Cross-sectional Properties Research Articles

Impact of Temperature and Substrate Type on the Optical and Structural Properties of AlN Epilayers: A Cross-Sectional Analysis Using Advanced Characterization Techniques

AlN, with its ultra-wide bandgap, is highly attractive for modern applications in deep ultraviolet light-emitting diodes and electronic devices. In this study, the surface and cross-sectional properties of AlN films grown on flat and nano-patterned sapphire substrates are characterized by a variety of techniques, including photoluminescence spectroscopy, high-resolution X-ray diffraction, X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy, and Raman spectroscopy. The results indicate that different sapphire substrates have minimal impact on the photoluminescence spectrum of the epitaxial films. As the temperature increased, the radius of curvature of the AlN films increased, while the warpage decreased. The AlN films grown on nano-patterned substrates exhibited superior quality with less surface oxidation. During the growth of AlN thin films on different types of substrates, slight shifts in the energy bands occurred due to differences in the introduction of carbon-related impurities and intrinsic defects. The Raman shift and full width at half maximum (FWHM) of the E2(low), A1(TO), E2(high), E1(TO), and E1(LO) phonon modes for the cross-sectional AlN films varied with the depth and temperature. The stress state within the film was precisely determined with specific depths and temperatures. The FWHM of the E2(high) phonon mode suggests that the films grown on nano-patterned substrates exhibited better crystalline quality.

Effect of Fiber Cross-Sectional and Surface Properties on the Degradation of Biobased Polymers.

Biobased polymers such as polylactic acid (PLA) and polybutylene succinate (PBS) break down naturally under certain environmental conditions. The efficiency of degradation can be linked directly to fiber surface properties, which influence polymer accessibility. Here, the degradation of PLA and PBS fibers with six different cross-sections was investigated. The fibers were aged by hydrolysis and UV exposure in an accelerated weathering test, followed by an ISO 20200 laboratory-scale disintegration test with non-aged fibers as controls. The polymers were analyzed by differential scanning calorimetry, Fourier transform infrared spectroscopy, and gel permeation chromatography, comparing the polymer granulate, virgin fibers, and UV-exposed fibers. It was found that the molecular mass and crystallinity of PBS changed more than PLA during spinning. Several PLA samples were completely degraded, whereas all the PBS samples remained intact. Furthermore, surface openings appeared on the PLA fibers during weathering, suggesting greater sensitivity to UV exposure and hydrolysis than PBS. A clear correlation between the fiber surface area and the degradation rate was observed for all samples, but the correlation was positive for PLA and negative for PBS. The slower degradation of PBS fibers with a larger surface area may reflect the ability of PBS to preserve itself by further crystallization during degradation processes at temperatures higher than the glass transition point. The data clearly show that the analysis of single degradation mechanisms is insufficient to predict the behavior of material under real-world conditions, where different degradation mechanisms may work in parallel or consecutively, and may show interdependencies.

Enhanced Olivine Reactivity in Wet Supercritical CO2 for Engineered Mineral Carbon Sequestration.

The success of CO2 mineralization as a potential solution for reducing carbon emissions hinges on understanding chemical interactions between basaltic minerals and CO2-charged fluids. This study provides a detailed analysis of olivine dissolution in CO2-water mixtures at 90 and 150 °C, 2-9 MPa, and for 8 and 24 h, in both water- and CO2-dominant conditions. By using olivine crystal sections instead of powders, surface agitation is prevented, closing the gap between laboratory studies and natural settings. Surface chemistry, texture, and cross-sectional properties were examined pre- and postreaction using a multiscale approach combining spectroscopic and imaging techniques. Results show that wet supercritical CO2 environments lead to significant olivine dissolution, forming Mg-depleted, Si-enriched etched surfaces, and under certain conditions, the formation of passivating silica precipitates. In contrast, reactions in aqueous fluids caused minimal changes in surface chemistry and texture with no silica precipitation. These observations indicate that reaction extent in the CO2-rich phase is greater relative to water-rich mixtures at equivalent temperature, pressure, and reaction duration. The presence of silica precipitates incorporating leached metals indicates limited transport of reactant away from reaction sites in a CO2-rich medium. This study semi-quantitatively evaluates reaction extents in both CO2-rich and aqueous systems across a wide range of parameters, demonstrating faster mineralization in CO2-rich environments and highlighting their potential for enhancing the CO2 storage efficiency.

