCC lattice reinforced with metal strips

The ultra-lightweight structures with high mechanical properties and energy absorption behaviors are focused on the innovation structural design. The design strategy of implementing novel unit cells within architecture materials such as lattice materials enables the attainment of unparalleled combinations of mechanical properties and functionalities while minimizing weight. The most common method to design light-weight lattice materials is optimizing the geometric configurations of the unit cells. However, changing the geometric boundary of lattice structures can also be a good solution to improve the mechanical characteristics and energy absorption behaviors of the lattice materials. In this work, a novel variable cross-section hollow (VCH) lattice was established to improve the energy absorption capacity. By adding metal strips on the edge of the VCH lattices, a new reinforced variable cross-section hollow (RVCH) lattice with metal strips was developed to further enhance the stiffness and energy absorption capacity. The stainless VCH and RVCH lattices were additively manufactured by Selective Laser Melting (SLM) using an EP-M450H metal 3D printer. The quasi-static compressive characteristics and energy absorption behaviors of RVCH lattices were studied experimentally. Finite element modeling was implemented to study the energy absorption mechanism of RVCH lattices. A parametric analysis based on the finite element models was conducted to study the influence of different metal strips on the energy absorption capacity of RVCH lattices. The results show that the RVCH lattices with metal strips attaching to the vertical edges can signally enhance energy absorption of lattice structures with good load uniformity. Furthermore, the natural frequencies analysis indicate that the higher bending stiffness and the tensile stiffness can be achieved for RVCH lattices. This novel lattice is more stable as a load-bearing structure and more efficient as an energy absorber, which can provide guidance in designing innovative lattice structures with excellent mechanical properties and energy absorption capacity.

Machine learning approach for predicting fire resistance of FRP‐strengthened concrete beams

AbstractThis paper presents a data‐driven machine learning (ML)‐based approach for predicting the fire resistance of fiber‐reinforced polymer (FRP)‐strengthened reinforced concrete beams. To this end, a comprehensive database of fire tests on FRP‐strengthened concrete beams reported in literature was compiled. The database comprised of varying geometric and material properties, sectional dimensions, steel reinforcement, FRP layers, and thermal insulation, as well as the load level. The compiled database was analyzed using three different ML algorithms including, support vector regression, random forest regressor, and deep neural network. The outcome of the analysis is a computational‐based ML approach for predicting fire resistance of FRP‐strengthened concrete beams. The results predicted from the ML approach were compared with those measured in fire tests to show reliability of the proposed approach. The results infer that the proposed ML approach can effectively predict the fire resistance of FRP‐strengthened concrete beams with varying cross sections, properties of constituent materials, and applied loading.

Influence of half open coil structures on overall continuous induction heating of variable cross section pipe before quenching

Resistance heating of variable cross-section pipes before quenching can cause austenite grain coarsening, leading to inferior properties in thin-wall segments. This method also suffers from low heating efficiency, high energy consumption, and is time-consuming. This study compared the effects of variable cross section (VCS) and equal cross section (ECS) coil structures on overall continuous induction heating, aiming to investigate rapid and uniform heating solutions for this type of pipe. The results showed that the workpiece could be heated to the quenching temperature of 890 °C within 30 min using both coils. The ECS coil demonstrated superior heating efficiency, while the VCS coil exhibited better heating quality along the axial direction. Optimizations in VCS coil, including dynamic power control and insulation measures significantly improved the heating quality, with the final temperature distribution of the workpiece basically meeting the quenching requirements. Furthermore, an induction heating experiment was conducted to validate the reliability of the analysis model, showing good alignment with the simulated results. Overall, the application of half-open coil induction heating for variable cross-section pipes is feasible, offering a high efficiency and qualified heating quality. However, this technology is better suited for large-scale manufacturing, as each coil structure can only match one product specification; otherwise, it could significantly increase equipment costs. Additionally, for heating large workpieces, the workshop should have sufficient electrical load capacity to meet the power supply requirements.

