Non-uniform Cross-section Research Articles

Performance evaluation of a novel monofilar helical antenna with tapered cross-section wire fabricated via metal additive manufacturing

This paper presents a novel formulation for a generalized helical antenna that incorporates non-uniform helix diameters, non-uniform helix spacing, and non-uniform wire cross-section, providing additional degrees of freedom for optimization. By carefully defining the transition between the helix and the center feed point, a thicker wire was used at the base to enhance the antenna’s operating bandwidth capability and mechanical strength, eliminating the need for additional support structures. The fabrication process utilized metal additive manufacturing (MAM) with Maraging steel. The results demonstrate that the helical antenna with a tapered cross-section wire (with a thicker base and a thinner tip) exhibits significantly better performance compared to the control models for operation in the X-band. This design amalgamates impedance matching from antennas with uniform thick wires and radiation characteristics from antennas with uniform thin wires. The major contribution of this work is the demonstration that employing tapered wire cross-sections can enhance helical antenna performance, thereby introducing a new design parameter in metal additive manufacturing. Specifically, we present an eight-turn helical antenna that achieved a measured reflection coefficient less than −10 dB and axial ratio less than 1 dB over the X band, with a peak realized gain in RHCP of 10.8 dBic.

FINITE ELEMENT MODELLING AND ANALYSIS OF FREE VIBRATIONS OF AXIALLY FUNCTIONALY GRADED BEAMS WITH NON-UNIFORM CROSS-SECTIONS

The finite element package Abaqus is used for modeling and analysis of free vibrations of axially functional graded beams with non-uniform cross-sections. Considerable attention has been paid to this aspect of the geometry, as it has a significant effect on the behavior of the beam as a structural component. User-defined material model subroutines (UMAT) were developed in a unified way for one- and three-dimensional models of the specified beams to provide numerical implementation of functional material gradients within each finite element. UMAT procedures were programmed in FORTRAN in the MS Visual Studio environment and compiled with the main program package using the Intel Fortran Compiler. In the procedures, material heterogeneity was assigned to each material integration point of appropriate standard one- and three-dimensional finite elements, eliminating the need to design graded finite elements via user-defined element subroutine. Frequencies and mode shapes of free vibrations of one- and three-dimensional axially functional graded beams with non-uniform cross-sections were found using the Lanczos method in Abaqus. An analysis of the accuracy and effectiveness of the proposed modeling approach was carried out, comparing the obtained results with data known in the literature. The presented modeling technique based on user-defined material subroutines provides valuable opportunities for scientists and engineers engaged in the dynamic analysis of structural components made of functionally gradient materials and having variable geometry along the axial direction. Keywords: axially functionally graded beams; non-uniform cross-section beams; free vibrations; graded finite element; Abaqus user defined subroutines

Pure bending of curved beam with non-uniform cross section

The purpose of this paper is to study the state of stress and displacement field of a curved beam with non-uniform cross section. The material of the beam is non-homogeneous isotropic linearly elastic. The curved beam is subjected to couple moment at the ends of geometry. Utilizing analytical closed form solutions are obtained for the radial and circumferential stresses and for the displacements and cross sectional rotation. A numerical example illustrates the applications of the derived formulae.

Transient numerical simulations in innovative thermoelectric power: A comprehensive study on material segmentation and cross-section design for multi-facetted excellence

In the pursuit of sustainable energy innovations, this study investigates the transformative potential of material segmentation and non-uniform cross-sections in the field of thermoelectric power generation. By analyzing four distinct thermoelectric models under varying optical concentration ratios (OCRs), our research is dedicated to optimizing exergy efficiency, economic viability, and thermo-mechanical performance. Model 3, representing a uniform cross-section segmented thermoelectric generator (TEG), emerges as the frontrunner in our study. The significance of this research lies in its potential to revolutionize thermoelectric power generation, offering a fresh perspective on sustainable energy production. Our primary aim is to elucidate the impact of innovative design strategies on thermoelectric performance. To achieve this, we employ numerical simulations and transient analyses to explore the dynamic behavior of these models under changing OCRs. Our key findings reveal the remarkable superiority of Model 3, which achieves a peak power output of 624.60 mW, exergy efficiency of 10.27 %, and CO2 savings of 1.08 kgyr−1, all under an OCR of 700. Notably, Model 3 outperforms conventional systems by 300.45 % in power output and 75.76 % in CO2 savings. Conclusively, our research provides valuable insights into the capacity of material segmentation and non-uniform cross-sections to reshape the realm of thermoelectric power generation, highlighting their potential in propelling sustainable energy solutions.

