Body Radius Research Articles

Age-related alterations in human cortical microstructure across the lifespan: Insights from high-gradient diffusion MRI.

The human brain undergoes age-related microstructural alterations across the lifespan. Soma and Neurite Density Imaging (SANDI), a novel biophysical model of diffusion MRI, provides estimates of cell body (soma) radius and density, and neurite density in gray matter. The goal of this cross-sectional study was to assess the sensitivity of high-gradient diffusion MRI toward age-related alterations in cortical microstructure across the adult lifespan using SANDI. Seventy-two cognitively unimpaired healthy subjects (ages 19-85 years; 40 females) were scanned on the 3T Connectome MRI scanner with a maximum gradient strength of 300mT/m using a multi-shell diffusion MRI protocol incorporating 8 b-values and diffusion time of 19 ms. Intra-soma signal fraction obtained from SANDI model-fitting to the data was strongly correlated with age in all major cortical lobes (r = -0.69 to -0.60, FDR-p < 0.001). Intra-soma signal fraction (r = 0.48-0.63, FDR-p < 0.001) and soma radius (r = 0.28-0.40, FDR-p < 0.04) were significantly correlated with cortical volume in the prefrontal cortex, frontal, parietal, and temporal lobes. The strength of the relationship between SANDI metrics and age was greater than or comparable to the relationship between cortical volume and age across the cortical regions, particularly in the occipital lobe and anterior cingulate gyrus. In contrast to the SANDI metrics, all associations between diffusion tensor imaging (DTI) and diffusion kurtosis imaging metrics and age were low to moderate. These results suggest that high-gradient diffusion MRI may be more sensitive to underlying substrates of neurodegeneration in the aging brain than DTI and traditional macroscopic measures of neurodegeneration such as cortical volume and thickness.

Automatic virtual reconstruction of acetabular fractures using a statistical shape model.

Automatic virtual reconstruction of complex fractures would be helpful for pre-operative surgical planning. We developed a statistical shape model (SSM) which contains data of 200 intact 3D hemipelves. It allows for quantification of shape differences and is able to reconstruct abnormal shaped pelvises. We applied our SSM to reconstruct elementary and associate type acetabular fractures and assessed the reconstruction performance of the SSM, by comparing the reconstructed shape with the intact contralateral hemipelvis. In this retrospective diagnostic imaging study, we used our SSM to virtually reconstruct fractured hemipelves of eighty-three patients with an acetabular fracture. A root mean square error (RMSE) was computed between the reconstructed shape and intact contralateral shape for the whole hemipelvis and for regions relevant for plate-fitting. These plate-fitting relevant regions were defined as: (1) Iliopectineal line length and radius; (2) ischial body line length and radius; (3) acetabular diameter, (4) quadrilateral slope and (5) weight-bearing acetabular dome. The median RMSE of the whole hemipelvis of the elementary type fractures was 2.2 (1.7-2.5) mm versus 3.2 (2.2-3.9) mm for the associate type fractures (p < 0.001). The median RMSE for the plate-fitting regions of elementary type fractures was 1.7 (1.4-2.1) mm versus 2.7 (2.0-4.1) mm for associate type fractures (p < 0.001). Using a statistical shape model allows for accurate virtual reconstructions of elementary and associate type acetabular fractures within a clinically acceptable range, especially within regions important for plate-fitting. SSM-based reconstructions can serve as a valuable tool for pre-operative planning in clinical practice, when a template of the contralateral hemipelvis is unavailable.

The impacts of structural parameters on performance and energy loss of the supersonic separator: A sensitivity analysis

The supersonic separator uses pressure energy to achieve highly efficient carbon capture and water vapor separation from the natural gas mixture. Structural parameters are crucial in determining both separation performance and pressure energy loss of the supersonic separator. However, a comprehensive understanding of how them influence flow behaviors and performance is hindered by their coupling effects and the limitations of numerical methods. This study introduces Euler-Lagrange-Euler model to predict separation performance and pressure energy loss of supersonic dehydration process with varying structural parameters. The results show that the expansion ratio of the divergent section, length of the convergent section, inlet radius of the inner body, and throat radius of the inner body significantly impact separation performance and pressure energy loss. Especially the first parameter, the swirl strength and centrifugal acceleration decay to 0.044 and 2.41 × 104 m s−2 as it increases. At the same time, the droplet removal rate significantly improves, but the separation performance does not increase indefinitely due to the shock waves. The dehydration efficiency first increases to 95.09 % at Er= 1.5 and then decreases; the dew point depression also expands to 25.28 K and then drops, and the corresponding pressure loss rises to 0.47 and then falls.