Research on Load Transfer Mechanism of Pre-Stressed High-Strength Concrete Nodular Pile Embedded in Deep Soft Soil

The pre-stressed high-strength concrete (PHC) nodular pile is a type of PHC pile with a variable cross-section of the pile shaft, and it has normally been applied in ground treatment projects in recent years. The PHC nodular pile shaft consists of nodules, which introduce differences for the load transfer mechanism of the PHC nodular pile compared to the conventional PHC pipe pile. In this paper, the load transfer mechanism and influencing factors of the bearing capacity of the PHC nodular pile were investigated based on a group of field tests and numerical simulations. The following conclusions were obtained based on the analysis of the field test and simulation results: the nodules along the pile could effectively increase the ultimate capacity of the PHC nodular pile, and the field test results showed that the ultimate capacity of 450 (500) mm PHC nodular piles was about 1.23–1.38 times of the 450 mm PHC pipe pile after being cured for 40 days, which can be used for the design of PHC nodular pile. The simulation results showed that the bearing capacity of the PHC nodular pile would decrease with the increase in nodular spacing and nodular length along the pile shaft, while increasing with the increase in nodular diameter, and the diameter of the nodule can be increased moderately to improve the ultimate capacity of the PHC nodular pile.

Effect of Composite Scanning Strategy on Forming Quality, Microstructure, and Tensile Properties of Laser Powder Bed Fusion Titanium Alloy

Laser powder bed fusion (LPBF) technology offers significant advantages in manufacturing complex‐shaped titanium alloy components. Traditional scanning strategies, such as zigzag and island scanning, however, often fall short in fabricating parts with variable cross sections. To enhance the forming quality of components featuring combined thin‐walled and bulk structures, a composite scanning strategy is proposed that adapts to the local characteristics of parts. This novel approach is designed to employ both island and zigzag scanning within the same deposition layer, aiming to optimize the balance between porosity and stress distribution. Notably, with a feature transition distance of 4 mm and a scan line offset of 0.67 mm, the specimens achieve a tensile strength of 1311.0 MPa, a yield strength of 1103.0 MPa, and an elongation of 8.8%. This strategy leads to the optimization of defects and a transition in microstructure for combined structural features. These promising outcomes lay the foundation for the intelligent allocation of scanning strategies and the high‐quality formation of complex‐shaped, high‐strength titanium alloy parts.

A prediction model for surface settlement during the construction of variable cross-section tunnels under existing structures based on stochastic medium theory

When predicting ground surface settlement caused by constructing a new tunnel beneath existing structures, traditional stochastic medium theory inadequately accounts for the effects of abrupt changes in the cross-sectional areas of variable-section tunnels and the presence of existing structures, potentially leading to significant errors. In this paper, an enhanced ground surface settlement prediction model, based on stochastic medium theory, is proposed. The model equates the settlement of the existing structure’s base slab to that of the overlying soil and divides the horseshoe-shaped tunnel cross-section into eight arc segments, which are calculated using a polar coordinate system. Furthermore, the model treats soil loss at the junctions of variable-section tunnels as a linear transition, introduces the concept of a linear transition segment for variable sections, and accounts for the superimposed effects of closely spaced twin-tunnel excavations. Based on this model, a general-purpose calculation program has been developed that enables the rapid prediction of ground surface deformation caused by a variable-section tunnel passing beneath existing structures, simply by inputting engineering parameters. Finally, the accuracy of the prediction model was validated through comparisons with field measurement data, finite element analysis results, and calculations based on traditional stochastic medium theory. The results indicate that the proposed prediction model demonstrates high consistency with field data and finite element analysis results, whereas traditional stochastic medium theory results exhibit significant errors. This model is scientifically valid and provides a reliable reference for predicting ground surface settlement in comparable variable-section metro tunnel construction projects.

Isolator shape transition impact on hypersonic internal waverider intake flow distortion

This paper examines the impact of scramjet isolator shape transition on hypersonic internal waverider (IWR) intake. The IWR intake is designed using the osculating axisymmetric flows and streamline-tracing methods. The new Internal Conical Flow “M” basic flowfield is utilized to provide the flow information for the design method. The intake is equipped with three isolators: one with a constant cross section and two with variable cross sections with circular and rectangular exits. The entrance shape and area of the three isolators are fixed to the intake throat shape and area. The exit area of the three isolators is maintained as the entrance one. Numerical computations of three-dimensional configurations reveal that the isolators with variable cross section shapes demonstrate a higher uniformity index than those with constant cross section shape. Thus, the isolator shape transition has decreased the flow distortion of the hypersonic IWR intake system. The three isolators exhibit varied wall pressure distribution depending on the isolator cross section shape, and the total pressure recovery ratios at the three isolators' exit planes are similar. The wall pressure distributions and key performance parameters at the intake throat section, including total pressure recovery, compression ratio, and Mach number, remained consistent across the first part of the intakes. Therefore, changing the cross section shape of the isolator while keeping the area constant could enhance the flow uniformity of compressed air without negatively impacting the intake system's performance. This allows a separate shape selection of the IWR intake throat and the scramjet combustor entrance to fulfill their special requirements.

