Total Thickness Ratio Research Articles

Analytical vibration of middle rotor of coaxial magnetic gear with complicated structure due to holes and screws

Coaxial magnetic gear is a cutting-edge technology introduced a few years ago. Its middle rotor is a rotating steel cylindrical shell with a variable array of holes that are filled by brass screws, hence it is such a complicated structure due to these holes. At first glance, it seems impossible to apply shear deformation theories to this unusual geometry, but for the first time, this article has introduced a novel mathematical methodology that creatively makes this possible. Consequently, an analytical formulation is presented for free vibration of this complicated structure, with no need to finite element software. The final aim is to extract natural frequencies and critical speeds in terms of different parameters. The formulation begins with the first-order shear deformation theory as the displacement field and continues with the Hamilton approach to gain governing equations of motion. Additionally, the effect of an external radial magnetic field is modeled by Maxwell’s relation. In the end, the Galerkin scheme is followed for discretization of the governing equations. This scheme is compared to an older article to guarantee its accuracy. Subsequently, the natural frequencies are estimated in terms of physical parameters of the rotor such as angle and number of holes, hole-thickness to total-thickness ratio, magnetic field and some other parameters. The mode shapes are also depicted for better interoperation of rotor’s behavior. The findings show that unlike geometric parameters (e.g., angle and number of holes), the radial magnetic field does not significantly affect the natural frequency.

Measurement of the Inner Macular Layers for Monitoring of Glaucoma: Confounding Effects of Age-Related Macular Degeneration

To investigate the confounding effect of nonexudative age-related macular degeneration (AMD), specifically drusen and outer retinal atrophy, on the architecture and automated segmentation of the inner retinal layers as measured with OCT. Observational cross-sectional study. Two hundred sixty-three consecutive eyes with nonexudative AMD were identified through a retrospective chart review. Exclusion criteria were a diagnosis of glaucoma or glaucoma suspect, other retinal pathology affecting the macula, axial length > 26.5 mm or spherical equivalent less than -6 diopters, any other optic nerve or neurologic disorders, or poor image quality. Drusen were automatically segmented on macular OCT B-scans with a publicly available and validated deep learning approach. Automated segmentation of the inner plexiform layer (IPL)/inner nuclear layer (INL) boundary was carried out with the device's proprietary software. Quality of segmentation of the IPL/INL boundary as a function of drusen size and presence of inner retinal layer displacement in the area of macular pathology (drusen or atrophy). One hundred twenty-five eyes (65 patients) met the inclusion criteria. Drusen size varied between 16 and 272 μm (mean, 118 μm). Automated segmentation had a 22% chance of failure if the drusen height was between 145 and 185 μm and was most likely to fail with drusen heights above 185 μm. When drusen height was normalized by total retinal thickness, segmentation failed 36% of the time when the drusen to total retinal thickness ratio was 0.45 or above. Images were likely to show displacement of inner retinal layers with drusen heights above 176 μm and a normalized drusen height ratio of 0.5 or higher. Eighty-seven percent of images with outer retinal atrophy displayed incorrect segmentation. Outer retinal diseases can alter the retinal topography and affect the segmentation accuracy of the inner retinal layers. Large drusen may cause segmentation error and compression of the inner macular layers. Geographic atrophy confounds automated segmentation in a high proportion of eyes. Clinicians should be cognizant of the effects of outer retinal disease on the inner retinal layer measurements when interpreting the results of macular OCT imaging in patients with glaucoma.

Tunable angle-selective optical transparency induced by photonic topological transition in Dirac semimetals-based hyperbolic metamaterials.

The tunable angle-selective transparency of hyperbolic metamaterials consisting of various multilayers of Dirac semimetal and dielectric materials are theoretically and numerically studied in the terahertz range. Three stack configurations are considered: alternating, sandwiched, and disordered. It is found that the proposed structures exhibit strong optical angular selectivity induced by photonic topological transition for transverse magnetic waves. Interestingly, the topological transition frequency can be flexibly modulated by changing the Fermi energy, temperature, and the releasing time of the Dirac semimetal, as well as the thickness ratio of the dielectric and semimetal layers. It is also noticed that the angular optical transparency properties are independent of the order of the proposed structure even in alternating/disordered/random configurations if the total thickness ratio of the semimetal to dielectric are the same, which makes the properties particularly easy to realize experimentally. The proposed hyperbolic metamaterial structures present a promising opportunity for wavefront engineering, offering crucial properties for applications in private screens, optical detectors, and light manipulation.

