scholarly journals Geometric nonlinear analysis of thin elastic paraboloid of revolution shaped shells with radial waves

2020 ◽  
Vol 21 (3) ◽  
pp. 208-214
Author(s):  
Mathieu Gil-oulbé ◽  
Aleksey S. Markovich ◽  
Prosper Ngandu ◽  
Svetlana V. Anosova
Keyword(s):  
Sheet Material ◽  
Outer Radius ◽  
Contact Boundary ◽  
Load Parameter ◽  
Spatial Form ◽  
Structural Behaviour ◽  
Inner Radius ◽  
Paraboloid Of Revolution ◽  
Different Types ◽  
Loaded State

From the old ancient types of roof and dome construction, various forms of shells have been discovered which attract special attention. A shell is a structure composed of sheet material so that the curvature plays an important role in the structural behaviour, realizing its spatial form. There are different types of shells, namely thick and thin shells. G. Brankov, S.N. Krivoshapko, V.N. Ivanov, and V.A. Romanova made interesting researches of shells in the form of umbrella and umbrella-type surfaces. The term nonlinear refers to a given structure undergoing a change in stiffness in its loaded state. There are basically three different types of nonlinearities: geometric, physical and contact (boundary condition nonlinearity). For further analysis of the stress-strain state, a paraboloid with an inner radius of 4 m and an outer radius of 20 m and the number of waves equal to 6 was considered. The test shell is made of reinforced concrete. The minimum load parameter at which the shell loses stability indicates a more than three times the margin.

Improved Diffuser/Volute Combinations for Centrifugal Compressors

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
T. Steglich ◽  
J. Kitzinger ◽  
J. R. Seume ◽  
R. A. Van den Braembussche ◽  
J. Prinsier
Keyword(s):  
Cross Sections ◽  
Pressure Ratio ◽  
Pressure Rise ◽  
Outer Radius ◽  
Inner Radius ◽  
Pressure Pipeline ◽  
The Cross ◽  
Improved Performance ◽  
High Pressure Pipeline ◽  
Original Configuration

Internal volutes have a constant outer radius, slightly larger than the diffuser exit radius, and the circumferential increase of the cross section is accommodated by a decrease of the inner radius. They allow the design of compact radial compressors and hence are very attractive for turbochargers and high-pressure pipeline compressors, where small housing diameters have a favorable impact on weight and cost. Internal volutes, however, have higher losses and lower pressure rise than external ones, in which the center of the cross sections is located at a larger radius than the diffuser exit. This paper focuses on the improvement of the internal volute performance by taking into account the interaction between the diffuser and the volute. Two alternative configurations with enhanced aerodynamic performance are presented. The first one features a novel, nonaxisymmetric diffuser̸internal volute combination. It demonstrates an increased pressure ratio and lower loss over most of the operating range at all rotational speeds compared with a symmetric diffuser̸internal volute combination. The circumferential pressure distortion at off design operation is slightly larger than in the original configuration with a concentric vaneless diffuser. Alternatively, a parallel-walled diffuser with low-solidity vanes and an internal volute allows a reduction of the unsteady load on the impeller and an improved performance, approaching that of a vaneless concentric diffuser with a large external volute.

On the Vibration of a Rotating Disk

1972 ◽  
Vol 39 (4) ◽  
pp. 1143-1144 ◽  
Author(s):  
S. Barasch ◽  
Y. Chen
Keyword(s):  
Approximate Calculation ◽  
Initial Conditions ◽  
Rotating Disk ◽  
Equation Of Motion ◽  
Outer Radius ◽  
Order Equation ◽  
System Of Differential Equations ◽  
Fourth Order Equation ◽  
First Order ◽  
Inner Radius

The equation of motion of a rotating disk, clamped at the inner radius and free at the outer radius, is solved by reducing the fourth-order equation of motion to a set of four first-order equations subject to arbitrary initial conditions. A modified Adams’ method is used to numerically integrate the system of differential equations. Results show that Lamb-Southwell’s approximate calculation of the frequency is justified.

scholarly journals Pengaruh Variasi Radius-Dalam Rim Terhadap Pengurangan Massa dan Momen Inersia Massa Dengan Studi Kasus Benda Putar Berdiameter 10 cm