Numerical investigations on the performance enhancement of a hydrogen-fueled micro planar combustor with finned bluff body for thermophotovoltaic applications

To achieve higher power output and energy conversion efficiency for micro-thermophotovoltaic (MTPV) systems, a hydrogen-fueled micro planar combustor with finned bluff body is proposed and compared to the micro planar combustor with/without bluff body. Numerical results indicate that among micro planar combustors without bluff body, with bluff body, and with finned bluff body, the micro planar combustor with finned bluff body obtains a higher and more uniform wall temperature, but the pressure loss is higher. This is due to that the Peclet number near the inner walls is significantly higher compared to those without bluff body, and the Peclet number in the center of the axis is significantly lower, which reveals a stronger convection effect in the non-recirculation region and diffusion effect in the recirculation region. Then, effects of finned bluff body position, fin length/bluff body radius ratio and fin angle on the performance of micro planar combustor are investigated. It is found that the micro planar combustor with a larger finned bluff body position, smaller fin length/bluff body radius ratio and larger fin angle is more practical for MTPV system.

Lewy body radius growth: The hypothesis of the cube root of time dependency

This paper presents a model for the growth of Lewy bodies (LBs), which are pathological hallmarks of Parkinson's disease (PD). The model simulates the growth of classical LBs, consisting of a core and a halo. The core is assumed to comprise lipid membrane fragments and damaged organelles, while the halo consists of radiating alpha-synuclein (α-syn) fibrils. The Finke-Watzky model is employed to simulate the aggregation of lipid fragments and α-syn monomers. Analytical and numerical exploration of the governing equations yielded approximate solutions applicable for larger times. The application of these approximate solutions to simulate LB radius growth led to the discovery of the cube root hypothesis, which posits that the LB radius is proportional to the cube root of its growth time. Sensitivity analysis revealed that the LB radius is unaffected by the kinetic rates of nucleation and autocatalytic growth, with growth primarily regulated by the production rates of lipid membrane fragments and α-syn monomers. The model indicates that the formation of large LBs associated with PD is dependent on the malfunction of the machinery responsible for the degradation of lipid membrane fragments, α-syn monomers, and their aggregates.

ДОСЛІДЖЕННЯ ЕНЕРГЕТИЧНИХ ПОКАЗНИКІВ ПОВЕРХНЕВОГО ОБРОБІТКУ ҐРУНТУ БОРОНОЮ З ГВИНТОВИМ РОБОЧИМ ОРГАНОМ

Restoration of the soil fertility is an important task for scientists and practitioners. Based on the constructed mathematical model of the surface of a screw-type working body, rotating around a fixed horizontal axis, there are determined the work and power of penetration of the screw-type working body into the soil, loosening the soil and overcoming the soil friction. It has been established that the cutting power is proportional to the square root of deepening of the working body (а1/2), and the radius of the working body (R1/2) is directly proportional to the speed of the unit V. On the basis of a complex of experimental studies, regression dependencies were derived to determine the traction resistance when cultivating the soil with a harrow, equipped with screw-type working bodies. It has been found that the dominant impact upon the value of the traction resistance Рх is exerted by the depth of tillage h, then by the angle of attack β of the battery of the screw-type working bodies, but the least impact is made by the change in the speed of the harrow V. The difference between the calculated and the experimental values of the traction resistance ranges from 9.6...11.2%.

Stiffness analysis of nutation face gear considering roughness

PurposeThe purpose of this paper is to calculate the meshing stiffness of nutation face gear considering the roughness, establish the calculation method of time-varying meshing stiffness of rough tooth surface and analyze the influence of roughness, load and other factors on the meshing stiffness of tooth surface.Design/methodology/approachThe Weierstrass–Mandelbrot (W-M) function in the Majumdar–Bhushan model is used to characterize the rough contact line of the tooth surface, the normal height and radius of the micro convex body are calculated and the contact flexibility of the contact point of the tooth surface is obtained. The contact flexibility and the bending shear deformation flexibility obtained previously are substituted into the improved deformation compatibility equation for iterative calculation, and the time-varying meshing stiffness of the nutation face gear considering the roughness is obtained.FindingsCompared with ABAQUS finite element simulation results, it is found that the meshing stiffness curve of rough tooth surface is more gentle than that of smooth tooth surface, the meshing stiffness value is smaller and the meshing stiffness change is smaller at the position where the number of gear teeth coincide changes.Originality/valueIn the process of calculating contact deformation, the fractal theory W-M function is used to characterize the contact line of the rough nutation face gear, and the deformation coordination condition considering roughness is improved. Therefore, the method of time-varying meshing stiffness considering roughness can obtain more accurate results, which provides theory and data for the subsequent dynamics analysis of the nutation face gear transmission.

