Trapezoidal Profile Research Articles

Design of polarization-independent multilayer dielectric gratings: a reflection-phase threaded approach

We present a method to design polarization-independent multilayer dielectric gratings. In this method the reflection phases in TE and TM polarizations of the multilayer stack thread surface-relief grating at the top and the multilayer stack at the bottom together, allowing the two parts first to be designed separately and efficiently, and then to be combined to achieve simultaneously high diffraction efficiency and large fabrication tolerance. We find numerically that in general a periodic stack is unable to provide the top-grating-demanded phase difference between TM and TE polarizations; adequate aperiodic layers atop of a periodic stack are needed. The analytic diffraction efficiency formula of a recent work [J. Opt. Soc. Am. A 41, 252 (2024)] is used at various places of the presented optimization algorithm to save computation time. An example grating with rectangular surface-relief profile and another with trapezoidal profile were successfully designed, validating the effectiveness of this design method.

Prestressed CFRP Plates and Tendon Strengthening of Steel–Concrete Composite Beams

This study aims to enhance the ultimate capacity and stiffness of steel–concrete composite beams through external strengthening with prestressed carbon fiber-reinforced polymer (CFRP) plates and post-tensioned CFRP tendons. A 3D finite element model was developed using ANSYS and validated using experiments. The impact of various parameters on the capacity of the beam was investigated, including the level of post-tensioning in the CFRP tendons, tendon profile, degree of shear connection, and beam load level when adding strengthening CFRP tendons. Results indicate that reinforcing composite beams with bonded CFRP plates using post-tensioning tendons with trapezoidal and parabolic profiles can increase maximum load capacity by 37% and 60%, respectively, while maintaining high stiffness. This study also indicates that the optimal strengthening conditions for the composite beam are when the beam is loaded up to 70% of its capacity and has a composite action degree of 100%.

Effect of corrugated plate arrangements on the performance of steel shear wall frames

Nowadays, the use of corrugated steel shear walls with sinusoidal, triangular, and trapezoidal profiles, which are stiffened steel walls without stiffener, is recommended for delaying the premature occurrence of buckling in the plate. The arrangement of corrugated plates in the structural frame alters seismic parameters; therefore, this research focuses on various arrangements of inclined corrugated plates. For this purpose, experimental specimens are first validated under cyclic quasi-static loading using ABAQUS finite element software. Subsequently, the design of four different arrangements of inclined corrugated plates with three profiles of trapezoidal, sinusoidal, and triangular is conducted and compared with vertical and horizontal arrangements. Based on the results, the triangular waveform demonstrated better energy absorption, initial stiffness, and ultimate strength. Investigation of different plate thicknesses for triangularly corrugated shear walls, including 0.75, 1.25, and 1.75 mm, showed that increasing the wall thickness improved the seismic behavior. Additionally, Arrangement No. 1 (inclined arrangement) provided the highest energy absorption and ultimate strength; however, its behavior in the hysteresis curve was asymmetric. This issue has been addressed by implementing a double arrangement of plates.

Heated-H3PO4 etching of (001) β-Ga2O3

β-Ga2O3 is a promising ultra-wide bandgap semiconductor with melt-grown substrates that are scalable, particularly in the (001) orientation. In this study, we report on the heated-phosphoric acid etching of (001) β-Ga2O3. A wagon wheel pattern with spokes aligned to a range of specific crystallographic directions was fabricated on (001) β-Ga2O3. At 160 °C, the (001) etch rate was 1.47 μm/h, which is comparable to etch rates obtained via dry etch techniques. The etched (001) surface had a morphology that was smoother than an inductively coupled plasma etched surface. All spokes possessed relatively smooth sidewalls. Spokes oriented along the [100] direction exhibited minimal SiO2 mask undercut rates at lower etch temperatures and symmetric trapezoidal profiles with near vertical (010)-like sidewalls, which are ideal for device structures with a trench geometry. Spokes oriented along the [010] direction exhibited significant SiO2 mask undercut rates and asymmetric trapezoidal profiles with different sidewall angles. These spokes also possessed reduced sidewall angles, which is favorable for field management at device corners and edges. The etch process was used to realize a dense array of [100]-oriented trenches with a height of 1.5 μm, a base width of 2.0 μm, and a mask width of 0.8 μm. The work highlights the potential for ion damage-free, standalone heated-H3PO4 etching as a viable alternative to the dry etching of (001) β-Ga2O3 for high-performance device applications.