Static stability and vibration behavior of graphene platelets reinforced porous sandwich cylindrical panel under non-uniform edge loads using semi-analytical approach

Buckling and free vibration characteristics of sandwich cylindrical panel with porous functionally graded graphene platelets (FG-GPL) core are investigated using semi-analytical approach. The effective mechanical properties are obtained by using properties of open cell foams and Halpin–Tsai micro mechanical model. The governing equations are obtained using Hamilton’s principle, considering a higher order theory to account the transverse shear and solved by Galerkin’s method. Effects of nature of in-plane edge load, distribution of porosity and GPL, porosity coefficient, GPL loading, core to total thickness ratio are analyzed in detail. It is shown that for a FG-GPL core sandwich cylindrical panel with high core thickness, even at higher amount of porosity the buckling resistance and free vibration frequency can be improved by properly tailoring both the GPL and porosity distribution. Moreover, a much variation in buckling and free vibration response with the type of in plane loading is observed and evident mode shape changes are observed with increase in aspect ratio. The cylindrical sandwich panel having a core with D-PD porosity variation and I-GPL-P pattern of GPL distribution has the maximum buckling resistance and free vibration frequency value.

Vertical Variability in Bark Hydrology for Two Coniferous Tree Species

As the outermost layer of stems and branches, bark is exposed to the influence of atmospheric conditions, i.e., to changes in the air’s relative humidity and wetting during storms. The bark is involved in water interception by tree canopies and stemflow generation, but bark–water relations are often overlooked in ecohydrological research and insufficiently understood. Relative to other canopy ecohydrological processes, little is known about vertical variation in bark properties and their effect on bark hydrology. Thus, the objective of this study was to analyze changes in physical properties (thickness, outer to total bark thickness ratio, density, and porosity) and hydrology (bark absorbability, bark water storage capacity, and hygroscopicity) vertically along stems of Norway spruce [Picea abies (L.) Karst.] and silver fir (Abies alba Mill.) trees. Our null hypotheses were that bark hydrology is constant both with tree height and across measured physical bark properties. We found that bark thickness and the ratio of outer-to-total bark thickness decreased with tree height for both species, and this was accompanied by an increase in the bark water storage capacity. In contrast, the bark’s density, porosity, and hygroscopicity remained relatively constant along stems. These results inform ecohydrological theory on water storage capacity, stemflow initiation, and the connection between the canopy water balance and organisms that colonize bark surfaces.

Dynamic stability of the double-bonded annular nanocomposite sandwich microplate on viscoelastic foundation

In this research, the dynamic stability of the double-bonded annular sandwich microplate is investigated. Face sheets are made from composite materials reinforced by carbon nanotubes in which mechanical properties are obtained by the extended rule of the mixture. Also, the core layer is made from a honeycomb aluminum which is defined by the geometric parameters of the unit cell and mechanical properties of the virgin core material. The equations of motion are derived from Hamilton’s principle and solved by the differential quadrature method (DQM) based on higher order shear deformation theory (HSDT) and modified couple stress theory (MCST). The results are compared with the obtained results by the other literature to examine the accuracy of the present formulation. The dynamic stability of the double-bonded annular sandwich microplate with hexagonal honeycomb core including variations of core thickness, inclined angle, and aspect ratio of the unit cell are discussed. Also, the effects of motion direction of the structure, viscoelastic foundation, material length scale parameter, volume fractions of CNTs in face sheets, and the core thickness to total thickness ratio on dynamic instability region are presented.