Finite-element-based cross-section analysis method for functionally graded sandwich members with arbitrary shapes and gradients

Recent advancements in manufacturing technologies have facilitated the efficient and cost-effective production of functionally graded (FG) sandwich members, offering exceptional structural performances. However, designing these members is challenging due to the difficulties in accurately determining their cross-sectional properties, especially within routine designs that rely on beam-column elements. To this end, this paper introduces a robust finite-element-based cross-section analysis method for FG sandwich sections considering arbitrary shapes and material gradients. A novel nonhomogeneous plane triangle (NPT) element is formulated to enhance the computational efficiency of the developed cross-section analysis approach. A new structural analysis software with a graphic user interface, namely MSASect2, is developed based on the proposed cross-section analysis approach for its convenient implementation in practice. Four examples are displayed to verify the correctness of the present study and MSASect2, indicating their potential to promote the broader application of FG sandwich sections.

Destruction mechanism of anterior cervical discectomy and fusion in frontal impact.

The aim of this study was to quantitatively study the effect of anterior cervical discectomy and fusion (ACDF) on the risk of spinal injury under frontal impact. A head-neck finite element model incorporating active neck muscles and soft tissues was developed and validated. Based on the intact head-neck model, three ACDF models (single-level, two-level and three-level) were used to analyze the frontal impact responses of the head-neck. The results revealed that various surgical approaches led to distinct patterns of vertebral damage under frontal impact. For single-level and three-level ACDFs, vertebral destruction was mainly concentrated at the lower end of the fused segment, while the other vertebrae were not significantly damaged. For two-level ACDF, the lowest vertebra was the first to suffer destruction, followed by severe damage to both the upper and lower vertebrae, while the middle vertebra of the cervical spine exhibited only partial damage around the screws. Fusion surgery for cervical spine injuries predominantly influences the vertebral integrity of the directly fused segments when subjected to frontal impact, while exerting a comparatively lesser impact on the cross-sectional properties of adjacent, non-fused segments.

Ontogenetic biomechanics of tufted (Sapajus) and untufted (Cebus) capuchin mandibles.

Cortical bone geometry is commonly used to investigate biomechanical properties of primate mandibles. However, the ontogeny of these properties is less understood. Here we investigate changes in cortical bone cross-sectional properties throughout capuchin ontogeny and compare captive versus wild, semi-provisioned groups. Tufted capuchins (Sapajus spp.) are known to consume relatively hard/tough foods, while untufted capuchins (Cebus spp.) exploit less mechanically challenging foods. Previous research indicates dietary differences are present early in development and adult Sapajus mandibles can resist higher bending/shear/torsional loads. This study utilized microCT scans of 22 Cebus and 45 Sapajus from early infancy to adulthood from three sample populations: one captive Cebus, one captive Sapajus, and one semi-provisioned, free-ranging Sapajus. Mandibular cross-sectional properties were calculated at the symphysis, P3, and M1. If the tooth had not erupted, its position within the crypt was used. A series of one-way ANOVAs were performed to assess differences between and within the sample populations. Mandible robusticity increases across ontogeny for all three sample populations. Sapajus were better able to withstand bending and torsional loading even early in ontogeny, but no difference in shear resistance was found. Semi-provisioned, free-ranging Sapajus tend to show increased abilities to resist bending and torsional loading but not shear loading compared to captive Sapajus. This study helps advance our understanding of the primate masticatory system development and opens the door for further studies into adaptive plasticity in shaping the masticatory apparatus of capuchins and differences in captive versus free-ranging sample populations.