Effect of trapezoidal plasma density region in bubble wakefield acceleration

In the process of bubble wakefield acceleration highly nonlinear region is developed inside plasma, which intuitively suggests that nonuniform plasma density having gradients may be more suited to achieve large nonlinearity in the system. Moreover, when an intense laser pulse propagates in a plasma, it is subjected to various instabilities and these instabilities can be controlled by plasma density profiles which effectively control the energy and flux of the accelerated particles. Considering all these points we investigate in the present work the scaling effect of up-ramp and down-ramp regions in plasma density profile on the bubble wakefield. These regions are separated by a plateau region (maximum density) enabling the density to have trapezoidal profile. With this density profile, the bubble wakefield acceleration is examined considering four different lengths of up-ramp and plateau regions keeping a constant down-ramp length. Increasing steepness of up-ramp length (larger density gradient), i.e., lowering the length of up-ramp and increasing the plateau length creates a bubble having higher wakefield strength, resulting into higher accumulation of plasma electrons at its tail and higher energy spectrum with higher kinetic energy gradient and Poynting flux of accelerated electrons.

Implementation of a motion planning technique for a low-frequency piezo-actuated inchworm drive

A novel piezoelectric inchworm drive capable of long-range motion has been designed, fabricated, and tested in this research work. To control the motion of the inchworm drive, trajectory planning has been proposed. The trajectory planning ensures that the inchworm drive achieves smooth and continuous motion with high accuracy. Two trajectory planning methods were incorporated for the developed inchworm drive: a linear function with a parabolic blend trajectory and a cubic polynomial trajectory. Simulations for both the cubic polynomial and trapezoidal trajectories were conducted, with the estimated displacement results closely verified through experimental validation. The fabricated inchworm drive is tested for varying input voltages and frequencies. The experimental findings demonstrate that the proposed piezoactuated Inchworm drive can achieve substantial displacement, constrained only by the linear slide’s length. When an input signal of 150 V peak to peak and frequency of 10 Hz is applied to the inchworm drive, it was capable of moving at a speed of 1425 μm/s. When incorporating trajectory planning for the Inchworm drive the experimental results show that the maximum percentage error for the trapezoidal motion profile is 1.56% and the cubic polynomial profile trajectory is within 1% for the corresponding target position for a travel range of 25 mm of the inchworm drive.

Aluminum-Based Plasmonic Photodetector for Sensing Applications

Plasmonic sensors have great potential for widespread usage. However, the prohibitive cost of noble metals restrains the wider adoption of these devices. The aim of our study is to develop a cost-effective Al-based alternative to common noble metal-based plasmonic detectors. We considered a structure consisting of an n-type doped Si wafer with a shallow p-n junction and an overlying Al grating with a trapezoidal groove profile. The RCWA (rigorous coupled-wave analysis) method was used to numerically calculate the distribution of absorbed light energy in the plasmonic detector layers and to optimize the grating parameters. Based on the simulation results, experimental samples of plasmonic photodetectors with optimal grating parameters (period—633 nm, relief depth—50 nm, groove filling factor—0.36, and thickness of the intermediate Al layer—14 nm) were manufactured, and their properties were studied. For these samples, we obtained a polarization sensitivity value of Ip/Is = 8, an FWHM of the resonance in the photocurrent spectrum ranging from 50 to 100 nm, a sensitivity at the resonance maximum of Iph = 0.04–0.06 A/W, and an angular half-width of photocurrent resonance of Δθ = 5°, which are comparable to noble metal-based analogs. Our results may be used for creating cost-effective high-sensitivity plasmonic sensors.

Research on the Influence of the Material Removal Profile of a Spherical Polishing Tool on the Mid-Spatial Frequency Errors of Optical Surfaces.

