Circular Disk Research Articles

Axisymmetric torsion of rigid disc parallel to penny shaped crack at the interface of layer bonded by two orthotropic half spaces

Two half-spaces and a layer of finite height of linear elastic orthotropic medium containing a penny-shaped crack and a circular rigid disk are considered such that the crack surface is parallel to the rigid disk, where both are situated at two different interfaces of layer and half-space and perpendicular to the axis of symmetry. The rigid disk is agitated by an axisymmetric torsion. The equations of equilibrium are solved with the use of Hankel’s integral transform method. Then, the tangential displacement components and shear stress components are determined. With the help of mixed-type boundary conditions, a system of integral equations is derived. After that, by utilizing a trial solution, these integral equations are transformed into a pair of simultaneous Fredholm integral equations of the second kind. The numerical results of the Fredholm integral equations are evaluated by converting it into a system of algebraic equations to interpret the physical quantity, like the stress intensity factor (SIF), which is demonstrated graphically. The obtained results are compared to the previously published article to ensure its accuracy.

Improved dynamic analysis for plane elasticity problems with a boundary meshfree method and distributed sources

In this paper, we present an improved dynamic analysis method to address plane elasticity problems. Distributed sources are employed in a boundary-free mesh-based approach known as Boundary Distributed Source (BDS). This method, which builds upon a modified Method of Fundamental Solutions (MFS), aims to eliminate singularities without the reliance on fictitious boundaries. Distributed sources are strategically positioned directly on the real boundary, centered over disks. The method's efficiency and simplicity are highlighted by its ability to operate without the need for precise data concerning adjacent points. The dual reciprocity method (DRM) is utilized to approximate the non-homogeneous inertial term. Furthermore, the present formulation investigates several factors that influence the convergence of the proposed method, including the number of collocation points, internal points, the radius of the circular disk, and the time step size. Based on the numerical results, it is evident that the method exhibits remarkable accuracy and efficiency when applied to plane elasticity problems including forced, harmonic, and free analyses. As compared to conventional numerical methods for dynamic analysis, the method outperforms in both accuracy and convergence rate.

Design and experimental analysis of magneto-rheological damper featuring a labyrinthic dual-channel valve

For the sake of improving the damping performance of the cab suspension system, the MR damper featuring the labyrinthic dual-channel valve (LDCV-MRD for short) is proposed in this paper, which is composed of a mixture of circular channel, circular disk channel and circular tube channel. The LDCV-MRD is designed structurally and the magnetic circuit is analyzed. The output damping force mathematical model is established, and the coil’s number of turns is computed. The magnetic field in the damping channel of LDCV-MRD is simulated and analyzed. The processed and fabricated LDCV-MRD is tested, and the experimental results are compared and analyzed with the simulation results. The results show that the simulated values of the maximum damping force and the adjustable coefficient fit well with the experimental results. The peak output damping force of the experiment achieves 21 008 N. The adjustable coefficient reaches about 5.61, when the input current gets to 2 A.

Modal analysis of a submerged elastic disk: A hypersingular integral equation approach

A method based on the hypersingular integral equation approach and the modal analysis is presented to consider the effects of the motion of a submerged elastic disk on the incoming waves. Initially, the governing boundary value problem is reduced to a two-dimensional integral equation with a hypersingular kernel. This integral equation is further reduced to a one-dimensional Fredholm integral equation of the second kind with the help of Fourier series expansions and a newly defined function. As a part of modal analysis, eigenfunction expansion based on natural modes of structural motion is considered to describe the motion of a thin circular elastic disk. Physical quantities, such as hydrodynamic force, added mass, damping coefficient, and surface elevation, are numerically evaluated. The computed numerical results are verified by comparing them with those for the rigid disk horizontally submerged in deep water. Apart from this, as a part of the analytical verification of our present analysis, the reciprocity relation has been included. The effects of different parameters (disk's rigidity, radius, submergence depth, and mode of vibrations) on the aforementioned physical quantities have been studied. The maximum hydrodynamic force occurs around Ka = 0.5, while the maximum added mass and damping coefficient occur around the wavenumber Ka = 0.3 and Ka = 0.5, respectively. The peaks of the hydrodynamic force and free surface elevation become sharper with the increasing values of the disk's size. The numerical results emphasize that the wave focusing can be controlled by changing the submergence depth, size, and rigidity of the disk.