Structural behavior of FRP grid reinforced geopolymer concrete sandwich wall panels subjected to concentric axial loading

A new type of precast concrete sandwich wall panel, consisting of two basalt fiber reinforced polymer (FRP) reinforced geopolymer concrete wythes and an insulation layer, which are connected with hollow tubular glass FRP connectors, is studied in this paper. Ten sandwich wall panels were prefabricated and subjected to concentric axial loading. The primary test variables included slenderness ratio of the wall panel (i.e., the effective height to total sectional thickness ratio), longitudinal spacing of connectors, and the ratio of the wythe thickness to the insulation layer thickness of the wall panel. The load–deflection relationships, failure modes, and load–strain relationships were carefully investigated. All the wall panels failed by crushing of concrete. The connectors were subjected to axial force, transverse shear and bending in order to allow two wythes to deform together. The axial load capacity of the wall panel was reduced by 26% as the slenderness ratio varied from 8 to 17. The spacing of FRP connectors was found to have a marginal impact on the axial load capacity because of the existence of capping beams at the end of panels. An increase in the insulation thickness while keeping the wythe thickness constant resulted in a significant rise in the ultimate axial load in the case of panels having a higher slenderness ratio. A theoretical second-order analysis was performed to predict the ultimate axial load of equivalently assumed solid wall panels, and the predicted results were compared with the experimental ones.

On the wave propagation in a multi-hybrid nanocomposite doubly curved panel

In the current report, characteristics of the propagated waves in a multi-hybrid nanocomposite (MHC) reinforced doubly curved panel is investigated. First-order shear deformable theory (FSDT) is applied to formulate the stress-strain relations. The rule of mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite panel. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of an analytical method. Afterward, a parametric study is carried out to investigate the effects of the (carbon nanotubes’) CNTs' weight fraction, various MHC patterns, small radius to total thickness ratio, and carbon fibers angel on the phase velocity of the MHC reinforced panel. The results show that the sensitivity of the phase velocity of the MHC panel to the and different face sheet patterns can decrease when we consider the core of the panel much thicker. Another consequence is that the highest and lowest phase velocity in all range of wave numbers could be seen for the MHC reinforced doubly carved panel with pattern 3 and 1, respectively. It is also observed that as the weight fraction of the CNTs rises, the sensitivity of the phase velocity to wavenumber and fibers angle will decrease. The useful suggestion of this study is that for designing a structure, we should have an attention to the pattern and higher value of the wavenumber, simultaneously. The presented study outputs can be used in ultrasonic inspection techniques and structural health monitoring.

Wave propagation simulation in an electrically open shell reinforced with multi-phase nanocomposites

Wave propagation simulation in a multi-hybrid nanocomposite (MHC)-reinforced doubly curved open shell covered with piezoelectric actuator is examined for the first time. The third-order shear deformation theory (third-order SDT) is applied to formulate the stress–strain relations. Rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constants of the MHC-reinforced open shell. By employing Hamilton’s principle, the governing equations of the structure are derived. Via the compatibility rule, the bonding between the smart layer and sandwich open shell is modeled. Also, with the aid of Maxwell's equation, the mechanics of the piezoelectric layer are formulated. Afterward, a parametric study is carried out to investigate the effects of the CNTs’ weight fraction, various FG face sheet patterns, small radius to total thickness ratio, the thickness of the smart layer, externally applied voltage, and carbon fiber angle on the phase velocity of the MHC-reinforced open shell. Another necessary consequence is that as the externally applied voltage to the piezoelectric layer of the smart open shell increases, there will be seen an enhancement on the phase velocity or wave response of the system and without a doubt this issue is much more substantial at the lower wave number. It is also observed that when the applied voltage is more than zero, we can find a range for the fiber angle that these values are the critical fiber angle and this critical range will expand by increasing the external electrical load. The useful suggestion of this study is that for designing the structure, we should attention to the FG pattern and higher value of the wavenumber, simultaneously. The presented study outputs can be used in ultrasonic inspection techniques and structural health monitoring.