Elastic spherical polishing tools effectively conform to the polishing surface and exhibit high efficiency in the removal of materials, so they are extensively used in the sub-aperture polishing stages of optical components. However, their processing is often accompanied by significant mid-spatial frequency (MSF) errors, which critically degrade the performance of optical systems. To suppress the MSF errors generated during polishing with spherical tools, this study investigates the influence factor of MSF errors during the polishing process through an analysis of the convolution effect in material removal. A material removal profile model is established, and a uniform removal simulation is conducted to assess the influence of different shape material removal profiles on MSF errors. Simulation and experimental results show that a Gaussian-like shape material removal profile is more effective in suppressing the MSF errors during polishing compared to the "W" and trapezoidal shape material removal profiles. In addition, based on the characteristics of the RMS decreasing in a serrated trend with the decrease in path spacing, a path spacing optimization method considering the polishing efficiency is proposed to improve the polishing efficiency while controlling the MSF errors, and the effectiveness of the path spacing optimization method is verified by comparing the MSF error at the maximum theoretical path spacing and the path spacing that is less than this. Finally, the path spacing optimization method is used to polish single-crystal silicon to further illustrate its practicality.

Biomechanical Analysis of Trapezoidal Thread Screw-Rod Fixation in Pedicle Section of Cervical Spine: A Finite-Element Analysis.

Cervical pedicle screw-rod fixation presents a complex approach in spinal surgery, offering enhanced spine stabilization in variable conditions considering traumatic injuries, degenerative changes, as well as orthopaedic and oncological ailments. This technique employs small diameter screw implants strategically placed to bolster the mechanical integrity of the spine. Notably, it involves minimally invasive procedures, resulting in smaller incisions and reduced patient discomfort. This study aims to assess the effects of trapezoidal thread screws in pedicle sections of the cervical spine during flexion-extension loadings, focusing on factors such as range of motion (ROM), implant stress, and stress on adjacent bone. Utilizing CT scan data, a finite element model of the cervical spine (C2-C7 vertebrae) was prepared. Trapezoidal thread screws were integrated into a single-level pedicle screw-rod fixation at the C5-C6 vertebrae. The C2 vertebra were given a compressive load of 50 N along with a moment of 1 Nm, resulting in the immobilization of the C7. The results indicate a reduction in ROM at the C5-C6 level by 69% to 77% compared to the intact spine during flexion-extension loading, with a slight increase in ROM observed at adjacent cervical spine levels. Stress analysis revealed that the trapezoidal thread screws induced stresses ranging from 24 MPa to 29 MPa in PEEK trapezoidal screw-rod implants, which fall below the material's yield stress. This suggests that the trapezoidal thread profile may be advantageous in minimizing stress concentration, attributed to its larger contact area with the vertebrae bone between the threads.

Identification of the effective crane hook's cross-section by incorporating finite element method and programming language

The crane hook is a widely utilized component in several industries for the purpose of lifting things. The crane hook must possess the capacity to withstand the intended load without encountering any complications, hence ensuring the safety of both personnel and the objects being lifted. The process of analysis is crucial for the effective utilization of a crane hook. The primary aim of this study was to determine the most efficient cross-sectional crane hook among five distinct geometric profiles. This was achieved through the application of finite element analysis using Solidworks software. Subsequently, the identified cross-sectional profile was further examined using the Python programming language, taking into account the classical equation of a curved beam. The five cross-sectional shapes seen in the study were circular, rectangular, trapezoidal, I-shaped, and T-shaped. For the purposes of this investigation, the chosen material for each cross-sectional crane hook model was 34CrMo4 steel. Despite the identical boundary constraints imposed on all the chosen cross-sectional crane hook profiles, it was observed that the trapezoidal cross-sectional crane hook exhibited superior performance compared to the others. The trapezoidal cross-sectional crane hook model exhibited a Von Mises stress of 203 MPa, with a corresponding factor of safety of 3.20. Further experimentation was conducted using Python to examine the trapezoidal profile. The results indicated that an increased level of parallelism in the inner side of the trapezoidal shape corresponded to a higher factor of safety. Hence, it is advisable to maintain the trapezoidal cross-sectional profile of the crane hook, with due consideration given to maximizing the length of the inner parallel side. The enhancement of design leads to a decrease in the likelihood of failure and the occurrence of undesirable accidents.