Gonadotropin-Releasing Hormone Agonist Therapy and Longitudinal Bone Mineral Density in Congenital Adrenal Hyperplasia.

Children with congenital adrenal hyperplasia (CAH) are at risk for early puberty. Gonadotropin-releasing hormone analog (GnRHa) is frequently used and can decrease bone mineral density (BMD). Our aim was to investigate the effect of GnRHa therapy on BMD in a longitudinal study of patients with CAH spanning both childhood and adulthood. Sixty-one patients with classic CAH due to 21-hydroxylase deficiency (20 treated with GnRHa) were followed with dual-energy X-ray absorptiometry (DXA) scans at puberty onset, attainment of adult height, and during early adulthood. Whole body, lumbar spine, femoral neck, total hip, and distal radius BMD z-score at adult height. Longitudinal BMD and adult height were also assessed. Twenty patients received GnRHa for an average of 4.5 ± 2 years. There were no differences in BMD between GnRHa-treated and -untreated groups at adult height for all sites. Overall, the follow-up DXA during early adulthood showed decreases in BMD z-scores for whole body (P = .01), lumbar spine (P < .0001), femoral neck (P = .06), total hip (P = .009), and distal radius (P = .05). GnRHa treatment correlated with improved height outcomes compared to predicted height at puberty onset after adjusting for midparental height (P = .02). Patients in both groups achieved similar adult height. In children with CAH, GnRHa does not compromise BMD. However, BMD decreases with time and during the second and third decades of life is a possible effect of chronic supraphysiologic glucocorticoids. Children with CAH who experience early puberty benefit from GnRHa treatment as evidenced by the positive effect on height.

Accelerated Bone Loss in Older Men With Severe Abdominal Aortic Calcification-the Prospective MINOS Study.

Data on the association between the severity of abdominal aortic calcification (AAC) and bone loss are discordant. Our aim was to assess the association between baseline AAC and prospectively assessed bone loss in older men. This prospective cohort study started in 1995 (MINOS). Men aged 50 to 85 years (n = 778) had AAC assessed on the lateral radiograph of the spine using Kauppila's semiquantitative score and was followed prospectively for 7.5 years. Bone mineral density (BMD) and bone mineral content (BMC) were measured by dual-energy x-ray absorptiometry every 18 months. Statistical analysis was performed using linear mixed models. In comparison to men without AAC (AAC = 0), severe AAC (>6) was associated with more rapid bone loss at the total hip (-0.62 ± 0.06 vs -0.32 ± 0.04%/year; P < .001), trochanter, and distal forearm (-0.72 ± 0.06 vs -0.45 ± 0.03%/year; P < .001). The highest decile (AAC >10) was associated with more rapid bone loss at the femoral neck, whole body, and ultradistal radius (-0.86 ± 0.12 vs -0.34 ± 0.05%/year; P < .001). The results were similar for BMD and for BMC. The patterns were similar in sensitivity analyses (eg, after excluding men with abdominal obesity, after excluding current smokers, after excluding men with ischemic heart disease or with diabetes mellitus, after excluding men with abnormal concentrations of lipids, bioavailable 17β-estradiol or 25-hydroxycholecalciferol, after excluding men with glomerular filtration rate <60 mL/min). Severe AAC is associated with faster bone loss in older men and may contribute to the higher fracture risk observed in this population.