On the wave propagation of the multi-scale hybrid nanocomposite doubly curved viscoelastic panel

In this paper, wave propagation analysis of multi-hybrid nanocomposite (MHC) reinforced doubly curved panel embedded in the viscoelastic foundation is carried out. Higher-order shear deformable theory (HSDT) is utilized to express the displacement kinematics. The rule of mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the MHC reinforced doubly curved panel. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of an analytical method. Afterward, a parametric study is carried out to investigate the effects of the viscoelastic foundation, carbon nanotubes’ (CNTs’) weight fraction, various MHC patterns, radius to total thickness ratio, and carbon fibers angel on the phase velocity of the MHC reinforced doubly curved panel in the viscoelastic medium. The results show that, by considering the viscous parameter, the relation between wavenumber and phase velocity changes from exponential increase to logarithmic boost. A useful suggestion of this research is that the effects of fiber angel and damping parameter on the phase velocity of a doubly curved panel are hardly dependent on the wavenumber. The presented study outputs can be used in ultrasonic inspection techniques and structural health monitoring.

On the phase velocity simulation of the multi curved viscoelastic system via an exact solution framework

The analysis of the wave propagation behavior of a sandwich structure with a soft core and multi-hybrid nanocomposite (MHC) face sheets is carried out in the framework of the higher-order shear deformation theory (HSDT). In order to take into account the viscoelastic influence, the Kelvin-Voight model is presented. In this paper, the constituent material of the core is made of an epoxy matrix which is reinforced by both macro- and nano-size reinforcements, namely carbon fiber (CF) and carbon nanotube (CNT). The effective material properties like Young's modulus or density are derived utilizing a micromechanical scheme incorporated with the Halpin–Tsai model. Then, on the basis of an energy-based Hamiltonian approach, the equations of motion are derived. The detailed parametric study is conducted, focusing on the combined effects of the viscoelastic foundation, CNT' weight fraction, core to total thickness ratio, small radius to total thickness ratio, and carbon fiber angle on the wave propagation behavior of sandwich structure. The results show that as well as increasing the phase velocity of the sandwich structure by increasing the wave number, this influence will be much more effective by increasing the damping factor. It is also observed that there is a critical value for the viscoelastic foundation that the relation between wave number and phase velocity will change from direct to indirect. The presented study outputs can be used in ultrasonic inspection techniques and structural health monitoring.

A computational framework for propagated waves in a sandwich doubly curved nanocomposite panel

In the current report, characteristics of the propagated wave in a sandwich structure with a soft core and multi-hybrid nanocomposite (MHC) face sheets are investigated. The higher-order shear deformable theory (HSDT) is applied to formulate the stresses and strains. Rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the multi-hybrid nanocomposite face sheets of the sandwich panel. By employing Hamilton’s principle, the governing equations of the structure are derived. Via the compatibility rule, the bonding between the composite layers and a soft core is modeled. Afterward, a parametric study is carried out to investigate the effects of the CNTs' weight fraction, core to total thickness ratio, various FG face sheet patterns, small radius to total thickness ratio, and carbon fiber angel on the phase velocity of the FML panel. The results show that the sensitivity of the phase velocity of the FML panel to the $${W}_{\rm{CNT}}$$ and different FG face sheet patterns can decrease when we consider the core of the panel more much thicker. It is also observed that the effects of fiber angel and core to total thickness ratio on the phase velocity of the FML panel are hardly dependent on the wavenumber. The presented study outputs can be used in ultrasonic inspection techniques and structural health monitoring.

Analytical solution and statistical analysis of buckling capacity of sandwich plates with uniform and non-uniform porous core reinforced with graphene nanoplatelets

This paper presents a robust and accurate analytical solution based on the refined higher-order shear deformation theory for establishing the buckling capacity of a series of simply-supported sandwich plates. Each sandwich plate consists of an open-cell metal foam core with various pore distributions and two metal face sheets. Cores with and without GNP-reinforcements are considered. Three different distributions of porosity are considered for the core (i.e., uniform and two different non-uniform distributions along the thickness of the core). The effective properties of the porous cores are estimated by employing the modified Halpin-Tsai micromechanical model and the rule of mixture. The governing differential equations are solved analytically using the Navier method. Subsequently, the Box-Behnken design (BBD) statistical method, which is a subset of the response surface methodology (RSM), is employed to investigate the simultaneous effect of the input variables (i.e., porosity coefficient, the core to total thickness ratio and the weight fraction of graphene nanoplatelets (GNPs)) on the buckling capacity of the sandwich plates. This is followed by the development of a set of simple and practical equations for evaluating the critical buckling capacity of the sandwich plates as a function of the input variables.

