Non-uniform Cross-section Research Articles

Free Vibration of Axially Functionally Graded Porous Beams with Varying Cross-Section

This study aims to determine the natural frequencies of axially functionally graded porous material (FGPM) beams with non-uniform cross-sections under a variety of boundary conditions. Two types of pore distribution were used: even and uneven. Initially, an analytical method was used to determine the natural frequencies of FGPM beams with different cross-sections. The Fredholm integral approach was used to obtain the characteristic equations. Furthermore, the collected results are confirmed and compared to the existing literature. The artificial neural network (ANN) technique is then used to predict the fluctuations in the natural frequency of a clamped–simply supported axially FGPM beam with a non-uniform cross-section. The prediction of natural frequencies by ANN is based on a large dataset of over 1[Formula: see text]100 data points acquired from the analytical solution obtained in this study and data available in the literature. This research conducts a parametric analysis to evaluate the influence of numerous aspects, including as beam characteristics, material properties, geometric details, gradient parameters, and porosity distribution, on functionally graded (FG) beam vibration behavior. Finally, both ANN and computational analysis demonstrate that porosity distributions and non-uniform cross-sectional area have a substantial effect on the natural frequencies of axially FG beams.

Structural damage detection for spatial frame structures with semi-rigid joints using multiple set wireless measurements

Damage detection of a complex spatial frame structure with semi-rigid joints is a challenging task. Most existing damage detection methods consider the joint as rigid and the nonuniform cross section of the member is not considered. This assumption results to a large error in the structural damage identification. A novel generic element is proposed for the nonuniform cross-section member with semi-rigid joints at both ends in this study. The finite element model of spatial structures with semi-rigid joints is established using the proposed element. The modal strain energy-based damage index is defined and its sensitivity to the member and joint damage has been investigated using numerical and experimental study. An 8-m long bridge model with the bolted connection at joints is built in the laboratory. Dynamic responses of the bridge under random excitations are monitored using 13 wireless tri-axis accelerometers. The spatial mode shapes of the bridge are extracted using the reference-based stochastic subspace identification from multiple set wireless measurements. The numerical model is validated using experimental results. Dynamic responses of the bridge with different damage scenarios have been simulated using the validated model and the corresponding damage indices are obtained. The results show that the proposed method is reliable and accurate to analyze dynamic behavior of the spatial structure with semi-rigid joints, and structural damage can be identified accurately using the modal strain energy-based damage index.

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.

Modelling and Characterisation of Orthotropic Damage in Aluminium Alloy 2024.

The aim of the work presented in this paper was development of a thermodynamically consistent constitutive model for orthotopic metals and determination of its parameters based on standard characterisation methods used in the aerospace industry. The model was derived with additive decomposition of the strain tensor and consisted of an elastic part, derived from Helmholtz free energy, Hill's thermodynamic potential, which controls evolution of plastic deformation, and damage orthotopic potential, which controls evolution of damage in material. Damage effects were incorporated using the continuum damage mechanics approach, with the effective stress and energy equivalence principle. Material characterisation and derivation of model parameters was conducted with standard specimens with a uniform cross-section, although a number of tests with non-uniform cross-sections were also conducted here. The tests were designed to assess the extent of damage in material over a range of plastic deformation values, where displacement was measured locally using digital image correlation. The new model was implemented as a user material subroutine in Abaqus and verified and validated against the experimental results for aerospace-grade aluminium alloy 2024-T3. Verification was conducted in a series of single element tests, designed to separately validate elasticity, plasticity and damage-related parts of the model. Validation at this stage of the development was based on comparison of the numerical results with experimental data obtained in the quasistatic characterisation tests, which illustrated the ability of the modelling approach to predict experimentally observed behaviour. A validated user material subroutine allows for efficient simulation-led design improvements of aluminium components, such as stiffened panels and the other thin-wall structures used in the aerospace industry.