Electrostatic conductive disc singularity resolved

The conventional electrostatic solutions for two-dimensional (2D) electrodes possess edge singularities for the surface charge density σ and the normal component of the electric field En. These singularities are generally non-physical because they admit infinite gradients of the concentration of free charge carriers. In particular, they are unacceptable in the studies of the local field sensitive effects, such as the electric breakdown and the ferroelectric domain reversal. We claim that account for diffusion of free charge carriers leads to the disappearance of the edge singularities. This generalization occurs consistently within the same basic concept of conduction. Specifically, we consider the case of U-biased circular disc electrode of radius a. Account for diffusion leads here to a strongly nonlinear integral 2D equation for the electrostatic potential φ(r). Numerical solution of this equation shows that the law σ(a)∝U2/a takes place. Outside a close vicinity of the disc edge, we stay close to the conventional electrostatic solution for φ and σ.

Diffraction of a pseudo nondiffracting Bessel beam by a circular perfect electromagnetic conductor disk.

This study examined the diffraction of a pseudo nondiffracting Bessel beam by a perfect electromagnetic disk. The geometric optics beam waves were written from the geometry of the problem and related boundary conditions. The diffracted beam waves were derived by utilizing the relation between geometric optics and diffracted waves at the transition boundaries, considering the high frequency asymptotic expression of the scattered wave. The uniform scattered beam waves were expressed in terms of Fresnel functions with the uniform geometrical theory of the diffraction method. Thus, finite magnitudes were read at the transition boundaries. Finally, the obtained uniform expressions were investigated numerically for different groups of parameters.

Analysis of elastic stresses in rotating cylinders made of Titanium and Bronze materials

ABSTRACT This study analytically investigated elastic stress distribution in rotating cylinders made of Titanium and Bronze material. The Von Mises yield criterion was applied under the assumption of plane strain conditions. The modelling process considered that the disc material remains unaffected by temperature variations. The thermal stresses of a thin circular disc are being studied. The determined temperatures are close to the maximum and minimum temperatures at which the material can work. The numerical analysis is one, and the results are depicted as a whole with graphs. This study also examined the changes in the temperature distribution on the stress distribution. At the end of the study, it was determined that the stresses occurring in the titanium material cylinder were higher than the bronze disc, and the pressures were inversely proportional to the increase in the grading parameter in the cylinders. Additionally, the ANSYS finite element program was utilised for validation.

Cytotoxicity Evaluation of Various Composite Resin Materials: An In Vitro Study.

Aim This study aimed to determine and comparethe cytotoxicity of light-cured composite resin (Enlight light cure composite (Ormco, Glendora, California, USA)), light-cured acrylic resin (Orthocryl LC (Dentaurum, Ispringen, Germany)), and the self-cure acrylic (DPI RR cold cure acrylic (Dental Products of India, Bombay Burmah Trading Corporation Ltd., Mumbai, India)) material and to determine which component is best to be used for the purpose of nasal stent fabrication in the nasoalveolar molding (NAM) technique for cleft therapy. Methods Circular discs made from Enlight light cure composite, Orthocryl LC, and self-cure acrylic were submerged for 24 hours in gingival fibroblast media (three discs of each material) and control medium (three discs of each material) that were both contained in plates. After analyzing the optical densities of the plates, the cytotoxicity of the products was assessed by measuring cell viability using the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay. The compiled data was analyzed using IBM SPSS Statistics for Windows, V. 23.0 (IBM Corp., Armonk, NY). The normality of the data was evaluated using the Shapiro-Wilk test.One-way analysis of variance (ANOVA) and pairwise comparison made with Tukey's honestly significant difference (HSD) post hoc test with a significance level (p) of 0.05 were considered. Results The percentage of cell viability was between 80% and 150%. A significantmean difference was noted in the cell viability between the three groups (p=0.009). High mean cell viability was seen in Orthocryl LC. However, there was no significant mean difference between Orthocryl LC and Enlight light cure composite material (p=0.854). Conclusion Both Orthocryl LC and Enlight light cure composite materials are less cytotoxic when compared to the self-cure acrylic resin material and can be used to fabricate the nasal stent component for infants with cleft defects, undergoing NAM procedure.

On the sound field of a resilient elliptical disk in an infinite baffle.

A resilient elliptical disk has zero mass and stiffness and is driven by a uniform pressure distribution rather than uniform velocity as would be the case for a rigid disk. It can represent the diffraction of a plane wave through an elliptical aperture in an infinite rigid screen of zero thickness as well as provide an idealized model of a loudspeaker of the electrostatic or planar magnetic type. Using the Fourier (Hankel) Green's function in cylindrical coordinates, together with the monopole Kirchhoff-Helmholtz boundary integral, rigorous analytical formulas are derived for calculating the surface velocity distribution, radiation admittance, on-axis pressure, and directivity pattern of an elliptical resilient disk in an infinite baffle and these are plotted over a range of normalized frequencies. The directivity is compared with that of a resilient circular disk and asymptotic low-frequency approximations are derived for the radiation resistance, reactance, and on-axis pressure.