Diagnostic Performance of 3-Dimensional Thickness of the Endothelium–Descemet Complex in Fuchs’ Endothelial Cell Corneal Dystrophy

To describe the diagnostic accuracy of 3-dimensional (3D) endothelium-Descemet's membrane complex thickness (En-DMT) in Fuchs' endothelial corneal dystrophy (FECD) and determine its potential role as an objective index of disease severity. Observational case-control study. One hundred four eyes of 79 participants (64 eyes of 41 FECD patients and 40 eyes of 38 healthy controls). All participants received high-definition OCT imaging (Envisu R2210; Bioptigen, Buffalo Grove, IL). Fuchs' endothelial corneal dystrophy was classified clinically into early-stage (without edema) and late-stage (with edema) disease. Automatic and manual segmentation of corneal layers was performed using a custom-built segmental tomography algorithm to generate 3D maps of total corneal thickness (TCT) and En-DMT of the central 6-mm cornea. Regional En-DMT, regional TCT, and central-to-peripheral total corneal thickness ratio (CPTR) were evaluated and correlated to the clinical severity of FECD. Intraclass correlation coefficients (ICCs) and Bland-Altman plots were used to assess the reliability of the repeated measurements in all eyes. Central-to-peripheral total corneal thickness ratio and average En-DMT and TCT of central, paracentral, and peripheral regions. In FECD, a significant increase in En-DMT, CPTR, and TCT was found compared to controls (P < 0.001). For identifying FECD, average En-DMT of paracentral and peripheral regions achieved 94% sensitivity and 100% specificity (cutoffs, 19 μm and 20 μm, respectively), whereas CPTR showed 94% sensitivity with a 73% specificity (cutoff, 0.97). Regarding early-stage FECD, average En-DMT of central zones achieved 92% sensitivity and 97% specificity (cutoff, 18 μm), whereas CPTR showed 90% sensitivity and 88% specificity (cutoff, 0.97). The average En-DMT of central, paracentral, and peripheral regions was correlated highly with FECD clinical stage (Spearman's ρ= 0.813, 0.793, and 0.721, respectively; all P < 0.001), compared with CPTR and mean TCT of paracentral zones (0.672 and 0.481, respectively; P < 0.001). The ICC values ranged from 0.98 (En-DMT) to 0.99 (TCT) with a good agreement between the automatic and manual measurements. Regional 3D En-DMT is a novel diagnostic tool of FECD that can be used to quantify the disease severity with excellent reliability.

Study on the pack rolling process factor of Ti-6Al-4V alloy

Pack rolling method is preferred to conventional rolling method to process thin sheets or foils out of titanium alloys because of their relatively narrow processing window and possible surface contamination during the elevated temperature processing. In this paper, the core sheets of 5mm thick with equiaxed alpha + transformed beta structure were encapsulated in mild steel cover material and hot rolled in a four high reversing hot rolling mill. The following results were obtained; The optimal pack assembly condition and pack rolling process factor were produced. The effect that the difference in deformation resistance of cover material and core material in pack rolling has been considered. The S45C mild steel is the most suitable for the cover material. The cover material is subjected to the same rolling process as the core material when the initial core and total thickness ratio is 0.3. The reduction in pack rolling should be selected in the range of 20% to 25% to produce flat sheet. Tensile properties of the pack rolled sheet are isotropic in both RD and TD rolling direction which meet the requirements of the standard AMS4911.

Vibration analysis of a fluid conveying sandwich cylindrical shell with a soft core

The free vibrations of a circular cylindrical sandwich shell with a flexible core containing a flowing fluid are investigated. Within the framework of the higher-order sandwich panel theory which assumes a variable displacement through the thickness, the core flexibility is taken into account. Using Hamilton’s extended principle, for an inviscid, non-rotational, laminar and incompressible flow, via the potential flow theory, the governing equations of the coupled structure and fluid system are derived. The eigenvalue problem’s equations are found by implementing a modal expansion method which has been validated by the existing results and is found to be accurate. The effect of the axial flow velocity, circumferential wave number, core to total thickness ratio and total thickness to mean radius ratio on the natural frequencies are investigated. It is found that taking into account the core's flexibility results in lower frequency values. The study shows that, unlike in dry shells, increasing the ratio of core thickness to total thickness reduces the natural frequencies monotonically in wet shells. For a constant total shell thickness, the critical velocity of the fluid decreases with increases in core thickness.