Wave propagation in bidirectional functionally graded tapered beams incorporating porosity effect

This study addresses wave propagation in beams made of bidirectional functionally graded materials (BDFG) and having nonuniform cross section by using a quasi-3D analytical solution. For the first time, this aspect will be studied. The mechanical characteristics of the beams are supposed to be variable in both axial and transvers direction according to a specific law depending on the porosity. The mathematical formulation used is based on a displacement field containing indeterminate terms and requiring a few variables to be determined. The thickness and width of the beams are assumed to be linearly variable in the longitudinal direction. The equations governing the simply supported beams are obtained by applying the principle of virtual work and are then analytically solved to obtain the phase velocities and wave frequencies. In addition, the validation results reveal excellent concordance of the proposed theory with those given in the literature. Then, a detailed parametric study is carried out to investigate the influence of the several geometrical and material parameters on the wave propagation in BDFG tapered beams. It is observed that these parameters have significant impact on the wave propagation in BDFG tapered porous beams. These results can be used as benchmark solutions for future studies.

Harnessing solar power: Innovations in nanofluid-cooled segmented thermoelectric generators for exergy, economic, environmental, and thermo-mechanical excellence

Addressing the imperative need for advancements in thermoelectric generation, this study pioneers an analysis of nanofluid-cooled solar segmented thermoelectric generators with non-uniform cross-sections. Insights into thermal management, structural integrity, and economic efficiency in thermoelectric systems are provided, employing a numerical model that accurately represents thermoelectric effects by accounting for temperature dependencies of semiconductor materials. Through research, exploration of diverse coolant strategies, including TiO2, Fe3O4, Al2O3, and graphene, offers key insights into their impact on cooling dynamics. Findings demonstrate that graphene nanofluid, operating at a flow velocity of 2 m/s, outperforms others, achieving optimal power generation of 221.77 mW and an exergy efficiency of 8.99 %. Additionally, at a concentrated irradiance of 595 kWm−2, graphene leads in environmental benefits, with the highest CO2 savings of 0.38 kgyr−1, and demonstrates economic advantages with a cost-effective dollar per mW value of 3.79×10−6 $mW−1. Furthermore, the study verifies the structural integrity of these systems, with graphene achieving an optimal von Mises stress of 1.35 GPa at a semiconductor height of 0.2 mm. These advancements contribute to environmentally friendly and high-performance generators for sustainable energy solutions, paving the way for future innovations in thermoelectric technology.

Підхід до визначення напружено-деформованого стану стрижнів з композиційних матеріалів з урахуванням внутрішнього самоврівноваженого напруженого стану

The subject of this research is methods of stress-strain state analysis of composite structures. The goal is to develop a mechanism to explain the phenomenon of warping of thin-walled composite sections with a non-uniform cross-section under thermal loading and to synthesize a model to determine the forces in the section elements. The objectives of this study are to predict the deformed states of composite sections at the manufacturing stage and to determine the temperature stresses that occur at the manufacturing stage, as well as after the assembly of the structure. The methods used are related to the mechanics of materials and structures. The following results were obtained. The possible deformation forms of composite plates with an asymmetric structure are analyzed and the rationale for the appearance of such deformations is given. A model of the force interaction of elements in a folded section is proposed. The proposed model can be extended to most sections of load-carrying aircraft structures. Based on the analysis of the mechanics of thin-walled folded sections, the mechanism of the occurrence of complex bending-torsional deformation of long-dimensional sections made of composites with a non-uniform cross-section under the action of an internal self-equilibrium stress state caused by a change in temperature or shrinkage of the binder or both is explained. The analysis of this mechanism makes it possible to design composite sections with minimal warping and to propose engineering methods to compensate for unwanted spatial movements in the case of arbitrary loading of section elements. Conclusions. The scientific novelty of the obtained results can be summarized as follows. A mechanism for the deformation of rods made of dissimilar composite materials when the temperature changes (after extraction from the tool or during operation) is proposed considering the difference in Poisson's coefficients. A model for determining the forces acting on the perimeter of section elements was synthesized, and the corresponding formulas were obtained, which form the basis for the theory of off-center compression of rods. The direction of further research in this field is currently being planned.