Inner structures of rapid free-surface granular avalanche over a small bump obstacle: Expansion fan, oblique shock wave, and contact anisotropy

This study investigates the inner flow characteristics of a rapid granular avalanche passing over a small bump obstacle fixed on an inclined chute using the discrete element method. Both the cross-sectional mean flow properties, such as free-surface height, mean flow velocity, and mean stresses, and the inner local flow properties, including granular temperature, coordination number, pressure, contact force orientation, and granular fabrics, were comprehensively investigated. Upstream of the obstacle, a wide compression region where mean stresses strengthen and exhibit anisotropy was observed. Employing the kinetic theory of granular gas, we revealed a smooth supersonic-to-subsonic transition near the obstacle, a phenomenon distinct from typical gas dynamics. These upstream flow phenomena are attributed to the generation of stream-wise-oriented contact force chains as the flow impacts the obstacle. Downstream of the obstacle, a complex non-monotonic expansion–compression–expansion process was observed. We demonstrated that this non-monotonic flow process reflects an inner gasdynamic-like phenomenon characterized by an expansion fan followed by an oblique shock wave. Moreover, the force chains and the inner shock structure were found to significantly influence the evolution of stream-wise velocity profiles. These findings underscore the significance of inner flow structures in shaping the dynamics of granular avalanche flow interacting with obstacles.

Line finite element method for geometrically nonlinear analysis of functionally graded members accounting for twisting effects

Functionally graded materials with spatially varying properties have gained widespread use in various engineering disciplines due to their exceptional mechanical characteristics. Nevertheless, these materials can lead to non-symmetric properties of cross-sections and an offset between centroid and shear center of functionally graded (FG) members, thereby significantly affecting the mechanical behavior. This phenomenon, known as twisting effects, poses a substantial challenge for the geometrically nonlinear analysis of FG members, as existing methods rely on traditional line elements that assume the centroid and shear center of the section coincide. Thus, this paper proposes a new framework for geometrically nonlinear analysis of FG members, incorporating twisting effects through a novel Timoshenko line element. An efficient finite-element-based approach that employs the nonhomogeneous plane triangle (NPT) element for calculating the cross-sectional properties of arbitrary FG cross-sections is presented. These cross-sectional properties are then utilized within the advanced line-element formulation to perform geometrically nonlinear analysis of FG structures considering twisting effects. The accuracy of the proposed method is validated through three examples, followed by several case studies to examine the impact of twisting effects on FG members. Furthermore, the proposed cross-section analysis method is integrated into a new structural analysis software MSASect2 to facilitate its application.

Experimental study of the two-phase flow distribution in helical-structured vertical headers

A vertical header is a crucial component of a microchannel heat exchanger that facilitates the distribution of the two phases of the refrigerant into horizontally aligned channels. Ensuring an even distribution of the refrigerant into the channels is imperative for achieving the designed optimal performance. Previous studies have indicated that the distribution characteristics of the vertical header are contingent upon the mass flow rate and geometric properties of the header. This study aims to investigate the distribution characteristics of two-phase flow resulting from structural modifications in the header, specifically by implementing a vertical header with a helical structure. Hence, an experimental device simulating a microchannel heat exchanger found in a commercial air conditioning system was employed. The distribution characteristics of the vertically oriented header with a helical structure were measured by varying the inlet conditions (mass flow rate: 50–100 kg h−1; vapor quality: 0.1–0.2). The measured distribution characteristics were compared with those obtained from a conventional straight vertical header possessing the same cross-sectional properties. The experimental findings demonstrated that the helical structure induced a distinctive flow pattern and facilitated the mixing of the two phases. Furthermore, this helical structure exhibited reduced inertial forces compared to the simple vertical header, leading to improved distribution performance.

Review of the Development of an Unbonded Flexible Riser: New Material, Types of Layers, and Cross-Sectional Mechanical Properties.