Acoustic Boundary Output Feedback Stabilization of Dynamic $n-\tau$ Model Flame via Duct With Variable Cross Section

Acoustic Boundary Output Feedback Stabilization of Dynamic $n-\tau$ Model Flame via Duct With Variable Cross Section

A State-Space Method for Vibration of Double-Beam Systems with Variable Cross Sections

A State-Space Method for Vibration of Double-Beam Systems with Variable Cross Sections

Research on Parametric Design and Mechanical Performance of Variable Cross-Section Diamond Lattice Structures

Research on Parametric Design and Mechanical Performance of Variable Cross-Section Diamond Lattice Structures

Free vibration of flexible two links manipulator with variable cross-sectional areas

This paper demonstrated the free vibration of a planar two-link flexible manipulator with harmonic drivers and non-uniformity in the cross-section of links. A dynamic model has been developed that incorporates flexibilities in both link and joint experiencing harmonic vibration, with joint flexibility modeled as torsional spring-inertia components combination. Two links were modeled based on Von Karman’s nonlinear strain relations and theory of the Euler-Bernoulli beam. The nonlinear governing equations were derived using the extended Hamilton’s principle for planar two-link flexible manipulators with variable cross-sections for each link. The coefficients of the obtained partial differential equations were as a function of spatial coordinates and were reduced to the ordinary differential equations for a family of cross-section geometries with exponentially varying widths of rectangular sections of each link. The frequency equation was obtained and analytical solutions of the vibration were achieved for different exponential shapes of each link (widening and narrowing beam for each link). Natural frequencies and mode shapes were presented for varying cross-section areas of the links. The effects of the end masses, payload, beam mass density, flexural rigidity ratio, and joint frequency were investigated on the mode shapes and natural frequencies when the power of the exponential function of the cross-sectional areas of two links was varied. The numerical results were verified with experimental results.

Research on the hydroforming law of variable cross-section shaped tubular automobile longitudinal arm

Research on the hydroforming law of variable cross-section shaped tubular automobile longitudinal arm

A multiscale Gaussian expansion method for low-frequency multimodal damping analysis of variable stiffness acoustic black hole beams

To address the issues of slow convergence and poor accuracy in existing dynamics methods caused by non-uniform variable cross-sections and layered material stiffness variations in variable stiffness acoustic black hole structure (VSABH). A multiscale Gaussian expansion method (MSGEM) is proposed in this paper. The structural dimensions are taken into account, and the structural parameters of multiple shape functions are adaptively selected based on stiffness and cross-sectional variation parameters. This results in the formation of shape function groups of various scales, which in turn creates the matrix of multi-scale Gaussian function groups. The feature information of the displacement field is realized to be extracted from multiple scales, and the fitting error of MSGEM to the displacement field of VSABH beam is within 2.02 %. The missing solution of eigenfrequency of Gaussian expansion method is avoided, and the modal vibration patterns are basically matched, which verifies the validity of MSGEM. Meanwhile, the advantages of low-frequency multimodal vibration reduction of VSABH beams are highlighted from several aspects, and the trend of the adjustment of the vibration reduction characteristics of VSABH beams by different parameters is clarified, which provides valuable design guidance for ABH metamaterials oriented to low-frequency vibration reduction.

Dynamic characteristics and damage identification with interface damage of slabs in movable point crossing

As the operating density of China’s high-speed railway increases, the phenomenon of interlayer debonding in movable point crossing (MPC) is becoming more prevalent, which can lead to failure of the frog’s slab track. Meanwhile, vehicle impacts and interlayer debonding can exacerbate abnormal vibration of the vehicle and even lead to derailment. Therefore, based on the theory of rigid-flexible coupling dynamics, a vehicle-turnout-slab coupling dynamics model is established for the first time. In this model, the crossing rails with variable cross sections is considered and the interlayer debonding between turnout slabs is modelled by nonlinear springs. Then, the characteristics of the debonding is identified by applying a wavelet transform to the dynamic response of the vehicle. Finally, different types and sizes of debonding between the layers are considered. The results show that different debonding can lead to two types of contact, partial contact and complete voiding, which can further lead to detrimental effects on vehicle safety. And the limit of the defect size that causes the track slab to void is 1 mm. On this basis, it was found that when MPC’s slab tracks were voided, longer debonding can cause high frequency vibration acceleration of approximately 700 Hz in the vehicle axle box. The new insights obtained by this study could provide guidance for the maintenance period and avoid the development of the damage. This study not only obtained a mechanism for the effect of interlayer debonding on the dynamic response of the vehicle-track system, but also provides a theoretical basis of detecting interlayer debonding for future study.