Trajectory Planning, Kinematics, and Experimental Validation of a 3D-Printed Delta Robot Manipulator

This paper presents the implementation, trajectory planning, kinematics, and experimental validation of an open-source 3D-printed delta robot manipulator. The robot’s hardware consists of three servo motors, an Arduino Uno microcontroller, and a Pulse Width Modulation (PWM) servo module. The software includes a trapezoidal velocity profile planner and an inverse and forward kinematics solver to calculate the motor angles required to achieve a desired end-effector position in task space. The 3D printed parts were obtained from an open-source Thingiverse project and assembled to form the robot’s kinematic structure. The robot’s performance was evaluated in terms of its accuracy, repeatability, and maximum speed for a pick-and-place task. Experimental results show that the robot can achieve a positioning accuracy of 2.2 mm, with a top speed of 0.4 m/s, 30 picks per minute, and load carrying capacity up to 200 g. These results are satisfactory, considering the ease of assembly and the cost-effectiveness of the robot. The comparison of the calculated motor angles with actual motor angles obtained through additional potentiometer wires soldering shows promising results. The proposed robot’s cost-effective characteristics, utilization of open-source additive manufacturing, and motion planning algorithms make it suitable for various applications, including education, research, and small-scale industrial applications.

Low-consumption stepper motor controller with real-time target position change responsiveness based on field programmable gate array.

In response to the demand for low resource consumption, parallel control, and real-time response to target position changes in precision measurement and manufacturing of multi-axis stepper motor controllers, this paper proposes a field programmable gate array-based method for generating trapezoidal velocity profiles and pulse generation, which can easily keep parallelism and independence during multi-axis control. By avoiding using multiplication and division, this controller not only reduces resource consumption but also enhances the pulse output frequency. To address the real-time responsiveness of the velocity profile generation algorithm to changes in the target position during the control process, the algorithm introduces a novel real-time comparative state transition logic for speed control, which makes it capable of adjusting the acceleration within a single clock cycle, enabling its application in scenarios that require higher levels of real-time performance. Finally, the designed controller is applied to a four-axis positioning system for performance validation.

Numerical analysis of stretching/shrinking fully wet trapezoidal fin

<p>The purpose of fins or extended surfaces is to increase the dissipation of heat from hot sources into their surroundings. Fins like annular fins, longitudinal fins, porous fins, and radial fins are used on the surface of equipments to enhance the rate of heat transfer. There are many applications of fins, including superheaters, refrigeration, automobile parts, combustion engines, electrical equipment, solar panels, and computer CPUs. Based on a wide range of applications, the effects of stretching/shrinking on a fully wet trapezoidal fin with internal heat generation is investigated. The shooting approach is used to calculate the trapezoidal fin's thermal profile, tip temperature, and efficiency. It is observed that with an increase in the shrinking and wet parameter, the temperature distribution decreases and efficiency increases. On the other hand, when stretching increases, the temperature distribution increases and efficiency diminishes. Using the computed results, it is concluded that shrinking trapezoidal fins improves the effectiveness and performance of the system.</p>