Unbonded flexible risers consist of several helical and cylindrical layers, which can undergo large bending deformation and can be installed in different configurations to adapt to harsh marine environments; thus, they can be applied to transport oil and gas resources from ultra-deep waters (UDW). Due to their special geometric characteristics, they can ensure sufficient axial tensile stiffness while having small bending stiffness, which can undergo large deflection bending deformation. In recent years, the development of unbonded flexible risers has been moving in an intelligent, integrated direction. This paper presents a review of unbonded flexible risers. Firstly, the form and properties of each interlayer of an unbonded flexible riser are introduced, as well as the corresponding performance and configuration characteristics. In recent years, the development of unbonded flexible risers has been evolving, and the development of machine learning on unbonded flexible risers is discussed. Finally, with emphasis on exploring the design characteristics and working principles, three new types of unbonded flexible risers, an integrated production bundle, an unbonded flexible riser with an anti-H2S layer, and an unbonded flexible riser with a composite armor layer, are presented. The research results show that: (1) the analytical methods of cross-sectional properties of unbonded flexible risers are solved based on ideal assumptions, and the computational accuracy needs to be improved. (2) Numerical methods have evolved from equivalent simplified models to models that account for detailed geometric properties. (3) Compared with ordinary steel risers, the unbonded flexible riser is more suitable for deep-sea resource development, and the structure of each layer can be designed according to the requirements of the actual environment.

Nonlinear Slippage of Tensile Armor Layers of Unbonded Flexible Riser Subjected to Irregular Loads

The unbonded flexible riser has been increasingly applied in the ocean engineering industry to transport oil and gas resources from the seabed to offshore platforms. The slippage of helical layers, especially the tensile armor layers of unbonded flexible risers, contribute to the nonlinear hysteresis phenomenon, which is a research hotspot and difficulty. In this paper, on the basis of a typical eight-layer unbonded flexible riser model, the nonlinear slippage of a tensile armor layer and the corresponding nonlinear behavior of an unbonded flexible riser subjected to irregular external loads are studied by numerical modeling with detailed cross-sectional properties of the helical layers, and are verified through a theoretical method considering the coupled effect of the external loads on the unbonded flexible riser. Firstly, the balance equation of each layer considering the effect of external loads is established based on functional principles, and the overall theoretical model of the unbonded flexible riser is set up in consideration of the contact between adjacent layers. Secondly, the numerical modeling of each separate layer within the unbonded flexible riser, including the actual geometry of the carcass and pressure armor layer, is established, and solid elements are applied to all the interlayers, thus simulating the nonlinear contact and friction between and within interlayers. Finally, after verification through test data, the behavior of the unbonded flexible riser under the cyclic axial force, torsion, bending moment, and irregular external and internal pressure is studied. The results show that the tensile armor layer can slip under irregular loads. Additionally, some suggestions related to the analysis of unbonded flexible risers under irregular loads are drawn in the end.

Comparative anatomy of the caudate nucleus in canids and felids: Associations with brain size, curvature, cross-sectional properties, and behavioral ecology.

The evolutionary history of canids and felids is marked by a deep time separation that has uniquely shaped their behavior and phenotype toward refined predatory abilities. The caudate nucleus is a subcortical brain structure associated with both motor control and cognitive, emotional, and executive functions. We used a combination of three-dimensional imaging, allometric scaling, and structural analyses to compare the size and shape characteristics of the caudate nucleus. The sample consisted of MRI scan data obtained from six canid species (Canis lupus lupus, Canis latrans, Chrysocyon brachyurus, Lycaon pictus, Vulpes vulpes, Vulpes zerda), two canid subspecies (Canis lupus familiaris, Canis lupus dingo), as well as three felids (Panthera tigris, Panthera uncia, Felis silvestris catus). Results revealed marked conservation in the scaling and shape attributes of the caudate nucleus across species, with only slight deviations. We hypothesize that observed differences in caudate nucleus size and structure for the domestic canids are reflective of enhanced cognitive and emotional pathways that possibly emerged during domestication.

