Variable Cross-section Research Articles

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.

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

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.

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

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.

Isogeometric vibration analysis of functionally graded material pre-twisted blades with three-dimensional theory

In this paper, the free vibration characteristics of a rotating functionally graded material (FGM) pre-twisted blades are investigated by the isogeometric method based on the three-dimensional (3D) theory. The effects of Coriolis force, centrifugal softening, and centrifugal rigidity of the FGM pre-twisted blades are considered in this vibration analysis model. The material properties of the FGM pre-twisted blades are assumed to change continuously along thickness direction. It is easy to satisfy the weak form requirements of the vibration control equation of the FGM pre-twisted blades by using the NURBS functions. Then, the dynamic equation of the pre-twisted rotating blades can be derived by using the Hamilton's variational principle. Finally, a standard eigenvalue equation is obtained through discretizing equations and expanding dimensions. Numerical examples showed that the current formulation has fast convergency and good accuracy. Additionally, the influence of installation angle, pre-twisted angle, variable cross-section, material properties and rotating speed on the vibration characteristics of the FGM pre-twisted blades under rotating conditions is explored in detail. The work can also shed some new lights on the vibration behaviors of pre-twisted blades composite materials.

DESIGN AND MANUFACTURE OF BENT AND VARIABLE SECTION TUBES MADE OF FRP COMPOSITE

Manufacturing of bent composite tubes with variable cross-section is a challenge. The traditional process in composite materials uses retractable mandrels that in case of inflated or bent tubes cannot be applied. The tubular composite elements are often used in high performance bicycles, in the manufacturing of frames, handlebars, saddle pipe supports, etc. This paper presents research on the design of a Mountain Bike (MTB) riser handlebar made of Fiber Reinforced Polymer (FRP). The handlebar is numerically analyzed to estimate the most suitable stacking sequence of Carbon Fiber Reinforced Polymer (CFRP) layers. Depending on the safety standard of bicycle handlebars, a case of longitudinal bending tests was numerically evaluated. Comparing the weight of the CFRP handlebar with the steel handlebar of the same shape, the mass reduction is 5.2 times. The obtained results indicate a two-fold reduction in the weight of the handlebar if it is compared to a handlebar made of aluminum alloys. The research also presents the manufacturing process of the composite mold, and CFRP tubular element. Prepreg CFRP materials are used to manufacture the handlebar, the employed technology being the vacuum bag forming and autoclave curing process.

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.

Investigation into forces on offshore piles with constant and linearly varying diameters using CFD and extended Morison equation under separate wave and current loadings

This study presents a comparative analysis of hydrodynamic forces on cylindrical offshore piles with both constant and linearly varying diameters utilizing computational fluid dynamics (CFD) simulations. The classical Morison equation is evaluated alongside an extended version to address limitations in predicting forces on geometrically complex structures. Mesh convergence studies are performed to select the optimum grid size for separate wave and current simulations. The focus is on test cases characterized by small Keulegan-Carpenter (KC) numbers and relatively high Reynolds (Re) numbers within both inertia-dominated and diffraction zones. Numerical simulation results are utilized to compare the force predictions of the classical Morison equation and the extended Morison equation. It is observed that the classical Morison equation performs adequately for constant diameter piles, but it fails to predict forces on variable diameter piles accurately. In contrast, the extended Morison equation, incorporating nonlinear effects and variable cross-sections, provides significantly more accurate force predictions, particularly in the diffraction zone compared to the numerical simulations. This study emphasizes the critical importance of accounting for geometric variations, such as linearly varying pile diameters, under separate waves and currents loadings in hydrodynamic force calculations. These considerations support the development of enhanced design methods and optimization strategies, leading to safer and more efficient offshore structures.

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.

Large amplitude and small size ultrasonic milling for BT40 tool holders

Abstract The current ultrasonic milling tool holders are relatively long in structure, and the tool is susceptible to generating detrimental radial vibrations during high-speed rotation. To achieve high-quality milling of difficult-to-machine materials, a longitudinal-torsional ultrasonic oscillator suitable for BT40 tool holders has been proposed, which can generate a large amplitude while maintaining a compact length. A longitudinal vibration ultrasonic transducer with an exponential front cover is designed using the analytical method. Based on the principle of acoustic wave reflection, four spiral grooves are introduced on the exponential variable cross-section bar to convert the longitudinal vibration into longitudinal-torsional composite vibration. The effects of groove width, groove depth, and spiral angle on the longitudinal-torsional resonance were analyzed using the single-factor method in finite element software, and the optimal spiral groove parameter combination was determined. The longitudinal-torsional ultrasonic transducer is assembled with the BT40 tool holder to construct a longitudinal-torsional ultrasonic tool holder model, and modal analysis was performed. The resonant frequency was determined to be 22, 845 Hz. An experimental platform was established to carry out impedance analysis and amplitude testing on the longitudinal-torsional ultrasonic tool holder. The results show that its resonant frequency is 22, 152 Hz, which is slightly different from the simulation value. The tool holder’s maximum longitudinal amplitude is 11.2 μm, and the maximum torsional amplitude is 4.3 μm, with a torsional-to-longitudinal ratio of 0.38. The performance of the longitudinal-torsional ultrasonic tool holder meets the processing requirements of most ultrasonic milling applications, and the correctness of the design method is verified.