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Eka Taufiq Firmansjah
Keyword(s):  
Outer Radius ◽  
Moment Of Inertia ◽  
Mass Reduction ◽  
Inner Radius ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Machine Elements ◽  
The Moment ◽  
The Masses

ABSTRAK Mesin terdiri dari sekumpulan elemen mesin yang diam dan bergerak. Elemen mesin yang bergerak dengan gerakan berputar disebut benda putar. Pada beberapa kasus seringkali diinginkan pengurangan massa dari benda putar tersebut untuk alasan ekonomis, biasanya untuk elemen mesin yag diproduksi massal. Namun pengurangan massa berakibat pada pengurangan momen inersia massa benda putar bersangkutan. Jika tuntutan perancangan tidak mempermasalahkan perubahan tersebut, maka pengurangan massa tidak menjadi masalah. Namun jika momen inersia massa tidak boleh terlalu rendah, maka harus dicari kompromi dimana pengurangan massa sebesar-besarnya namun penurunan momen inersia massa sekecil-kecilnya. Pada penelitian ini dilakukan studi kasus terhadap benda putar berjari- jari 10 cm jari-jari dalam hub 2 cm dan jari-jari luar hub 4 cm. Jumlah jari-jari ada 4 dengan lebar 1 cm dan tebal benda putar 0,5 cm. Variasi pengurangan massa dilakukan dengan memvariasikan jari-jari- dalam rim. Untuk tiap variasi, dilakukan perhitungan untuk mendapatkan jumlah massa yang dapat dikurangi dan momen inersia massa dari benda putar. Ternyata pada nilai jari-jari dalam tertentu, dapat diperoleh nilai kompromi dari permasalahan diatas. Kata kunci: benda putar, penghematan bahan, momen inersia massa.  ABSTRACT Machine consists of a set of machine elements that still and moving. Machine elements that move in a circular motion called rotary object. In some cases it is often desirable reduction in the mass of the rotating object for economic reasons, usually for a mass production of machine elements. But the mass reduction results in a reduction in moment of inertia of the mass. If the demands of the design allow this decrease of moment of inertia, mass reduction is not a problem. But if the moment of inertia of the masses should not be too low, it must find a compromise in which a mass reduction profusely but the decrease in the mass moment of inertia of the smallest. In this research conducted a case study of rotating element radius of 10 cm, radius of the hub 2 cm and outer radius hub 4 cm. The number of spoke are 4 with a width of 1 cm and uniform thickness 0.5 cm all over rotating element. Variations mass reduction is done by varying the inner radius of the rim. For each variation, calculation is performed to obtain the amount of mass that can be reduced and the mass moment of inertia of the rotating object. It turned out that in the certain value of inner radius of the rim in particular, can compromise the values obtained from the above problem. Keywords: rotating element, reducing material, mass moment of inertia.

scholarly journals Numerical Simulation Investigation on the Windage Power Loss of a High-Speed Face Gear Drive

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2093 ◽  
Author(s):  
Yu Dai ◽  
Feiyue Ma ◽  
Xiang Zhu ◽  
Jifu Jia
Keyword(s):  
Power Loss ◽  
High Speed ◽  
Outer Radius ◽  
Face Gear ◽  
Optimal Distance ◽  
Inner Radius ◽  
Common Goals ◽  
Cfd Method ◽  
Gear Drives ◽  
The Impact

Reducing the energy consumption and improving the efficiency of high-speed transmission systems are increasingly common goals; the windage power loss is not negligible in these methods. In this work, the multi-reference frame (MRF) and periodic boundary conditions (PBC) based on the computational fluid dynamics (CFD) method were adopted to investigate the windage phenomena of a single face gear with and without a shroud, and the impact of the gear speed on the windage power loss was analyzed. Furthermore, the effects on the distribution of static pressure due to the distances between the shroud and the gear body in different directions, including the outer radius direction, the inner radius direction, and the addendum direction were investigated. The results indicate that the gear speed significantly affected the windage loss, as the higher the gear speed was, the greater the windage power loss. Additionally, the shroud could effectively reduce the windage power loss, where the optimal distance from the addendum to the shroud was not the minimum distance; however, for the distances from the shroud to the inner radius and the outer radius, the smaller the distance was, the smaller the windage loss. The results can provide a theoretical basis and technical reference for reducing the windage power loss of various face gear drives.