Compressive Behavior of Concrete Subjected to High Rate of Loading Using SHPB

Concrete is the most widely used construction material for strategic structures which are subjected to high rate of loading (impact and blast loading). Hence, the study of the concrete material becomes essential day by day for the structural engineers for the analysis and design of the concrete structures for safety and security purposes. This paper focuses on investigating the dynamic compressive response of the standard concrete (M35) and high-strength concrete (M60) under impact loading by using the newly developed split Hopkinson pressure bar setup (SHPB) apparatus. First, the calibration of SHPB performed at a 4.90[Formula: see text]ms[Formula: see text] impact velocity generates almost similar incident and transmission trapezoidal profile waves with minor reflection showing accuracy. Second, the dynamic compression tests were performed on the standard concrete (SC) and high-strength concrete (HSC) specimens of 29.5[Formula: see text]mm in diameter and [Formula: see text][Formula: see text]mm in length with an aspect ratio of about 1([Formula: see text]) and a comparative study of strain rate effect and quasi-static compressive strength on the material properties has been investigated. The dynamic compression behavior of SC and HSC thus studied under varying strain rates has been presented in terms of the compressive strength, dynamic increase factor, stress–strain relationship, material failure, and fragmentation. Compressive strength increments of 114% and 41% were observed in SC and HSC as the loading condition changed from quasi-static to dynamic. In addition, the HSC described the [Formula: see text]% and [Formula: see text]% higher compressive strength corresponding to 290[Formula: see text]s[Formula: see text] and 131[Formula: see text]s[Formula: see text] strain rate as compared to SC describing that the HSC is more sensitive to the strain rate. The dynamic mechanical properties increased with an increase in the strain rate, and the DIFs were found to vary in the range of 1.42–2.14 and 1.07–1.41 for SC and HSC, respectively. The critical strain and ultimate strain were also found to be sensitive to strain rate and increased with increase in strain rate for both grades of concrete. Moreover, strain rates exert a noteworthy influence on fragmentation, leading to an increase in the percentage weight of fine fragments and a decrease in the percentage weight of large fragments as the strain rate increases. Additionally, there is an overall increase in the quantity of fragments for both SC and HSC specimens under these conditions. The flaky, elongated, angular, and irregular shape fragments were observed but their quantity and size varied significantly with strain rate.

Analysis of an actively controlled composite box manipulator without external actuator

This study focuses on active vibration control for a single-link composite box manipulator by using a single actuator for driving and control actions. Model extraction and system identification techniques are studied to obtain mathematical models of the manipulator. The state space model is extracted from the finite element model using modal analysis conducted in ANSYS, while the system identification approach is an experimental modeling method using the input and output signals of the system. The input signals are defined as triangular and trapezoidal motion profiles, while the output signals are the acceleration signals of the manipulator. Proportional derivative and positive position feedback controllers are implemented on the obtained mathematical models to reduce residual vibrations. The simulation results are successfully verified by experiments, and uncontrolled/controlled results are evaluated with reduction rates.

Simplified nonlinear analysis of doubly corrugated cold‐formed steel arches

AbstractDoubly corrugated steel arches are made by pressing transverse corrugations on trapezoidal cold‐formed steel sheets. Several studies show that these transverse corrugations may have a significant detrimental effect on the stiffness and load‐bearing capacity of the original trapezoidal profile. This paper presents an experimental campaign aimed at investigating the effects of transverse corrugations on the behaviour of arches. The campaign includes reduced tests on flat sheets and sheets with a single corrugation, as well as full tests on arches with spans ranging from 10 to 20 m. Subsequently, a simplified design procedure based on nonlinear 2D beam finite element models is proposed. The models account for the transverse corrugation effects by using intermediate rotational springs and equivalent beam section areas, which are calibrated from the results of the reduced experiments. A brief sensitivity study of the finite element results with respect to different modelling factors is conducted, and the different effects of the corrugation assessed. Finally, the simplified finite element models are validated by comparing the experimental and numerical force‐displacement curves, which show reasonably good agreement. However, further research is needed to refine and extend the proposed procedure.

Vibration Control of Flexible Manipulators by Active Cable Tension

The end point vibrations of the serial manipulator should be controlled during motion or working process. In this study the residual vibrations of the flexible manipulator were controlled with cable tensions. The finite element model was established in ANSYS Mechanical APDL. The open loop and closed loop control simulations were performed under the trapezoidal velocity motion profiles. Zero and three different initial strain values were assigned to the cables. As a result, the end point vibration amplitudes, axial forces of the cables and the bending strain values of the one element near the fixed end were observed in order to define the limitations of the sensors and actuators which will be selected for experimental setup.