Quasi-one-dimensional treatment of heat transfer in beams of non-uniform cross-section

We test performance of a quasi-one-dimensional approach to steady state heat transfer in broadening beams, characterized by variable cross-sectional area. The results obtained analytically and by solving the governing equation numerically in Python, for three different instances, are compared to FEM simulations. We demonstrate that the quasi-one-dimensional model gives accurate predictions for beam suitably averaged temperatures but the range of Biot numbers for which it can be accurately applied to is currently limited by a crucial parameter.

A Unified Numerical Approach to the Dynamics of Beams with Longitudinally Varying Cross-Sections, Materials, Foundations, and Loads Using Chebyshev Spectral Approximation

Structures with inhomogeneous materials, non-uniform cross-sections, non-uniform supports, and subject to non-uniform loads are increasingly common in aerospace applications. This paper presents a simple and unified numerical dynamics model for all beams with arbitrarily axially varying cross-sections, materials, foundations, loads, and general boundary conditions. These spatially varying properties are all approximated by high-order Chebyshev expansions, and discretized by Gauss–Lobatto sampling. The discrete governing equation of non-uniform axially functionally graded beams resting on variable Winkler–Pasternak foundations subjected to non-uniformly distributed loads is derived based on the Euler–Bernoulli beam theory. A projection matrix method is employed to simultaneously assemble spectral elements and impose general boundary conditions. Numerical experiments are performed to validate the proposed method, considering different inhomogeneous materials, boundary conditions, foundations, cross-sections, and loads. The results are compared with those reported in the literature and obtained by the finite element method, and excellent agreement is observed. The convergence, accuracy, and efficiency of the proposed method are demonstrated.

A General Approach to Construct Full-Field Responses and High-Resolution Mode Shapes of Bridges Using Sparse Measurements

The full-field responses and high-resolution mode shapes are of paramount importance in the detection of bridge damage and finite element model updating. As enlightened by the Fourier series expansion of the mode shapes for a bridge, this study proposes an approach for compressive sensing-based reconstruction of the full-field responses and identification of high-resolution mode shapes, in which a general basis matrix is newly formulated, with particular application to beam-like continuous or non-uniform bridges. The merits of the proposed approach are model-free, output-only, and easy to implement, especially the need of a few sensors. The effectiveness of the approach is validated through both numerical and experimental examples by considering various bridge boundary conditions and non-uniform cross-sections, from which the potential application of this general approach is foreseeable.

Dynamic Analysis of Non-Uniform Functionally Graded Beams on Inhomogeneous Foundations Subjected to Moving Distributed Loads

Inhomogeneous materials, variable foundations, non-uniform cross-sections, and non-uniformly distributed loads are common in engineering structures and typically complicate their mechanical analysis considerably. This paper presents an accurate and efficient numerical method for the dynamic analysis of non-uniform functionally graded beams resting on inhomogeneous viscoelastic foundations subjected to non-uniformly distributed moving load and investigates the effects of non-uniformities and inhomogeneities on material, foundation, and load. Based on the Timoshenko beam theory and a Chebyshev spectral method, a consistent discrete dynamic model is derived, which can deal with all axially varying properties. A series of numerical experiments are carried out to validate the convergence and accuracy of the proposed method. The results are compared with those obtained through finite element analysis or in the literature, and excellent agreement is observed. Then, the dynamic response of an axially functionally graded beam resting on an inhomogeneous viscoelastic foundation and subjected to a non-uniformly distributed moving load is investigated. The results show that the material gradient and the inhomogeneous foundation can alter the vibration amplitudes and critical speeds of the beam significantly. Compared with more realistic non-uniformly distributed moving load models, idealized concentrated and uniformly distributed moving load models produce apparent computation errors in vibration amplitudes.

Analysis of the Heat Transfer and Pressure Drop by the Turbulator Having a Non-Uniform Triangular Cross-Section in Air-Type PV/T Collector

Analysis of the Heat Transfer and Pressure Drop by the Turbulator Having a Non-Uniform Triangular Cross-Section in Air-Type PV/T Collector

Antiresonant fiber structures based on swarm intelligence design.