Displacement and Stress Fields in a Functionally Graded Fiber-Reinforced Rotating Disk With Nonuniform Thickness and Variable Angular Velocity

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Y. Zheng ◽  
H. Bahaloo ◽  
D. Mousanezhad ◽  
A. Vaziri ◽  
H. Nayeb-Hashemi
Keyword(s):  
Radial Direction ◽  
Volume Fraction ◽  
Rotating Disk ◽  
Outer Radius ◽  
Functionally Graded ◽  
Circumferential Direction ◽  
Stress Fields ◽  
Fiber Reinforced ◽  
Inner Radius ◽  
Nonuniform Thickness

Displacement and stress fields in a functionally graded (FG) fiber-reinforced rotating disk of nonuniform thickness subjected to angular deceleration are obtained. The disk has a central hole, which is assumed to be mounted on a rotating shaft. Unidirectional fibers are considered to be circumferentially distributed within the disk with a variable volume fraction along the radius. The governing equations for displacement and stress fields are derived and solved using finite difference method. The results show that for disks with fiber rich at the outer radius, the displacement field is lower in radial direction but higher in circumferential direction compared to the disk with the fiber rich at the inner radius. The circumferential stress value at the outer radius is substantially higher for disk with fiber rich at the outer radius compared to the disk with the fiber rich at the inner radius. It is also observed a considerable amount of compressive stress developed in the radial direction in a region close to the outer radius. These compressive stresses may prevent any crack growth in the circumferential direction of such disks. For disks with fiber rich at the inner radius, the presence of fibers results in minimal changes in the displacement and stress fields when compared to a homogenous disk made from the matrix material. In addition, we concluded that disk deceleration has no effect on the radial and hoop stresses. However, deceleration will affect the shear stress. Tsai–Wu failure criterion is evaluated for decelerating disks. For disks with fiber rich at the inner radius, the failure is initiated between inner and outer radii. However, for disks with fiber rich at the outer radius, the failure location depends on the fiber distribution.

scholarly journals Detection of a double-peaked H α component from the accretion disc of NGC 4958

2019 ◽  
Vol 486 (1) ◽  
pp. 1138-1145
Author(s):  
T V Ricci ◽  
J E Steiner
Keyword(s):  
Active Galactic Nuclei ◽  
Galactic Nuclei ◽  
Outer Radius ◽  
Accretion Disc ◽  
Line Of Sight ◽  
Broad Component ◽  
Line Region ◽  
Inner Radius ◽  
The Galaxy ◽  
Narrow Line Region

Abstract Active Galactic Nuclei are objects associated with the presence of an accretion disc around supermassive black holes found in the very central region of galaxies with a well-defined bulge. In the optical range of the spectrum, a possible signature of the accretion disc is the presence of a broad double-peaked component that is mostly seen in H α. In this paper, we report the detection of a double-peaked feature in the H α line in the nucleus of the galaxy NGC 4958. The narrow-line region of this object has an emission that is typical of a low-ionization nuclear emission-line region galaxy, which is the usual classification for double-peaked emitters. A central broad component, related to the broad-line region of this object, is seen in H α and also in H β. We concluded that the double-peaked emission is emitted by a circular relativistic Keplerian disc with an inner radius ξi  = 570 ± 83, an outer radius ξo  = 860 ± 170 (both in units of GMSMBH/c2), an inclination to the line of sight i = 27.2 ± 0.7° and a local broadening parameter σ  = 1310 ± 70 km s−1.

Reply to Discussion by J. R. Hearst and R. C. Carlson

Geophysics ◽  
1979 ◽  
Vol 44 (8) ◽  
pp. 1464-1464
Author(s):  
J. R. Hearst ◽  
R. C. Carlson
Keyword(s):  
Outer Radius ◽  
The Other ◽  
Gradient Term ◽  
The Earth ◽  
Other Hand ◽  
Free Air ◽  
Inner Radius ◽  
The Mean ◽  
The Difference

Our equations (3) and (4) are correct. They represent the difference between the attraction of the shell viewed from [Formula: see text], the outer radius of the shell, and [Formula: see text], its inner radius. (The attraction of the shell viewed from [Formula: see text] is zero.) On the other hand, equations (5) and (6) of Fahlquist and Carlson represent the difference in attraction of the entire earth from the same viewpoints and thus, as they say, include a free‐air gradient term. However, their equation (5) would be correct only if the mean density of the earth were equal to that of the shell, and the free‐air gradient obtained by their equation (10) is correct only under these circumstances.