Fracture toughness determination for epoxy-based polymer concrete mixtures: Applicability of different rectangular beam and circular disc specimens

The purpose of this study was to examine the potential impact of the testing procedure, the shape of the test sample, loading method and sample size on the KIc value of polymer concrete (PC) materials. The research involved experimental investigations using five different testing techniques and specimen types, namely the single edge notched beam (SENB), short bend beam (SBB), semi-circular bend (SCB), edge notch disc bend (ENDB), and center cracked Brazilian disc (CCBD). A typical PC mixture made of mineral silicious aggregate, ML506 epoxy resin, chopped E-glass, and foundry sand filler. Despite the difference in the shape and loading type of the tested samples, the KIc data obtained from all groups of specimens are in good agreement with together and with the SENB proposed by RILEM. Depending on the test type, the KIc value varied from 1.43 to 1.74 MPa.m0.5 and the discrepancy between the data was mainly attributed to the type of loading (compression or bending) and the crack type (center crack or edge crack). The T-stress affects the fracture toughness for different testing samples and configurations. The lowest fracture toughness corresponds to the CCBD specimen (the center cracked disc loaded diametrically). The other test samples with edge cracks and loaded by a three-point bend setup showed KIc = 1.7 - 1.74 MPa.m0.5. Moreover, the fracture toughness data for PC mixtures can be achieved by utilizing sub-sized samples like SBB (for smaller amounts of PC material) instead of larger beam samples (i.e., SENB).

Isotropic elasticity of dilatational conical inclusion. An analytical approach

In this article, the analytical solution for the isotropic elasticity problem for the cone-shaped inclusion with dilatational eigenstrain in an infinite medium is given. The conical inclusion is modeled by dilatational infinitesimally thin circular disks distributed continuously along the cone z-axis with the radii of the disks being proportional to z-coordinate. The displacements, strains, and stresses of the conical inclusion are given in spherical coordinates with the origin in the cone-apex in the form of the series with Legendre polynomials. The maps of the displacements and the stresses are presented. A comparison of the displacements of the conical inclusion with the displacements of the finite cylindrical and hemispherical inclusions is provided. It is also shown, as expected, that the energy of the dilatational inclusion does not depend on its shape. In Discussion section, the specific features of an “hourglass” dipole inclusion consisting of two conical inclusions with different sign eigenstrains are demonstrated.

Study on fracture characteristics and mechanisms of red sandstone under high-voltage pulse discharge

To investigate the influences of geometrical size and discharge voltage of the pulse discharge equipment on the fracture characteristics and mechanisms of sandstone under high-voltage pulses, a series of experiments was conducted using a high-voltage pulse discharge device on sandstone circular disc specimens of sandstone with a thickness of 10 mm. These experiments covered a range of disc diameters ranging from 50 mm to 142 mm and discharge voltages from 15 kV to 40 kV. Through these experiments, the fracture characteristics of sandstone at both macroscopic and microscopic levels were investigated. In the experiments, a quantitative analysis of surface fracture was undertaken based on fracture density and fractal damage. Additionally, using the principle of energy equivalence, numerical simulation methods were used to study the damage evolution process in sandstone. The research results indicate that the formation and distribution of fractures in the sandstone specimens are significantly affected by geometrical size and discharge voltage. By analyzing the interaction between stress waves and fracture propagation, combined with indoor experimental results, the fracture mechanism was revealed. The high temperature and shock wave generated by the plasma channel leads to the crushing zone near the electrode, while the circumferential tensile component of the stress wave can result in radial fractures, and the reflected tensile wave leads to circumferential and radial fractures near the boundary.

Thermal constriction resistance of a functionally graded material plate heated by a circular disc heat source on one face and isothermal on the opposite face

This article presents a study of the thermal constriction phenomenon for the Functionally Graded Materials (FGM). The studied configuration is that of a plate subjected to a circular disc heat source. The study is carried out under steady-state conditions, considering axisymmetric heat conduction. An analytical solution is developed to calculate the temperature and thermal constriction resistance. Thermal conductivity, which varies as a function of position in the depth direction of the plate, is modeled by a law that allows to consider several possible evolutions (slow, rapid or linear). The thermal constriction resistance resulting from these thermal conductivity evolutions is studied and analyzed as a function of the geometric and physics parameters of the problem. As a verification, we compared the proposed solution with the same configuration but in the asymptotic case of homogeneous conductivity. Both solutions lead to the same result. In a second step, a homogeneous apparent thermal conductivity, which would be that measured by conventional methods, is introduced. It is shown that the calculation of thermal constriction resistance using a homogeneous apparent thermal conductivity differs from that of a calculation using the full developed analytical solution. This difference is small in the case of very thin plates but becomes very significant with increasing plate thickness.