Low-frequency sound attenuation by coiled-up meta-liner with nonuniform cross sections under grazing flow

We report a kind of coiled-up meta-liners with nonuniform cross sections (CMNC), which can efficiently attenuate low-frequency sound waves under grazing flow with a deep subwavelength thickness (e.g., ∼λ/17 at 500 Hz). At a grazing flow Mach number of 0.26, the average transmission loss of the meta-liner is 12.6 dB at 500–1000 Hz, which is twice as much as that of a double-degree-of-freedom acoustic liner of the same size. Physically, the nonuniform cross-sectional distribution and significant cross-sectional area ratio enhances vortex shedding, thus resulting in severe acoustic energy dissipation. The excellent low-frequency acoustic attenuation performance of CMNC is investigated thoroughly with experimental, theoretical, and numerical methods. This work provides an avenue for low-frequency noise reduction in grazing flow scenarios (e.g., in a high bypass ratio turbofan engine).

Investigation on temperature effect of local structural stress during non-uniform cross-section steel bridge deck pavement paving

During the process of gussasphalt concrete paving on the orthotropic steel bridge deck of a non-uniform cross-section box girder bridge, the high-temperature asphalt mixture often produces temperature stresses that can affect bearings safety. In this study, a refined model of a steel box girder bridge with a 660 m scale was developed and numerical simulations were conducted using the finite element software. The temperature field was applied to the orthotropic steel bridge deck in a quasi-dynamic fashion, leading to the determination of a safe width for concrete paving. To assess the accuracy of the computational predictions, field paving was performed under the safe width condition determined from the calculations, and the temperature and local stress data were measured in the field. The results demonstrate that the finite element predictions are in good agreement with the yield strength of the bearing’s local structure, and the measurements also show a close correspondence with the structural yield strength, validating the reliability of the quasi-static simulation approach. The proposed method offers a computational tool and a reliability criterion for future finite element analyses of large-span non-uniform cross-section steel box girder bridges, as well as a safe width example for subsequent gussasphalt mixture paving on orthotropic steel bridge decks.

Analysis of compliant mechanisms with series and parallel substructures through the ellipse of elasticity theory

Compliant mechanisms with complex hybrid configurations have been designed to meet the requirements of specific applications demanding high performance. Kinetostatic analysis, fundamental at the early stage of design, can become difficult for compliant systems characterized by series and parallel substructures. In the present paper, the ellipse of elasticity method is implemented for the analysis of a compliant mechanism with hybrid topology. Firstly, the ellipses associated to the different flexure hinges, characterized by uniform or non-uniform cross-sections, and by constant or variable initial curvature, are determined. Then, the unique ellipse representing the compliant mechanism is obtained by means of series and parallel compositions. By exploiting the antiprojective polarity properties of the ellipse, the kinetostatic analysis of the compliant system is reduced to a geometric problem with a straightforward solution. Linear and nonlinear finite element analyses and experimental tests are performed to verify the theoretical results.

Peeling fingers in an elastic Hele-Shaw channel

Using experiments and a depth-averaged numerical model, we study instabilities of two-phase flows in a Hele-Shaw channel with an elastic upper boundary and a non-uniform cross-section prescribed by initial collapse. Experimentally, we find increasingly complex and unsteady modes of air-finger propagation as the dimensionless bubble speed $Ca$ and level of collapse are increased, including pointed fingers, indented fingers and the feathered modes first identified by Cuttle et al. (J. Fluid Mech., vol. 886, 2020, A20). By introducing a measure of the viscous contribution to finger propagation, we identify a $Ca$ threshold beyond which viscous forces are superseded by elastic effects. Quantitative prediction of this transition between ‘viscous’ and ‘elastic’ reopening regimes across levels of collapse establishes the fidelity of the numerical model. In the viscous regime, we recover the non-monotonic dependence on $Ca$ of the finger pressure, which is characteristic of benchtop models of airway reopening. To explore the elastic regime numerically, we extend the depth-averaged model introduced by Fontana et al. (J. Fluid Mech., vol. 916, 2021, A27) to include an artificial disjoining pressure that prevents the unphysical self-intersection of the interface. Using time simulations, we capture for the first time the majority of experimental finger dynamics, including feathered modes. We show that these disordered states evolve continually, with no evidence of convergence to steady or periodic states. We find that the steady bifurcation structure satisfactorily predicts the bubble pressure as a function of $Ca$ , but that it does not provide sufficient information to predict the transition to unsteady dynamics that appears strongly nonlinear.