Dispersal Characteristics Dependence on Mass Ratio for Explosively Driven Dry Powder Particle

An investigation on the dispersal characteristics of the cylindrically packed material of dry powder particles driven by explosive load is presented. By establishing a controllable experimental system under laboratory conditions and combining with near-field simulation, the particle dispersal process is described. Additionally, Kelvin–Helmholtz instability is observed during the process of jet deceleration dispersal. The characteristic parameters of radially propagated particles are explored under different mass ratio of particle-to-charge (M/C). Results indicate that, when the charge mass remains constant, an increase in M/C leads to a decrease in dispersed jet number, void radius and maximum velocity, wherein the maximum velocity correlates with calculations by the porous Gurney model. The case of the smaller M/C always has a higher outer-boundary radius and area expansion factor. Findings indicate that when particles detach from the jet upon reaching minimum acceleration and entering low-speed far-field stage from high-speed near-field stage, the outer-boundary radius is 30~36 times the initial particles’ body radius under different M/C. In addition, particle concentration distribution over time and distance is qualitatively analyzed by the grayscale image method. This research can be referential for improving the fire-extinguishing capacity of extinguishing bombs and the damage property of fuel air explosive (FAE).

Effects of the swirler on the performance of an advanced vortex combustor

Trapped vortex combustors have garnered significant interest due to the cavity vortex's insensitivity to flow disturbances. Swirling combustion is also highly desirable due to its excellent mixing performance. This study explores the potential of combining vortex combustors with swirling combustion under reacting conditions. Steady-state Reynolds-averaged Navier–Stokes equations are solved through three-dimensional numerical simulations. The results demonstrate a significant improvement in combustion efficiency, from 55% in original vortex combustor to over 99% in swirling vortex combustor, and fuel–air mixing effectiveness. The spatial spiraled vortex structure forms in the cavity and behind the blunt body when the swirler is used. The position of the blunt body influences the shape of the cavity vortex, with a round vortex structure forming when the cavity length to the total combustion chamber length ratio is around 0.2. When the radius of the blunt body to the radius of the combustion chamber, varying from 0.2 to 0.7, is 0.6, two main recirculation zones can be created in the model. Increasing the swirling number results in a larger recirculation zone in the cavity, with an elongated recirculation area appearing behind the blunt body at a blade installation angle of 60°, corresponding to the swirling number is 1.251. However, an excessively high swirling number leads to uneven pressure distribution in the outlet. These findings provide novel insights for advanced vortex combustor research and optimization.

Turbulent Anisotropy and Length Scale Variation Over Multiple Shaped Structure

AbstractThe turbulent flow characteristics over bed-mounted three different cubical shape bluff bodies are examined experimentally in the water channel facility. The steady and fluctuating flow fields are investigated to analyze the effect of corner radius and shapes of the bluff body on turbulent flow structure, particularly in the wake region. It is found that the sharp corner region significantly impacts the flow separation and alters the characteristics of the shear-layer flow. In particular, the relatively suitable change in geometry resulted in a remarkable variation of the mean flow in the wake is observed. The anisotropic nature of flow is analyzed using the turbulence triangle for the different cubical structures. The variation of the turbulent length scales is presented in the near- and far-wake regions of the submerged obstacles.

Experimental studies of pneumatic disc atomizer for low volume spraying

The article presents the results of experimental studies to determine the dependence of the rotational speed of a pneumatic disc sprayer with coaxial air flow on the flow rate of the working fluid. To refine the parameters of the working body, studies were carried out within the liquid flow rate q, corresponding to the first and second spraying modes, at different rotation speeds ω, the working body's radius r, and the number of radial channels np. At the same time, the mass of the rotating part of the pneumatic disk atomizer was determined. The quality of dispersion of the working fluid obtained experimentally by a multi-disk atomizer in a film version driven by an air flow corresponds to a low-volume liquid atomization mode.

Longitudinal wave propagation in an extended cylindrical body with external Coulomb friction

The propagation of elastic longitudinal waves in an extended cylindrical body located inside an unstrained body and interacting according to the Coulomb law is considered in the article. The problem is studied in a two-dimensional statement; therefore, the friction force (i.e., the interaction conditions) is included in the system of equations as a boundary condition. The Coulomb friction force arises due to the deformation of a cylindrical body. The reliability of numerical calculations is substantiated by solving test cases and comparing the calculations with experimental results. The numerical results obtained are presented in the form of graphs and analyzed. It is shown that the parameters (stresses and strains) of waves propagating in an elastic cylindrical body with external Coulomb dry friction decay with distance. The mechanism for reducing the stress-strain state and wave parameters is explained by the consumption of elastic energy to overcome the friction force that occurs on the contact surface. The results of the two-dimensional problem are also compared with the results of a similar problem in the one-dimensional theory, where the friction force enters directly into the equations of motion. The deviations of the results of the one-dimensional theory are up to 8-15% depending on the accepted values of the friction coefficient, i.e. the violation of the plane section hypothesis taken in one-dimensional calculations amounts to 15%. With a decrease in the radius of a cylindrical body, these deviations are reduced.