Skeletal consequences of preterm birth in pigs as a model for preterm infants.

Preterm birth affects about 10% of all live births with many resultant health challenges, including metabolic bone disease of prematurity (MBDP), which is characterized by elevated alkaline phosphatase, suppressed phosphate, and deficient skeletal development. Because of the lack of an animal model, very little is known about bone structure, strength, and quality after preterm birth. This study investigated the utility of a pig model to replicate clinical features of preterm birth, including MBDP, and sought to determine if early postnatal administration of IGF-1 was an effective treatment. Preterm pigs, born by caesarean section at 90% gestation, were reared in intensive care facilities (respiratory, thermoregulatory, and nutritional support) and compared with sow-reared term pigs born vaginally. Preterm pigs were systemically treated with vehicle or IGF-1 (recombinant human IGF-1/BP-3, 2.25mg/kg/d). Tissues were collected at postnatal days 1, 5, and 19 (the normal weaning period in pigs). Most bone-related outcomes were affected by preterm birth throughout the study period, whereas IGF-1 supplementation had almost no effect. By day 19, alkaline phosphatase was elevated, phosphate and calcium were reduced, and the bone resorption marker C-terminal crosslinks of type I collagen was elevated in preterm pigs compared to term pigs. Preterm pigs also had decrements in femoral cortical cross-sectional properties, consistent with reduced whole-bone strength. Thus, the preterm pig model replicates many features of preterm bone development in infants, including features of MBDP, and allows for direct interrogation of skeletal tissues, enhancing the field's ability to examine underlying mechanisms.

Punching Shear of FRP-RC Slab–Column Connections: A Comprehensive Database

Several design standards have been developed in the last two decades to estimate the punching capacity of two-way reinforced concrete (RC) slabs reinforced with fiber-reinforced polymer (FRP) reinforcement. FRP-RC design standards include the recently published ACI 440.11-22, CSA/S806-12, and JSCE-2007. These models are either based on empirical data or semi-empirical methods and calibrated using different databases. Additionally, these standards do not have provisions for connections with shear reinforcement. Therefore, a reliable worldwide database for developing and assessing the applicability of such provisions with test results is vital. This study presents a worldwide and up-to-date database for punching shear of FRP-RC slabs. The database includes 197 tested connections, comprising interior and edge connections, with and without shear reinforcement, and a wide range of materials and cross-sectional properties. The database was used to evaluate the accuracy of the mentioned standards in predicting the punching shear capacity. For connections without shear reinforcement, it was determined that the three design standards yielded similar performance with different conservatism levels. ACI 440.11-22 yielded the most conservative results, with average Vexp/Vpred ratios of 2.04 compared to 1.28 and 1.3 for other models. For connection with shear reinforcement, specimens with Evf> 100 GPa resulted in Vexp/Vpred ratios less than 1.0 for ACI and CSA standards.

Changes in limb bone diaphyseal structure in chimpanzees during development.

This study tests if femoral and humeral cross-sectional geometry (CSG) and cross-sectional properties (CSPs) in an ontogenetic series of wild-caught chimpanzees (Pan troglodytes ssp.) reflect locomotor behavior during development. The goal is to clarify the relationship between limb bone structure and locomotor behavior during ontogeny in Pan. The latex cast method was used to reconstruct cross sections at the midshaft femur and mid-distal humerus. Second moments of area (SMAs) (Ix, Iy, Imax, Imin), which are proportional to bending rigidity about a specified axis, and the polar SMA (J), which is proportional to average bending rigidity, were calculated at section locations. Cross-sectional shape (CSS) was assessed from Ix/Iy and Imax/Imin ratios. Juvenile and adult subsamples were compared. Juveniles and adults have significantly greater femoral J compared to humeral J. Mean interlimb proportions of J are not significantly different between the groups. There is an overall decreasing trend in diaphyseal circularity between the juvenile phase of development and adulthood, although significant differences are only found in the humerus. Juvenile chimpanzee locomotion includes forelimb- and hindlimb-biased behaviors. Juveniles and adults preferentially load their hindlimbs relative to their forelimbs. This may indicate similar locomotor behavior, although other explanations including a diversity of hindlimb-biased locomotor behaviors in juveniles cannot be ruled out. Different ontogenetic trends in forelimb and hindlimb CSS are consistent with limb bone CSG reflecting functional adaptation, albeit the complex nature of bone functional adaptation requires cautious interpretations of skeletal functional morphology from biomechanical analyses.