New analytical approach for buckling of composite sandwich pipes with iso-grid core under uniform external lateral pressure

In this paper, a new analytical approach is developed for buckling of composite sandwich pipes with iso-grid core under uniform external lateral pressure. Firstly, the stiffness contributions of iso-grid cores are evaluated through the new force and moment effect analysis. Then, iso-grid core is transformed into a solid pipe, as the middle layer of the sandwich pipe. The outer, inner, and middle pipes are transformed into an equivalent single-walled pipe. Therefore, composite sandwich pipe with iso-grid core is equalized with a single-walled pipe of the same stiffness. The Rayleigh–Ritz energy method is used to calculate the critical buckling pressure of the composite sandwich pipes with iso-grid cores. The efficiency and accuracy of the presented approach are confirmed by comparing the analytical solutions with finite element results obtained from ABAQUS and other works, showing a good agreement with each other. A parametric study is then carried out to investigate the effect of the scale of the structure, outer and inner pipes ply stacking sequence, radius to total thickness ratio, stiffener to outer and inner pipe thicknesses ratio, and stiffener angle on the buckling of sandwich pipes. Finally, applications of the present approach were demonstrated for designing of tending toward constant various structural applications such as offshore pipelines.

Aeroelastic analysis of sandwich cylinder with fractional viscoelastic core described by Zener model

The flutter of a sandwich circular cylindrical shell, with the fractional order Zener constitutive relationship is studied. Based on the Donnell–Mushtari theory for facing layers and first order shear deformation theory for viscoelastic layer, the structural formulation of the sandwich cylinder is obtained and the aerodynamic pressure due to the fluid flow is evaluated by piston theory. The Lagrange method along with Rayleigh–Ritz method is implemented to derive and solve the governing equations. To determine the stability margin of three-layered cylinder the obtained set of ordinary differential equations are solved. In the following, the effects of variation of the geometric parameters such as length to radius ratio, radius to total thickness ratio and thickness of core layer, constraining layer and mechanical properties of viscoelastic material on flutter boundaries of sandwich cylindrical shell are investigated.

Dynamic analysis of isotropic sandwich cylindrical shell with fractional viscoelastic core using Rayleigh–Ritz method

This paper presents the dynamic behavior of a sandwich circular cylindrical shell with a constrained fractional viscoelastic layer. Based on the Donnell-Moshtari theory, the structural formulation of the cylinder is obtained using the Lagrange method and the Rayleigh–Ritz method is implemented to solve the discretized governing equations. To describe the mechanical properties of the viscoelastic layer, the fractional order standard solid model is applied. The effects of variation of the governing parameters such as the length to radius ratio, the radius to total thickness ratio, ratio of core to facing thickness, fractional order parameter and the ratio of non-relaxed to relaxed modulus on the frequency and loss factor of sandwich cylindrical shells are investigated and some conclusions are outlined.

Dynamic structural response of laminated glass panels to blast loading

This paper presents an analytical model of ‘fully-clamped’ laminated glass panel subjected to pulse-pressure loading in an air-blast. The dynamic structural response of the laminated glass panel is decoupled into two distinct phases of motion: phase I is controlled by the elastic deformation of the brittle glass plies whilst phase II is dominated by the large inelastic deformation of the Polyvinyl Butyral (PVB) interlayer. Transition between the two phases follows the large scale fragmentation of the glass plies – this will be captured through a stress-based damage criterion. Following the work of others, the PVB interlayer is idealised as a rigid-perfectly plastic material which allows its large inelastic response to be modelled within the constitutive framework of limit analysis. An interactive yield criterion is adopted to capture the simultaneous influence of bending and membrane stretch that governs plastic flow in the interlayer. Predictions by the analytical model are validated against existing experimental data and they will be shown to be in good agreement. Parametric studies were performed to elucidate the effects of total mass (per unit area) and thickness ratio on the maximum transverse deflection. The efficacy of Youngdahl’s technique on desensitising pulse shape effects is also studied.