Buckling Loads of Variable Stiffness Columns Loaded by Top Load and Linearly and Parabolically Distributed Loading

This work presents approximate, numerical and exact series solutions for the buckling of variable cross-section columns. The loading on the columns includes tip load, distributed load along the column, and several combinations of these. Solutions are presented for nine combinations of boundary conditions at the two ends of the column. The analysis includes constant cross-section columns with constant distributed load and linearly varying distributed loads. Variable cross-section cases include columns with linear variations of the stiffness, bi-linear variations variation of the stiffness, parabolic variations and bi-parabolic variations variation of the stiffness for columns with rectangular cross-section. The results are compared by the three methods. Many new benchmark results are given for all these cases.

An integrated approach toward digital design and simulation of the automated overbraiding process for composite manufacturing

The study presents a new integrated hybrid modeling framework that combines kinematic models with Finite Element Analysis (FEA) to simulate the overbraiding process on non-circular and variable cross-section mandrels in composite manufacturing. By combining the computational efficiencies of kinematic models with the detailed physical insights from FEA simulations, this hybrid method provides a holistic solution for designing and prototyping overbraided structures. Specifically applied to a complex rectangular-to-square mandrel, the approach accurately predicts braid angles, validated against physical braiding experiments covering a range of target angles. The achieved results highlight the model's accuracy and emphasize its potential to boost the efficiency and precision of overbraiding in industrial settings, thereby reducing the need for costly and time-consuming physical braiding iterations.

Better than linear strength scaling of multifunctional ceramic truss lattice materials

Driven by the goal of creating exceptionally strong and lightweight thermal insulators to enable the operation of a vacuum airship on Venus, conditions where ceramic truss lattice materials provide better than linear scaling of strength with respect to variations in relative density have been found. This enhanced scaling relationship is a consequence of the pressure sensitive shear strength of ceramic materials. A new Gibson-Ashby type scaling relationship is developed between strength and relative density. Elementary analysis is used to formulate theoretical limits for the compressive strength, minimum density, and minimum thermal conductivity for truss lattice materials subjected to hydrostatic pressure loads. Shape optimization using the covariance matrix adopted evolutionary strategy (CMA-ES) and highly resolved finite element models is conducted on silicon carbide Kelvin cells with variable cross-section axisymmetric struts considering three failure modes: buckling, tensile rupture, and shear failure. The optimized designs closely adhere to and validate the newly developed analytical scaling relationship with better than linear strength scaling. These optimized designs are found to withstand the extreme loading conditions on Venus while providing up to 43 kgm3 of buoyancy. The thermal conductivity of the optimized designs are computed and found to be less than 0.5 WmK, with one design outperforming silica aerogels at elevated temperature.

Dynamic responses of large-diameter variable-section group-piles subjected to shaking-table tests with varying scour depths

Scouring leads to soil loss around piles, which, in turn, changes the ground-vibration characteristics and influences the seismic performance of bridges. In this study, the Xiang’an Bridge was used as a reference for constructing a large shaking-table test model to investigate the dynamic characteristics of the pore-pressure ratio of saturated sandy soils, accelerations, and bending moments of the piles, as well as the horizontal displacements of the pile-top at scouring depths of 10, 20, and 32 cm, with ground-vibration intensities ranging from 0.10-0.45 g. The results indicated that as the scour depth increased, the pile acceleration of the group piles increased and changed abruptly at the variable cross-section and soil-stratum interface. The peak values of the horizontal displacement of the pile-top and bending moment of the pile exhibited an increasing trend. As the ground-shaking intensity increased, the pore-pressure ratio of the saturated sandy soil, pile acceleration of the group piles, horizontal displacement of the pile-top, and bending moment of the pile body gradually increased, whereas the base frequency of the pile foundation gradually decreased. This study can serve as a reference for the seismic design and reinforcement of scour bridges in areas prone to seismic activity.

Experimental study of NH3/H2/Air premixed flame in a variable cross-section pipe with bluff body

Ammonia's distinctive chemical makeup, coupled with its ability to combust fully without carbon emissions, position it as a promising carbon-free fuel but requires careful management to mitigate NOx emissions. In practice, supplementing ammonia with hydrogen addresses its slow combustion rate and high ignition energy requirements. Meanwhile, the introduction of a bluff body (BB) within the pipe can alter the way of flame propagation. This study examines the combustion dynamics of the premixed ammonia/hydrogen/air flame in a pipe with a variable cross-section. The experimental findings demonstrate that increasing both equivalence ratio (Φ) and hydrogen volume fraction (αH2) significantly alters the flame front velocity (FFV) and maximum overpressure (Pmax), while also enhancing the symmetry of the flame across variable cross-section. The addition of BB creates a vortex in the flame, the formation of which intensifies the combustion of the flame behind the BB, which can promote the generation of Helmholtz oscillations, elevate the amplitude of the pressure, improve FFV, and shorten the flame propagation time in the pipe. With the increase of Φ and αH2, the time is shortened less. When Φ = 0.8, αH2 = 40%, the flame propagation time was shortened by 709 ms. When Φ = 1.2, αH2 = 60%, the flame propagation time was shortened by 5.67 ms only. In addition, Pmax and maximum flame front velocity (FFVmax) are more sensitive to αH2 than Φ. After the addition of BB, the increase amplitude of Pmax and FFVmax is increased. However, when Φ = 1.0 and Φ = 1.2, the amplitude of FFVmax increase decreases with the increase of αH2. This study can provide some suggestions for the application of NH3/H2 fuels in variable cross-sections as well as under obstacles.