In this work, we obtained a new, to the best of our knowledge, structure of anti-resonant fiber (ARF) by an adaptive particle swarm optimization (PSO) algorithm. Different from the prior method of stacking elemental parts and optimizing parameters through experience or algorithm, we decompose some classic structures into points and optimize the positions of these points through swarm intelligence. The fiber structure is reconstructed by interpolation, and some new structures with low confinement loss (CL) and high higher order mode extinction ratio (HOMER) are obtained. These novel ARFs exhibit similar structural characteristics, and are named as "the bulb-shaped ARFs". Among these structures, the minimum achieved CL is 2.21 × 10-5dB/m at 1300 nm and the maximum achieved HOMER exceeds 14,000. This work provides a method with high degree of freedom in the design of non-uniform cross-section waveguides and helps to discover new fiber structures.

Surface direct conversion of 511 keV gamma rays in large-area laminated multichannel-plate electron multipliers

We have used the TOPAS simulation framework to model the direct conversion of 511 keV gamma rays to electrons in a micro-channel plate (MCP) constructed from thin laminae of a heavy-metal-loaded dielectric such as lead-glass, patterned with micro-channels (LMCP). The laminae serve as the converter of the gamma ray to a primary electron within a depth from a channel-forming surface such that the electron penetrates the channel surface (‘surface direct conversion’). The channels are coated with a secondary-emitting material to produce electron multiplication in the channels. The laminae are stacked on edge with the channels running from the top of the resulting ‘slab’ to the bottom; after assembly the slab is metalized top and bottom to form the finished LMCP.The shape of the perimeter of a lamina determines the dimensions of the slab at the lamina location in the slab, allowing non-uniform cross-sections in slab thickness, width, and length. The slab also can be non-planar, allowing curved surfaces in both lateral dimensions. The laminar construction allows incorporating structural elements in the LMCP for modular assembly in large-area arrays.The channels can be patterned on the laminae surfaces with internal shapes and structure, texture, and coatings optimized for specific applications and performance. The channels can be non-uniform across the LMCP and need not be parallel in either transverse direction.Surface direct conversion of the gamma ray to an electron eliminates the common two-step conversion of the gamma ray into an optical photon in a scintillator followed by the conversion of the photon into an electron in a photodetector. The simulations predict an efficiency for conversion of 511 keV gamma rays of ⪆ 30% for a 2.54 cm-thick lead-glass LMCP. The elimination of the photocathode allows assembly at atmospheric pressure.

Electrical and Thermal Performances of a Single-Pass Double-Flow Photovoltaic-Thermal Collector Coupled with Nonuniform Cross-Section Rib

The air-based photovoltaic-thermal collector (PVTC) is a system that can generate electricity and heated air simultaneously from solar energy. This study investigates the electrical and thermal performances of an air-based single-pass double-flow photovoltaic-thermal collector (SPDFPVTC) coupled with a nonuniform cross-section rib (NUCSR) under various operating conditions. The rib is installed at the rear of the photovoltaic panel to enhance the heat transfer performance between the photovoltaic panel and the flowing air. Based on the energy balance equations, a mathematical model of the proposed SPDFPVTC is established and validated by experimental results. The solar intensity, air mass flow rate, and wind speed are selected as operating conditions. The effects of these operating conditions on the electrical and thermal performance of the SPDFPVTC have been discussed. In addition, this study evaluates the daily performance of SPDFPVTC with and without NUCSR. The average electrical, thermal, and overall efficiency were 17.59%, 43.96%, and 61.55%, respectively, for SPDFPVTC with NUCSR and 16.97%, 38.87%, and 55.83%, respectively, for SPDFPVTC without NUCSR. Consequently, installing NUCSR could enhance the daily electrical, thermal, and overall energy output of SPDFPVTC by 4.33%, 13.23%, and 10.63%, respectively.