Bending performance changes during prolonged canine eruption in saber-toothed carnivores: A case study of Smilodon fatalis.

The canine of saber-toothed predators represents one of the most specialized dental structures known. Hypotheses about the function of hypertrophied canines range from display and conspecific interaction, soft food processing, to active prey acquisition. Recent research on the ontogenetic timing of skull traits indicates the adult canine can take years to fully erupt, but the consequences of prolonged eruption on inferences of canine functional morphology are missing from current discourse and have not been quantified. Here I evaluate hypotheses about adult canine bending strength and stiffness, respectively, during eruption in the felid Smilodon fatalis. Simulated eruption sequences of three adult canines were generated from specimen models to assess shifting cross-sectional geometry properties, and bending strength and stiffness under laterally directed loads were estimated using finite element analysis. Consistent with beam theory expectations, S. fatalis canine cross-sectional geometry is optimized for increased bending strength with increased erupted height. However, canine cross-sectional geometry changes through eruption exaggerate rather than minimize lateral deflection. Spatial constraint for maximum root length from adjacent sensory structures in the maxilla and the recently identified universal power law are hypothesized to limit the growth capacity of canine anteroposterior length and, consequently, maintenance of bending stiffness through eruption. Instead, the joint presence of the deciduous and adult canines for >50% of the adult canine eruption period effectively increases canine mediolateral width and brings bending strength and stiffness estimates closer to theoretical optima. Similarly prolonged retention of deciduous canines in other sabertooths suggests dual-canine buttressing is a convergently evolved strategy to maximize bending strength and stiffness.

New insights into patterns of integration in the femur and pelvis among catarrhines.

Integration reflects the level of coordinated variation of the phenotype. The integration of postcranial elements can be studied from a functional perspective, especially with regards to locomotion. This study investigates the link between locomotion, femoral structural properties, and femur-pelvis complex morphology. We measured (1) morphological integration between femoral and pelvic morphologies using geometric morphometrics, and (2) covariation between femoral/pelvic morphologies and femoral diaphyseal cross-sectional properties, which we defined as morpho-structural integration. Morphological and morpho-structural integration patterns were measured among humans (n = 19), chimpanzees and bonobos (n = 16), and baboons (n = 14), whose locomotion are distinct. Baboons show the highest magnitude of morphological integration and the lowest of morpho-structural integration. Chimpanzees and bonobos show intermediate magnitude of morphological and morpho-structural integration. Yet, body size seems to have a considerable influence on both integration patterns, limiting the interpretations. Finally, humans present the lowest morphological integration and the highest morpho-structural integration between femoral morphology and structural properties but not between pelvic morphology and femur. Morphological and morpho-structural integration depict distinct strategies among the samples. A strong morphological integration among baboon's femur-pelvis module might highlight evidence for long-term adaptation to quadrupedalism. In humans, it is likely that distinct selective pressures associated with the respective function of the pelvis and the femur tend to decrease morphological integration. Conversely, high mechanical loading on the hindlimbs during bipedal locomotion might result in specific combination of structural and morphological features within the femur.

Cortical bone architecture of hominid intermediate phalanges reveals functional signals of locomotion and manipulation.