Generalized Coronal Loop Scaling Laws and Their Implication for Turbulence in Solar Active Region Loops

Recent coronal loop modeling has emphasized the importance of combining both Coulomb collisions and turbulent scattering to characterize field-aligned thermal conduction, which invokes a hybrid loop model. In this work, we generalize the hybrid model by incorporating a nonuniform heating and cross section that are both formulated by a power-law function of temperature. Based on the hybrid model solutions, we construct scaling laws that relate loop-top temperature (T a ) and heating rate (H a ) to other loop parameters. It is found that the loop-top properties for turbulent loops are additionally power-law functions of the turbulent mean free path (λ T ), with the functional forms varying from situation to situation, depending on the specification of the heating and/or areal parameters. More importantly, both a sufficiently footpoint-concentrated heating and a cross-sectional expansion with height can effectively weaken (strengthen) the negative (positive) power-law dependence of T a (H a ) on λ T . The reason lies in a notable reduction of heat flux by footpoint heating and/or cross-sectional expansion in the turbulence-dominated coronal part, where turbulent scattering introduces a much weaker dependence of the conduction coefficient on temperature. In this region, therefore, the reduction of the heat flux predominately relies on a backward flattening of the temperature gradient. Through numerical modeling that incorporates more realistic conditions, this scenario is further consolidated. Our results have important implications for solar active region (AR) loops. With the factors of nonuniform heating and cross section taken into account, AR loops can bear relatively stronger turbulence while still keeping a physically reasonable temperature for nonflaring loops.

A hydrodynamic model of capillary flow in an axially symmetric tube with a non-slowly-varying cross section and a boundary slip

The capillary flow of a Newtonian and incompressible fluid in an axially symmetric horizontal tube with a non-slowly-varying cross section and a boundary slip is considered theoretically under the assumption that the Reynolds number is small enough for the Stokes approximation to be valid. Combining the Stokes equation with the hydrodynamic model assuming the Hagen–Poiseulle flow, a general formula for the capillary flow in a non-slowly-varying tube is derived. Using the newly derived formula, the capillary imbibition and the time evolution of meniscus in tubes with non-uniform cross sections such as a conical tube, a power-law-shaped diverging tube, and a power-law-shaped converging tube are reconsidered. The perturbation parameters and the corrections due to the non-slowly-varying effects are elucidated, and the new scaling formulas for the time evolution of the meniscus of these specific examples are derived. Our study could be useful for understanding various natural fluidic systems and for designing functional fluidic devices such as a diode and a switch.

Performance optimization of nanofluid-cooled photovoltaic-thermoelectric systems: A study on geometry configuration, steady-state and annual transient effects

In this study, we explored Photovoltaic-Thermoelectric (PV-TE) systems in-depth, addressing complexities in both steady-state and annual transient performance under realistic conditions. The analysis involved twelve distinct PV-TE configurations featuring diverse thermoelectric designs incorporating various semiconductors, multi-staging, non-uniform cross-sections, and material segmentation. Model 6, the PV-TE system with a multi-stage segmented rectangular design, emerged as the top performer, exhibiting a remarkable 12% increase in electric power output during peak sunlight compared to the base model, despite a marginal decrease in efficiency. Furthermore, this research delved into the potential of advanced nanofluid cooling, investigating options such as distilled water, titanium oxide, aluminum oxide, iron oxide, and graphene. The results underscores graphene nanofluid's superiority, demonstrating a significant enhancement in thermal management at an optimal flow velocity of 2 m/s. This improvement in thermal management refers to the effective heat dissipation and temperature control within the PV-TE system. This study underlines the critical role of strategic system design and component selection in optimizing the performance of PV-TE systems. By providing a comprehensive foundation for future developments in effective and sustainable energy solutions, this research contributes to advancing the understanding and implementation of PV-TE technology.