The Changing Dynamics of a Universe in Transition

It is shown in this paper that the distorted space model of matter can describe a universe transitioning between conception and an open-ended finality. We use the verbiage “distorted” to communicate the concept of “energetic-manifold-warping” and to distinguish “spatial-warping” from “classical matter-warping”, although the concept of “matter” is in fact, in the present “distorted-geometry” context, the “geometric distortion energy” of the spatial manifold itself without a classical “matter stress-energy source”. An energy conserving alternative to black-body radiation-emission structural-modeling is manifest as an energetically unstable Universe (an originally stable but subsequently collapsing state, followed by an explosive expansion, thereby exhibiting an energy-creation process of one day!). The energy transition dynamics are described for a spherical, gravitational, and electromagnetic, geometrically-based mimic of matter existing at quantitative measures of a size challenging observation, that is, at a calculated Universe (gravitational body) [Formula: see text][Formula: see text]m and [Formula: see text][Formula: see text]J. The Universe (electromagnetic body) radius is calculated [Formula: see text][Formula: see text]m. We have modeled the structure with a composite, two-component, geometric-coupling_constant and initial structural conditions representing Friedmann’s critical density, [Formula: see text]_critical energy-density (8.898(–10)[Formula: see text][Formula: see text]J/m3) for the gravitational energy-density and [Formula: see text]_electron (8.7(10)[Formula: see text][Formula: see text]J/m3)[Formula: see text][Formula: see text][Formula: see text]the [Formula: see text]_critical energy-density for the geometric-electromagnetic extremum; the geometric extrema are curvature and energy-density extrema. A collapsing initial-phase-1 state, posited as a Friedmann-defined, distorted-geometry (DG) configuration with two equal-energy species or energy-density states, transitions electromagnetically, via an intermediate “mediator or force carrier” state (a W-boson structure in beta-decay), to a final 3-component state (ala a mimic of the beta decay transition process).

A new approach automatic separation of the Bouguer gravity anomaly, using a new concept for 2D-semi-inversion of the sphere-shaped model

ABSTRACT The present research represents a new, fast and easy-to-apply semi-inversion technique for the direct separation of the Bouguer gravity anomaly to its corresponding depths or thicknesses of the prior known rock formations from a borehole (as a control point). As well as the possibility of tracing these formations on the profile points to the Bouguer gravity map according to their density contrasts with basement rock. The proposed method is based on the fact that the sum of the gravitational effect at a point on the Earth’s surface is equal to the sum of the subsurface gravity effects arising from the points of masses of the causal bodies along the vertical line between the Earth’s surface and the basement rocks. In this method, two sedimentary basin models were built based on the distribution of densities from a prior known borehole. Assuming that the depths of the pointed tops of these rock formations can be replaced by the centres of sphere bodies (or point masses) as causative sources of gravitational effect and by the use of a simple algorithm, it was possible to calculate the depths of the rock formations and trace them on the profile, using a new concept called the zero-offset gravity measurement. In this concept, the measuring gravity is vertically above the centre of the sphere-shaped body as it represents the causative source, and its depths are equal to the radius of the sphere body. The present method was assessed on hypothetical models and synthetic data and applied to two real data in field cases which vary in geological and lithological aspects. The first assessed location is Abu Roash Dome Area, southwest Cairo, Egypt, and the second location is the Mors Salt Dome, North Jutland, Denmark.

Differentiation time scales of small rocky bodies

The petrologic and geochemical diversity of meteorites is a function of the bulk composition of their parent bodies, but also the result of how and when internal differentiation took place. Here we focus on this second aspect considering the two principal parameters involved: size and accretion time of the body. We discuss the interplay of the various time scales related to heating, cooling and drainage of silicate liquids. Based on two phase flow modeling in 1-D spherical geometry, we show that drainage time is proportional to two independent parameters: μm/R2, the ratio of the matrix viscosity to the square of the body radius and μf/a2, the ratio of the liquid viscosity to the square of the matrix grain size. We review the dependence of these properties on temperature, thermal history and degree of melting, demonstrating that they vary by several orders of magnitude during thermal evolution. These variations call into question the results of two phase flow modeling of small body differentiation that assume constant properties. For example, the idea that liquid migration was efficient enough to remove 26Al heat sources from the interior of bodies and dampen their melting (e.g. Moskovitz and Gaidos, 2011; Neumann et al., 2012) relies on percolation rates of silicate liquids overestimated by six to eight orders of magnitude. In bodies accreted during the first few million years of solar-system history, we conclude that drainage cannot prevent the occurrence of a global magma ocean. These conditions seem ideal to explain the generation of the parent-bodies of iron meteorites. A map of the different evolutionary scenarios of small bodies as a function of size and accretion time is proposed.