Reconstruction of fossil hominin manual behaviors often relies on comparative analyses of extant hominid hands to understand the relationship between hand use and skeletal morphology. In this context, the intermediate phalanges remain understudied. Thus, here we investigate cortical bone morphology of the intermediate phalanges of extant hominids and compare it to the cortical structure of the proximal phalanges, to investigate the relationship between cortical bone structure and inferred loading during manual behaviors. Using micro-CT data, we analyze cortical bone structure of the intermediate phalangeal shaft of digits 2-5 in Pongo pygmaeus (n = 6 individuals), Gorilla gorilla (n = 22), Pan spp. (n = 23), and Homo sapiens (n = 23). The R package morphomap is used to study cortical bone distribution, cortical thickness and cross-sectional properties within and across taxa. Non-human great apes generally have thick cortical bone on the palmar shaft, with Pongo only having thick cortex on the peaks of the flexor sheath ridges, while African apes have thick cortex along the entire flexor sheath ridge and proximal to the trochlea. Humans are distinct in having thicker dorsal shaft cortex as well as thick cortex at the disto-palmar region of the shaft. Variation in cortical bone distribution and properties of the intermediate phalanges is consistent with differences in locomotor and manipulative behaviors in extant great apes. Comparisons between the intermediate and proximal phalanges reveals similar patterns of cortical bone distribution within each taxon but with potentially greater load experienced by the proximal phalanges, even in knuckle-walking African apes. This study provides a comparative context for the reconstruction of habitual hand use in fossil hominins and hominids.

Finite element based dynamic analysis of a porous exponentially graded shaft system subjected to thermal gradients

Abstract In modern applications, demand for the rotor shafts made of FGM has increased in aerospace, gas turbine and turbo jet engines due to its improved dynamic characteristics at elevated temperatures. The dynamic vibration response of a functionally graded Jeffcott rotor-bearing system with induced porosities has been studied for non-uniform porosity distributions. The functionally graded (FG) shaft’s radial direction exhibits continuous variation in the material qualities. The FG rotor’s cross-sectional material properties have been graded using the exponential law. The temperature gradients have been considered to be varied across the cross-section based on exponential temperature distribution. For the first time, using the FE method, it has been possible to study the impact of induced porosities on the free vibration frequencies and steady-state vibration responses of the functionally graded rotor-bearing system. This has led to the development of a two-node porous functionally graded rotor element with uneven porosity distributions using the Timoshenko beam theory. It has been observed that the free vibration frequencies and the FG rotor-bearing system critical speeds are affected by increased porosity and thermal gradients. The frequency responses demonstrate that as temperature gradient and volume fraction of porosity rise, the FG rotor-bearing system’s critical speeds shift to the left.

A new theoretical method for torsional-flexural vibrations response of thin-walled beams with closed cross-sections under uniform distributed moving load

This article presents a new theoretical method for the torsional-flexural vibration response of a thin-walled beam with closed cross sections under a uniformly distributed moving load. Based on Vlasov’s theory and restrained torsion theory, a comprehensive equation of motion for torsional flexural vibration is established by considering the effects of additional torque caused by the change of the shear center and the center of mass and the warpage coefficient. Using the Fourier transform, Laplace transform, and their inverse transformations, the torsional-flexural vibration response expression of thin-walled beams with closed cross-sections under a uniformly distributed moving load was derived. The results calculated by the analytical solutions in this study were compared with those from finite element method, demonstrating the reliability and superiority of the analytical solutions. Compared with the method that ignores the warpage coefficient, the lateral displacement and torsion angle of the beam calculated by the proposed theoretical method decreased by more than 12.00%. The effect of the cross-sectional properties on the natural frequency of the torsional-flexural vibration of thin-walled beams is analyzed, and the results show that the moment of inertia and mass per unit length have a considerable influence on the torsional-flexural frequency, which increases with the moment of inertia and decreases with an increase in the mass per unit length. The influences of the load magnitude, load velocity, and load eccentricity on the dynamic response were further investigated. According to the results, the lateral displacement of the beam increased significantly with increases in the load eccentricity and load magnitude. In practical engineering, the conclusions of this study can be used to limit the torsional-flexural vibration response of simple maglev support bridges to ensure the safety of vehicles and passengers.