Mechanical and fracture characteristics in center cracked circular discs of coal specimens with different sizes: An experimental investigation

The propagation of cracks on a small scale can result in dynamic disasters, such as rock bursts induced by large-scale fractures in coal seams. To gain insights into the mechanism of fracture-induced disasters in deep coal seams, this study investigates the micro-process and size effect of crack propagation in coal specimens featuring different sizes of center-crack circular discs (CCCD). We conducted Brazilian splitting tests on coal samples with varying dimensions and employed acoustic emission (AE) and digital image correlation (DIC) techniques to quantitatively describe the crack propagation process. Additionally, coal specimens of different diameters were compared for the size effect characteristics of different fracture parameters during the tensile failure process. The results show that as the specimen size increases, quasi-brittle failure characteristics become pronounced, tensile strength gradually decreases and stabilizes, while fracture toughness and fracture process zone length gradually increase and tend to stabilize. The macroscopic cracks in the coal specimens generally extend from the centre of the specimen to both ends along the precracks. Large energy events are mainly concentrated at the lower end of the precracks. As coal specimen size increases, the number of AE events decreases, while the proportion of large energy events gradually increases, and the critical crack opening quantity exhibits a linear increase with specimen size. By conducting the fracture size effect experiment on coal specimens, we extend the relevant mechanical parameters from laboratory-scale tests to field engineering scales. This provides fundamental parameters for the analysis of large-scale fracture process of in-situ coal based on fracture mechanics.

Axisymmetric Stokes flow of a spherical droplet or slip particle in the presence of a circular disk

This article deals with the axisymmetric flow of a Newtonian fluid droplet moving along the axis of a thin circular disk under the conditions of a low Reynolds number in the quasi-steady limit. The system is immersed in a second Newtonian fluid. With the same geometry, the motion of a slip spherical particle is treated also. Basic solutions are constructed in cylindrical and spherical coordinates according to the appropriate flow region. A combined analytic-numerical solution procedure in conjunction with a dual integral equation is used. Numerical results show that the normalized drag force coefficient acting on the droplet/ slip particle is obtained with good convergence for various values of viscosity ratio, slip parameter, and clearance parameter. The findings demonstrate that the results of the drag coefficient are in good agreement with the limiting cases available in the literature.

Fracture analysis of Brazilian circular hole disk under mixed mode loading

The paper presents an investigation into a Brazilian disk specimen featuring a concentric circular hole, accompanied by two internal edge radial cracks. By introducing rotations of the cracks relative to the vertical axis, a combination of fracture modes I and II is induced. Employing the finite element method, we compute stress intensity factors related to fracture modes I and II, alongside T-stresses, while varying geometric parameters such as inner and outer diameters, crack length-to-ring width ratio, and crack inclination angle. Experimental analyses of ebonite's fracture toughness in the mixed mode are conducted, subjecting samples to static loading until complete failure. Each test provides the angle at which crack initiation occurs and the corresponding critical load. Three distinct fracture criteria - the generalized maximum tangential stress criterion (GMTS), extended maximum tangential strain criterion (EMTSN), and generalized strain energy density (GSED) criterion - are employed to predict fracture direction and critical load. The outcomes exhibit good correspondence between experimental critical loads and theoretical predictions.

Circular disk solar absorber heater design for industrial heaters based on Fe2O3–Si structure

Industrial heaters nowadays work on renewable energy concepts and one of the important green energy sources is solar energy and we have used solar energy to design industrial heaters. The solar absorber converts the solar energy into heat which is used for industrial heaters. We developed a new solar absorber construction with three different layers by using different materials for each layer construction. Aluminium (Al) is for the top (resonator) layer, iron (III) oxide (Fe2O3) is for the middle (substrate), and silicon is used in the ground (based) layer respectively. A thin graphene layer is constructed between the Al resonator and the Fe2O3 substrate sections to develop better absorption by this design. In the wavelength range (μm) of 1.86 and 3, the explored absorption rate is 95.43 % with a 1740 nm bandwidth. The absorption rate performs above 97 % (97.23 %) at a 540 nm bandwidth with a wavelength (μm) difference between 1.96 and 2.5. The overall absorption for design explores 91.23 % (greater than 90 %) with a 2800 nm bandwidth range by the wavelength contribution from 0.2 to 3 μm. To highlight the explored amounts in variation, the four high wavelengths (in micrometers) are selected with λ1 = 0.45, λ2 = 1.1, λ3 = 2.1, and λ4 = 2.5 respectively. Concerning the presentation of this design, the construction steps from the beginning to the complete stage distribution, Air Mass (AM) exploration and equations, parameter analysis with the respective color extractions, polarization situation by changing incident angle (degree) from 0 to 80, electric and magnetic field analysis section, and a comparison table will be included in this work. This design can be achieved in the development of renewable energy such as the large amount of electricity generation by solar energy (green energy) systems, the process of heating and cooling systems of water, and multiple transportation systems.