Analytic Light Curve for Mutual Transits of Two Bodies Across a Limb-darkened Star

We present a solution for the light curve of two bodies mutually transiting a star with polynomial limb darkening. The term “mutual transit” in this work refers to a transit of the star during which overlap occurs between the two transiting bodies. These could be an exoplanet with an exomoon companion, two exoplanets, an eclipsing binary and a planet, or two stars eclipsing a third in a triple-star system. We include analytic derivatives of the light curve with respect to the positions and radii of both bodies. We provide code that implements a photodynamical model for a mutual transit. We include two dynamical models, one for hierarchical systems in which a secondary body orbits a larger primary (e.g., an exomoon system) and a second for confocal systems in which two bodies independently orbit a central mass (e.g., two planets in widely separated orbits). Our code is fast enough to enable inference with Markov Chain Monte Carlo algorithms, and the inclusion of derivatives allows for the use of gradient-based inference methods such as Hamiltonian Monte Carlo. While applicable to a variety of systems, this work was undertaken primarily with exomoons in mind. It is our hope that making this code publicly available will reduce barriers for the community to assess the detectability of exomoons, conduct searches for exomoons, and attempt to validate existing exomoon candidates. We also anticipate that our code will be useful for studies of planet–planet transits in exoplanetary systems, transits of circumbinary planets, and eclipses in triple-star systems.

Fuzzy-theory-based pedestrian dynamics models for studying the waiting passenger distribution at the subway platform

The behavior of waiting area choice of passengers at the subway platform can directly affect the travel efficiency, thereby affecting the service level of the station. Combining fuzzy logic theory and cellular automata model/social force model, a waiting area choice model for passengers at the subway platform is proposed, which can be used to predict the distribution of passengers. The distance from passengers to waiting areas, the number of passengers in the waiting area, and the length of the remaining waiting area are selected as the main influence factors after the analysis of field investigation, which are defined as the input variables of the fuzzy logic system. The choice probability of passengers to each waiting area is defined as the output variable. The waiting area with the highest probability is taken as the destination of passengers, thereby the static field value in the cellular automata model and the desired direction in the social force model can be determined. The total error of the established method can be as low as 10.13%, which shows a relatively good prediction effect. The effects of passenger attributes, stair attributes, and passable area size on the waiting area choice behavior are simulated. The results show that the influence degree of passenger companion behavior on passenger distribution depends much on the proportion of passengers in the company. The body radius and the desired speed of passengers have a great impact on the distribution balance of waiting passengers based on the analysis of the Gini coefficient and random forest method. The interval of multiple stairs should be the same as far as possible. The setting of a passable area is conducive to the flow of passengers during peak hours. The number of passengers is most pronounced in the distribution balance of passengers by comparing five different influence factors. Guidance strategies can be released through the LED display screen on the basis of the predicted distribution information. This paper provides a new idea for modeling the waiting area choice behavior of passengers, which lays a theoretical basis for the design and transformation of platform facilities.

Dynamics Analysis of Rotating Cantilever Beams with Free End Mass

An improved modeling method for the dynamics analysis of rotating cantilever beams with free end mass is introduced. The proposed improved modeling method is based on the nonlinear Green strain theory in this study. By using the Hamilton principle and the Galerkin method, the discrete dynamic equations of the axial and chordwise motions are obtained. Meanwhile, the equations for free vibrations analysis of the rotating cantilever beam with free end mass are derived by introducing the equilibrium axial deformation into both axial and chordwise motions. Numerical simulations are performed to validate the proposed model, and the results are compared and discussed with the other modeling methods. The comparison shows that even a small free end mass has an important influence on the dynamic characteristics of the rotating beam. Furthermore, the influences of various parameters on the vibration frequencies and axial deformations of the rotating cantilever beams are analyzed, such as the angular speed, the free end mass to beam mass ratio, and the center body radius to beam length ratio. Under the same conditions, the influence of the free end mass on the variation in the first- and high-order frequencies with the increasing angular speed are different.