Magnetic Field Effect on the Binding Energy of a Hydrogenic Donor Impurity in Cylindrical Quantum Ring

2013 ◽  
Vol 380-384 ◽  
pp. 4841-4844 ◽  
Author(s):  
Guang Xin Wang ◽  
Xiu Zhi Duan
Keyword(s):  
Magnetic Field ◽  
Binding Energy ◽  
Magnetic Field Effect ◽  
Internal Surface ◽  
Outer Radius ◽  
Quantum Ring ◽  
Donor Impurity ◽  
Hydrogenic Donor Impurity ◽  
Inner Radius ◽  
Hydrogenic Donor

The binding energy of a hydrogenic donor impurity in cylindrical GaAs quantum ring (QR) subjected to an external magnetic field is calculated within the effect mass approximation using variational method. The binding energy as a function of the QR size (the inner radius, the outer radius), the impurity position and the applied magnetic field is investigated. The results demonstrate that the ground state binding energy behaves as an decreasing function of the outer radius, and the magnetic field. Likewise, the binding energy is an increasing function of the inner radius. The binding energy firstly increases and then decreases with shifting the impurity ion from the internal surface of the QR to the external surface, indicating that there is a maximum.

Stress Concentrations at the Rounded Edges of a Shaft-Hub Interference Fit Expressed in Terms of a Coefficient Normalizing the Coupling Geometry and the Young’s Modulus Effects

2012 ◽  
Author(s):  
Antonio Strozzi ◽  
Andrea Baldini ◽  
Matteo Giacopini ◽  
Enrico Bertocchi ◽  
Luca Bertocchi
Keyword(s):  
Stress Concentration ◽  
Young’S Modulus ◽  
Elastic Stress ◽  
Young's Modulus ◽  
Outer Radius ◽  
Stress Concentrations ◽  
Interference Fit ◽  
Press Fit ◽  
Fillet Radius ◽  
Inner Radius

The elastic stress concentrations developed from the keyless, frictionless, static press-fit of a solid shaft into a hub with bore rounded edges are addressed. Derived from an analytical approach, a normalising parameter Φ is employed that accounts for the combined effects on the hub stress concentration of the fillet radius of the hub bore, the shaft radius, the interference, and the Young’s modulus. Compiled with the aid of Finite Elements, several design charts are presented that report the elastic stress concentrations within the hub versus the normalising parameter Φ. Each curve is valid for prescribed ratios of a) the hub inner radius to the outer radius, and b) the fillet radius to the shaft radius. An approximating expression of ample validity is also presented for a prompt evaluation of the hub stress concentration factor.

scholarly journals Saint-Venant's principle and the anti-plane elastic wedge

1996 ◽  
Vol 31 (3) ◽  
pp. 231-234 ◽  
Author(s):  
N G Stephen ◽  
P J Wang
Keyword(s):  
Plane Deformation ◽  
Wedge Angle ◽  
Stress Singularity ◽  
Outer Radius ◽  
Geometric Effect ◽  
Linear Elastic ◽  
Inner Radius ◽  
Elastic Fracture ◽  
Acting In Concert ◽  
Root Stress

The stress field due to self-equilibrating loading on the inner or outer radius of a wedge sector, consistent with anti-plane deformation, will be affected by two agencies: a geometric effect of increasing or decreasing area and decay as anticipated by Saint-Venant's principle. When the load is applied to the inner radius the two effects are acting in concert; however, when the load is applied to the outer radius the two effects act in opposition. For a wedge angle in excess of the half-space the geometric effect is dominant over Saint-Venant decay and the stress increases the greater the distance from the loaded outer radius, indicating a breakdown in Saint-Venant's principle. For the wedge angle 2α = 360°, the unique inverse square root stress singularity at the crack tip, which is at the heart of linear elastic fracture mechanics, can be attributed to this breakdown of Saint-Venant's principle for just one eigenmode.

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