Antagonistic activity of secondary metabolites from rhizofunctional bacteria extracts against <i>Fusarium</i>species

Background: Fusarium species remain important fugal pathogens that produce several mycotoxins with adverse effects on both plant and animals. This work aimed to identify biocontrol agent from rhizofunctional bacteria and assess its antagonistic activity against Fusarium sp. using dual culture technique.
 Methodology: Briefly a circular disc of the Fusarium sp. was inoculated at the center of Potato Dextrose Agar (PDA) plate and incubated for three days. The bacterial isolates were then inoculated about 2cm from the Fusarium hyphal tips and incubated for three days, and zone of inhibition was examined. Isolates that showed antagonistic activities against the fungi were subculture in nutrient broth for three days and the metabolites were extracted using ethyl acetate. The metabolic extracts were tested against the fungi using the agar disc diffusion method.
 Results: Of the 20 rhizofunctional bacterial isolates screened for antagonistic activities against Fusarium sp., 5 showed active antagonism against the fungi with observed clear zone of inhibition in the dual culture, and microscopic examination of the fungal hyphae showed excessive and diffused hyphal branching with hyphal swelling. Ethyl acetate extracts from nutrient broth cultures did not show any zone of inhibition in dual culture against the Fusarium sp. All the 5 bacterial isolates were Gram positive strains but only 2 isolates (2a and 3K) were lipase positive, which may indicate that the mechanisms of antagonism could be due to the production of enzymes that have the ability to hydrolyze the cell wall and membrane lipids of the fungi.
 Conclusion: The rhizoplane and rhizosphere of plants could be great sources of biocontrol agents and that bacterial isolates 2a and 3K have the potential to be used as antifungal agents against Fusarium sp. Molecular identification of 2a and 3K bacterial isolates to the species level is recommended.

Highly sensitive optical fibre Bragg grating contact pressure sensor embedded in a polymer layer: Modelling and experimental validation

This paper discusses mathematical modelling and experimental validation of a highly sensitive optical fibre Bragg grating (FBG) contact pressure sensor developed for healthcare applications. Bare FBGs are not very sensitive to pressure (∼3 × 10−3 nm/MPa) but this can be increased by embedding the FBG in a polymer layer which acts as transducer to convert transverse load (pressure) applied to an axial strain, measured by the FBG sensor. The pressure sensitivity of the FBG sensor depends on the mechanical and physical properties such as Young’s modulus, shape and size of the polymer. A finite element analysis (FEA) model is developed to optimise the design parameters of the FBG sensor in order to achieve a high sensitivity. A transfer matrix mathematical formulism is then used to relate the reflection spectrum of the FBG to the strain experienced. Three different shapes, three different sizes and three different polymer materials with different Young’s moduli have been simulated and their wavelength sensitivities related to the transverse pressure. According to the simulation results, the pressure sensitivity of a bare FBG can be increased ∼ 270 times (0.8179 nm/MPa) by selecting an FBG of 3 mm length, embedding it at the horizontal centre of a polymer layer of Young’s modulus of 20 MPa, in the shape of a circular disc with a diameter 5.5 mm and thickness of 1 mm.

The problem of axisymmetric torsion of a rigid disk parallel to an internally penny crack and interface in a bilayer medium

The aim of this work was to investigate an axisymmetric problem involving a penny-shaped crack embedded in a bi-material with finite thickness under torsion. This torsion is caused by a circular rigid disk attached to the upper layer and fixed by an undeformable support at the lower layer. The location of the crack can be found in the upper layer (case 1) or the lower layer (case 2), both cases are considered. The problem was solved by applying the Hankel transform to reduce it to a system of dual integral equations, which further simplified into Fredholm integral equations of the second-kind, These equations were then solved numerically using the Gaussian quadrature rule. Dimensionless plots were presented to demonstrate the influence of layers thickness, the distance between the support and the crack, and the shear modulus ratio between layers on the stress intensity factor of the crack. The obtained results illustrated the agreement between the analytical solution and the numerical results.