Impact of web perforation size and shapes on structural behavior: a finite element analysis

Purpose Various designs of corrugated webs include trapezoidal, sinusoidal, triangular and rectangular profiles. The increasing use of curved plates has prompted the creation of I-sections made of steel with a corrugated web design. This study aims to examine the effectiveness of an I-beam steel section that features a perforated-triangular web profile. Design/methodology/approach In the current study, finite element analysis was conducted on corrugated-perforated steel I-sections using ANSYS software. The study focused on inspecting the design of the perforations, including their shape (circle, square, hexagon, diamond and octagon), size of perforations (80 mm, 100 mm and 120 mm) and layout (the position of web perforation), as well as examining the geometric properties of the section in term of bending, lateral torsional buckling, torsion and shear behavior. Findings The study revealed that perforations with diamond, circle and hexagon shapes exhibit good performance, whereas the square shape performs poorly. Moreover, the steel section’s performance decreases with an increase in perforation size, regardless of loading conditions. In addition, the shape of the web perforations can also influence its stress distribution. For example, diamond-shaped perforations have been found to perform better than square-shaped perforations in terms of stress distribution and overall performance. This was because of their ability to distribute stress more evenly and provide greater support to the surrounding material. The diagonal alignment of the diamond shape aligns with principal stress directions, allowing for efficient load transfer and reduced stress concentrations. Additionally, diamond-shaped perforations offer a larger effective area, better shear transfer and improved strain redistribution, resulting in enhanced structural integrity and increased load-carrying capacity. Originality/value Hence, the presence of lateral-torsional buckling and torsional loading conditions significantly impacts the performance of corrugated-perforated steel I-sections.

Trapez Hız Profilinin Ayarlanması Yoluyla Hareketli Bir Kütle Altındaki Kirişin Titreşim Kontrolü

In this article, the residual vibration of a simply supported beam with a moving mass is studied. The mass moves from a starting point to an end point on the beam with a trapezoidal velocity profile having accelerating, constant velocity and decelerating time intervals. The residual vibration of the mid-point of the beam after the mass stops is analyzed. The mathematical model of the system is developed using the finite element (FE) theory. Newmark method is used for the solution of FE model having time dependent matrices because of the moving mass. The model is verified by comparing the solution results with the results given in the previous studies in the literature. It is seen that the relationship between the natural frequency of the system and the velocity profile of the moving mass has an effect on the residual vibration of the structure. If the natural frequency of the system and the inverse of the deceleration time interval of the moving mass are equal while the moving mass is at the stopping position, residual vibrations occur at a minimum level. It seen that with the right speed profile selection, the decrease in vibration levels approaches 70% during the movement and 80% after stopping.

Towards a continental-scale riverine bathymetry dataset using readily-available data and simple hydraulic models

Channel bathymetry data is important to both advanced hydraulic models and mobility analyses. Yet, obtaining bathymetry data at large scales is difficult. Here, we propose a method to create a continuous topobathymetric dataset that can be applied at large-scales with high-resolution using simple hydraulic models, gridded digital elevation model (DEM) data, a stream network dataset, and an average flow rate for every stream being evaluated (the latter two are often available from continental-scale streamflow models). The approach “burns-in” one of three bathymetric profiles (trapezoidal, triangular, or parabolic) into autogenerated cross-sections sampled from the DEM. Using spatial averaging, the cross-sections are then used to create a continuous topobathymetric dataset, which provides a realistic initial elevation surface for use in advanced hydraulic models. The ability of the bathymetric profiles to replicate maximum depth and hydraulic geometry was tested in the Mississippi River Basin at 11 sites with observed bathymetry data. For the majority of test sites, the observed maximum depth fell between the minimum and maximum thalweg depths calculated using the three bathymetric profile shapes, with the trapezoidal profile being the most accurate in capturing maximum depth (relative depth error of −4.2%). Based on hydraulic geometry, the triangular bathymetric profile performed best in the smaller streams while the trapezoid performed best in larger rivers. A test case along the Missouri River showed the topobathymetric dataset generated is easily implemented into advanced hydraulic models.