Buckling load of heavy columns with variable cross section and flexible end restraints

AbstractEffective and economical design of heavy columns, taking into account their own self weight is a common problem in engineering. The degree of restraint provided at the ends of the column should also be taken into account and it is addressed by adding rotational and/or translational springs to simulate several levels of fixity. In this work results are given for five different combinations of boundary conditions at the two ends, and for several restraint rigidities at the supports. An approximate solution using Rayleigh's method is presented and compared to numerical finite element results and to the exact solution previously derived for general cases of variable cross section columns with variable axial force.

Characteristics of Gas–Liquid Two-Phase flow in rectangular narrow slits with varying cross sections driven by large pressure drop

Pressure pipelines and vessels inevitably contain some defects. Under the most unfavorable load combinations, these defects may gradually develop into through-wall cracks. High-pressure subcooled fluid leaks through these cracks, and two-phase gas–liquid flow often occurs within the cracks. In this study, natural through-wall cracks were replaced with narrow rectangular slits with varying cross sections. Experiments were conducted to investigate the variation patterns of gas–liquid two-phase leakage flow rates and pressure drops. The study focused on four types of rectangular narrow slits with varying cross sections, a width of 28 mm, a length of 80 mm, and a gap gradually ranging from 0.134 to 0.334 mm. The liquid-phase mass flow rate ranged from 150 to 700 kg/h, whereas the gas-phase mass flow rate varied from 0 to 20 kg/h. A one-dimensional homogeneous flow model was established by coupling two-phase velocity of speed calculations. This calibrated model was then used to predict pressure drops and flow parameters for gas–liquid two-phase flow in narrow rectangular slits with varying cross sections. The experimental data were analyzed to determine the two-phase leakage characteristics of different test pieces. The results show that the inlet–outlet pressure drop and flow quality are key factors affecting the two-phase leakage flow rate. The frictional pressure drop constitutes a major part of the total pressure drop along the flow path in different test pieces. Compared with the acceleration pressure drop in the expanding slit, that in the constricting slit is higher, with an increase of approximately 32 %. Among several commonly used empirical formulas for calculating two-phase viscosity, the McAdams and Dukler empirical correlations were found to be less suitable for high-velocity two-phase flows. In contrast, the Cicchitti empirical correlation provides better predictions, with a mean absolute deviation (MAD) and mean relative deviation (MRD) of no more than 8 %. The viscosity of the gas-phase medium affects the two-phase flow characteristics in narrow slits, which should be considered in practical engineering applications.

Semi-analytical modeling and vibration characteristics analysis of the orthogonally stiffened cylindrical shell with variable cross-sections of stiffeners

The stiffened shell with variable cross-sections of stiffeners (SS-VC) has important applications in aerospace and other fields. Its excellent mechanical properties provide new possibilities for the design and performance improvement of stiffened structural parts. However, its dynamic modeling problems have been urgent to be solved. In this study, the dynamic model of the orthogonally stiffened cylindrical shell with variable cross-sections of stiffeners (OSCS-VC) is established by the semi-analytical method (SAM) and it can be described as follows. The displacement allowable functions of the structure are constructed by using the Gram-Schmidt orthogonalization method. Based on Sanders shell theory, the stress-strain relationships of the longitudinal and ring stiffeners with variable cross-sections are derived under the variable limit integration. The boundary spring stiffness is obtained by the inverse identification technique. The dynamic equation of OSCS-VC is established and solved by using the Lagrange equation. Then, a case study is carried out, the rationality of the semi-analytical dynamic model of OSCS-VC is verified by ANSYS engineering software, literature and the experiment system. Finally, based on the semi-analytical model of OSCS-VC, the influence of the characteristic parameters of cross-sectional functions (CSF) for the longitudinal and ring stiffeners on the natural frequencies is analyzed.