An extended model to assess Jeffery–Hamel blood flow through arteries with iron-oxide (Fe2O3) nanoparticles and melting effects: Entropy optimization analysis

Abstract Nanofluids are utilized in cancer therapy to boost therapeutic effectiveness and prevent adverse reactions. These nanoparticles are delivered to the cancerous tissues under the influence of radiation through the blood vessels. In the current study, the propagation of nanoparticles within the blood in a divergent/convergent vertical channel with flexible boundaries is elaborated computationally. The base fluid (Carreau fluid model) is speculated to be blood, whereas nanofluid is believed to be an iron oxide–blood mixture. Because of its shear thinning or shear thickening features, the Carreau fluid model more precisely depicts the rheological characteristics of blood. The arterial section is considered a convergent or divergent channel based on its topological configuration (non-uniform cross section). An iron oxide ( F e 2 O 3 {\rm{F}}{{\rm{e}}}_{2}{{\rm{O}}}_{3} ) nanoparticle is injected into the blood (base fluid). To eliminate the viscous effect in the region of the artery wall, a slip boundary condition is applied. An analysis of the transport phenomena is preferred using the melting heat transfer phenomena, which can work in melting plaques or fats at the vessel walls. The effects of thermal radiation, which is advantageous in cancer therapy, biomedical imaging, hyperthermia, and tumor therapy, are incorporated in heat transport mechanisms. The governing equation for the flow model with realistic boundary conditions is numerically tickled using the RK45 mechanism. The findings reveal that the flow dynamism and thermal behavior are significantly influenced by melting effects. Higher Re \mathrm{Re} can produce spots in which the track of the wall shear stress fluctuates. The melting effects can produce agitation and increase the flow through viscous head losses, causing melting of the blockage. The maximum heat transfer of 5 % 5 \% is achieved with We {\rm{We}} when the volume friction is kept at 1 % 1 \% . With higher estimation of inertial forces Re \mathrm{Re}\hspace{1em} and same volume friction, the skin drag coefficient augmented to 34 % 34 \% . The overall temperature is greater for the divergent flow scenario.

Effect of porosity on free vibration and buckling of functionally graded porous beams with non-uniform cross-section

Effect of porosity on free vibration and buckling of functionally graded porous beams with non-uniform cross-section

One-Dimensional vs. Three-Dimensional Models in Free Vibration Analysis of Axially Functionally Graded Beams with Non-Uniform Cross-Sections

One-Dimensional vs. Three-Dimensional Models in Free Vibration Analysis of Axially Functionally Graded Beams with Non-Uniform Cross-Sections

Nonlinear response and resonance analysis of beam with non-uniform cross-section under harmonic and impulse excitations: an analytical approach

Nonlinear response and resonance analysis of beam with non-uniform cross-section under harmonic and impulse excitations: an analytical approach

Analysis of Natural Frequencies in Non-uniform Cross-section Functionally Graded Porous Beams

Analysis of Natural Frequencies in Non-uniform Cross-section Functionally Graded Porous Beams

Integrated Design and Fabrication of Pneumatic Soft Robot Actuators in a Single Casting Step.

Bio-inspired soft robots have already shown the ability to handle uncertainty and adapt to unstructured environments. However, their availability is partially restricted by time-consuming, costly, and highly supervised design-fabrication processes, often based on resource-intensive iterative workflows. Here, we propose an integrated approach targeting the design and fabrication of pneumatic soft actuators in a single casting step. Molds and sacrificial water-soluble hollow cores are printed using fused filament fabrication. A heated water circuit accelerates the dissolution of the core's material and guarantees its complete removal from the actuator walls, while the actuator's mechanical operability is defined through finite element analysis. This enables the fabrication of actuators with non-uniform cross-sections under minimal supervision, thereby reducing the number of iterations necessary during the design and fabrication processes. Three actuators capable of bending and linear motion were designed, fabricated, integrated, and demonstrated as 3 different bio-inspired soft robots, an earthworm-inspired robot, a 4-legged robot, and a robotic gripper. We demonstrate the availability, versatility, and effectiveness of the proposed methods, contributing to accelerating the design and fabrication of soft robots. This study represents a step toward increasing the accessibility of soft robots to people at a lower cost.