Nonlinear dynamic study of non-uniform microscale CNTR composite beams based on a modified couple stress theory

This study aims at investigating the nonlinear dynamic behavior of microscale carbon nanotube reinforced (CNTR) composite Euler–Bernoulli beams with a non-uniform cross-section, based on a modified couple stress theory (MCST). The nonlinear partial differential equations (PDEs) of motion are established based on the Von-Karman nonlinear strain–displacement relationship and Hamiltonian principle. The coupled PDEs are reduced to a single PDE, by neglecting the effects of the axial inertia and considering two different types of boundary conditions (i.e. clamped–clamped and clamped–free). At the same time, the single PDE is reverted to a nonlinear ordinary differential equation (ODE) by means of the Galerkin approach, and it is solved by using a semi-inverse method and the method of multiple time scales (MTS) for a free and forced vibration analysis, respectively. A large systematic numerical analysis is here performed to check for the sensitivity of the nonlinear response of CNTR composite beams to different boundary conditions and reinforcement parameters, with useful scientific insights for further computational investigations on the topic.

Compressive mechanical properties of open-cell cubic and rhombic dodecahedron lattice structures of variable cross section fabricated by fused deposition modeling

Foams are known as structures with a high percentage of empty spaces and pores within them. Foams are classified into two categories, open-cell, and closed-cell, depending on their geometry and structure. Investigation of open-cell foams with non-uniform cross sections has been among the topics of recent studies. This research investigates the static analysis of cell foams fabricated through the additive manufacturing method. For this purpose, two structures with rhombic dodecahedron and cubic unit cells were placed under static loads using experimental, analytical, and numerical approaches. Thus, both unit cells with different relative density samples, were made with non-uniform cross-sections and validated with numerical values. Furthermore, the mechanical properties from analytical relationships were obtained for a uniform cross-section and further validated with numerical values. The open-cell porous structure built by additive manufacturing for Polylactic acid was investigated. The samples were tested under uniaxial compression with a constant strain rate, and the data obtained from the test was used to assess the structure's mechanical properties. For the analytical section, Timoshenko beam theory was utilized. Timoshenko beam theory was used in analytical solutions close to numerical results regarding yield stress, elastic modulus, and Poisson's ratio. In both unit cells, yield stress and elastic modulus were found to be increased proportionately with increasing relative density, in uniform and non-uniform conditions. By comparing the unit cells' yield stress, the impact of non-uniformity used for rhombic dodecahedron was found to be greater than cubic.

Broadband Vibration-Based Energy Harvesting for Wireless Sensor Applications Using Frequency Upconversion.

Silicon-based kinetic energy converters employing variable capacitors, also known as electrostatic vibration energy harvesters, hold promise as power sources for Internet of Things devices. However, for most wireless applications, such as wearable technology or environmental and structural monitoring, the ambient vibration is often at relatively low frequencies (1-100 Hz). Since the power output of electrostatic harvesters is positively correlated to the frequency of capacitance oscillation, typical electrostatic energy harvesters, designed to match the natural frequency of ambient vibrations, do not produce sufficient power output. Moreover, energy conversion is limited to a narrow range of input frequencies. To address these shortcomings, an impacted-based electrostatic energy harvester is explored experimentally. The impact refers to electrode collision and it triggers frequency upconversion, namely a secondary high-frequency free oscillation of the electrodes overlapping with primary device oscillation tuned to input vibration frequency. The main purpose of high-frequency oscillation is to enable additional energy conversion cycles since this will increase the energy output. The devices investigated were fabricated using a commercial microfabrication foundry process and were experimentally studied. These devices exhibit non-uniform cross-section electrodes and a springless mass. The non-uniform width electrodes were used to prevent pull-in following electrode collision. Springless masses from different materials and sizes, such as 0.5 mm diameter Tungsten carbide, 0.8 mm diameter Tungsten carbide, zirconium dioxide, and silicon nitride, were added in an attempt to force collisions over a range of applied frequencies that would not otherwise result in collisions. The results show that the system operates over a relatively wide frequency range (up to 700 Hz frequency range), with the lower limit far below the natural frequency of the device. The addition of the springless mass successfully increased the device bandwidth. For example, at a low peak-to-peak vibration acceleration of 0.5 g (peak-to-peak), the addition of a zirconium dioxide ball doubled the device's bandwidth. Testing with different balls indicates that the different sizes and material properties have different effects on the device's performance, altering its mechanical and electrical damping.

Cooling channel free surface optimisation for additively manufactured casting tools

In the present study, an algorithm has been developed using the adjoint method to optimise the position and cross-section of an internal cooling channel for a 3D printed tool steel insert for use in the aluminium die-casting process. The algorithm enables the development of an optimised complex industrial mould with relatively low computational cost. A transient model is validated against multiple experimental trials, providing an adapted interface heat transfer coefficient. A steady state thermal model, based on the casting cycle and thermal behaviour at the mould surface, is developed to evaluate the spatial distribution of temperature and to serve as the initial solution for the subsequent optimisation stage. The adjoint model is then applied to optimise the cooling channel emphasising the minimisation of the temperature standard deviation for the mould surface. The original transient model is applied to the optimised mould configuration via calibration using experimental data obtained from a dedicated aluminium furnace. The optimised cooling channel geometry, which uses a non-uniform cross-section across the entire pipe surface region, improves the pressure drop and cooling uniformity across the mould/cast interface by 24.2% and 31.6%, respectively. The model has been used to optimise cooling channels for a range of industrial high-pressure aluminium die-casting (HPADC) inserts. This has yielded a significant improvement in the mould operational lifetime, rising to almost 130,000 shots compared to 40,000 shots for prior designs.

Coupled axial-bending vibration of axially functionally graded Timoshenko cantilever beams of non-uniform cross-section with an attached rigid body

Coupled axial-bending vibration of axially functionally graded Timoshenko cantilever beams of non-uniform cross-section with an attached rigid body

Solution for Determining Modulus of Elasticity of Natural Materials Using Vibrations of Non-Uniform Circular Cross-Section Cantilevers.

The article presents an original method for determining the modulus of elasticity of natural materials. A studied solution was based on vibrations of non-uniform circular cross-section cantilevers solved using Bessel functions. The derived equations, together with experimental tests, allowed for calculating the material's properties. Assessments were based on the measurement of the free-end oscillations in time using the Digital Image Correlation (DIC) method. They were induced manually and positioned at the end of a cantilever and monitored in time using a fast Vision Research Phantom v12.1 Camera with 1000 fps. GOM Correlate software tools were then used to find increments of deflection on a free end in every frame. It provided us with the ability to make diagrams containing a displacement-time relation. To find natural vibration frequencies, fast Fourier transform (FFT) analyses were conducted. The correctness of the proposed method was compared with a three-point bending test performed on a Zwick/Roell Z2.5 testing machine. The presented solution generates trustworthy results and can provide a method to confirm the elastic properties of natural materials obtained in various experimental tests.

Free vibration of viscoelastic nonlocally damped tapered axially functionally graded beams using the state-space formulation

For the first time, this paper presents an efficient solution for the vibration analysis of damped axially functionally graded beams with non-uniform cross-sections subjected to the axial force based on the Galerkin method and state-space formulation. Euler-Bernoulli and Rayleigh’s theories are considered to derive the governing equations of motion. Currently, simply supported beams are under investigation due to their easy fabrication and typical applications in various bridge components, buildings, and machine tools. Likewise, the proposed method is applicable to other continuous systems without any limitation on boundary conditions, material properties, or arbitrary representation of cross-sections. Moreover, complex and purely real eigenvalues are determined by outlining the state-space framework. Compared to the conventional method, the present formulation reduces computational complexity and simplifies computer implementation, especially in the case of inhomogeneous materials. Then, an extensive parametric study is performed to evaluate the effect of various characteristics on the dynamic behavior of the viscoelastic nonlocally damped beams. Results reveal that the inhomogeneity index in material constituents has a considerable influence on the eigensolutions. Additionally, it is shown that when the relaxation constant and length parameter tend to infinity there would be a decline in the increasing rate of eigenvalues.

Buckling analysis of non-uniform Timoshenko columns under localised fire

The buckling analysis of non-uniform steel columns with various boundary conditions under localised fire is investigated based on the Timoshenko beam theory (TBT). The temperature-dependent (TD) material properties are taken into account. First, based on the differential quadrature (DQ) method, the temperature field in the column is determined by solving the heat transfer equation considering the convection and radiation boundary conditions. Then, a segmented model is presented to solve the stability problem for the column with the variable flexural rigidity resulting from the non-uniform temperature distribution and cross-section. The transfer-matrix method is employed to obtain the critical buckling load and corresponding buckling mode. Finally, an example is conducted to study the temperature field and buckling response of tapered circular hollow steel columns under localised fire. The feasibility of the present method is verified by comparing the present results with those predicted by the finite element (FE) method and those reported in the literature. Numerical results show the influences of the localised fire and shear deformation on the buckling response of the column.