Vertex Angle Of Cone Research Articles

Torsional buckling response of FG porous thick truncated conical shell panels reinforced by GPLs supporting on Winkler elastic foundation

In the present research, torsional buckling response of thick truncated conical shell panels supporting on Winkler-type elastic medium has been surveyed. The shell is constructed from a porous metal material reinforced by graphene platelets (GPLs) in which the porosity and volume weight fraction of nanofillers are graded along the thickness of shell. Three functions for porosity distribution and five patterns of GPLs are examined. To estimate the Young modulus of the shell, Tsai-Halpin micromechanical model, and for its mass density, extended rule of mixture is employed. Linear theory of 3D elasticity in conjunction with the virtual work principle and numerical graded finite element method (FEM) are applied to derive the state of equilibrium in pre-buckling mode. Torsional buckling forces are derived by applying nonlinear Green strains and by deriving geometric stiffness matrix of the system. The effect of various parameters such as coefficient of porosity, various distributions of porosity and different nanofiller patterns, weight fraction of graphene nanofillers, semi vertex angle of cone, span angle, stiffness of elastic medium and various boundary conditions on torsional buckling loads of functionally graded (FG) porous truncated conical panel reinforced by GPLs have been presented. The main purpose of this research is obtaining the best distribution of porosity and GPLs pattern and investigating the influence of adding nano particles on the torsional buckling forces of the shell. Results denote that employing GPL-X pattern in conjunction with porosity distribution 1 provides the maximum value of buckling loads. Besides by adding the nano particles, the amount of buckling loads will increase 100%.

Active vibration control of truncated conical shell under harmonic excitation using piezoelectric actuator

Abstract In this study, active vibration control of an FGM truncated conical shell, subjected to the harmonic excitation, is investigated via a semi-analytical method. The governing equations of truncated conical shells in conjunction with piezoelectric layers are derived using Donnell shell theory and von Karman's non-linearity. Then, the dynamic equation of the system is discretized using Galerkin method to obtain the ordinary differential equation of system. Using the semi-analytical method by means of perturbation theory, the frequency response of superharmonic and sub-harmonic analysis of the system is performed. Then, using the piezoelectric smart materials, the active vibration control for the truncated conical shell is investigated and frequency-amplitude functions are analyzed for the superharmonic and subharmonic resonances. The results presents the influence of excitation amplitude and cone vertex angle on the frequency-amplitude response and in specific the effect of different control gain coefficients on the system's vibration behavior. Finally, the performance of active control strategy is investigated by means of the time response of system equipped with piezoelectric layers for different types of the FG distribution in thickness direction.

Vertex angles effects in the energy absorption of axially crushed kenaf fibre-epoxy reinforced elliptical composite cones

Abstract Experimental quasi-static crushing tests were conducted by using a universal testing machine format kenaf-epoxy composite elliptical cones. The work focused on the vertex angle's effects on energy absorption capability; the vertex angles vary from 0° to 24° in 6 increments. The failure modes of the kenaf fibre epoxy composite elliptical cones were observed utilising delegate photos taken during the quasi-static crushing test. Load-deformation curves and deformation histories of typical specimens are presented and discussed. Moreover, the effects of cone vertex angles on the load carrying capacity and the energy absorption capability are also discussed. The results show that the energy absorption abilities significantly influence the ellipticity vertex angle as the load carrying capacity. We concluded that the quasi-static axial crushing behaviour of elliptical mat laminated composite cones is strongly affected by their structural geometry and the specific energy absorbed by the composite elliptical cones with vertex angles of 6°, 12°, 18°, and 24°, which is more than an elliptical cone with the vertex angle of 0° (the elliptical tube) at any given deformation. However, the specific energy absorption for the elliptical composite cone showed a positive correlation, i.e., the more the angle increased, the more energy was absorbed. In this regard, an elliptical composite cone with a 24° angle exhibited the best energy absorption capability.

Investigation of the Free Vibrations of Composite Anisogrid Lattice Conical Shells Formed by Geodesically Spiral and Circumferential Ribs

This paper focuses on the dynamic behavior of composite anisogrid lattice conical shells. Lattice composite conical shell consists of composite helical and circumferential ribs and thin outer skin. The free vibration analysis of anisogrid composite lattice conical shell is presented. A smeared method is employed to calculate the variable coefficients of stiffness of conical shell and more close to the realistic applications. The lattice part of conical shell is modeled as a beam, so in addition to the axial loads, ribs endure shear loads and bending moments. The first-order shear deformation shell theory is used to account for the effects of transverse shear deformations and rotary inertia. The current results are verified with 3D finite element model of conical shell by ANSYS Software and those reported in the literature. Some special cases as influences of geometric parameters of lattice part of shell, effects of boundary conditions and circumferential wave number on natural frequencies of the shell are discussed. It was concluded that employment of the smear method could be recommended for determining the coefficients of stiffness of the composite lattice conical shells with outer skin. Also increasing the vertex angle of cone increases the natural frequencies of conical shell.

Investigation of the vibration of lattice composite conical shells formed by geodesic helical ribs

In this paper free linear vibration of lattice composite conical shells will be investigated. Lattice composite conical shell consists of composite helical ribs and thin outer skin. A smeared method is employed to obtain the variable coefficients of stiffness of conical shell. The ribs are modeled as a beam and in addition to the axial loads, endure shear loads and bending moments. Therefore, theoretical formulations are based on first-order shear deformation theory of shell. For verification of the obtained results, comparison is made with those available in open literature. Also, using FEM software the 3D finite element model of composite lattice conical shell is built and analyzed. Comparing results of analytical and numerical analyses show a good agreement between them. Some special cases as variation of geometric parameters of lattice part, effect of the boundary conditions and influence of the circumferential wave numbers on the natural frequencies of the conical shell are studied. It is concluded, when mass and the geometrical ratio of the composite lattice conical shell do not change, increment the semi vertex angle of cone leads to increase the natural frequencies. Moreover for shell thicknesses greater than a specific value, the presence of the lattice structure has not significant effect on the natural frequencies. The obtained results have novelty and can be used for further and future researches.

Influence of panel/back thickness on impact damage behavior of alumina/aluminum armors

Using modified SHPB device, damage behaviors of alumina/aluminum armors under impact load were studied. The influences of panel/back thickness on the target damage characteristics were investigated. The transmitted stress wave increased and the reflected stress wave decreased distinctly with the increase of back thickness, while the panel thickness variation had little influence on the stress wave propagation features. The vertex angle of ceramic inverted cone increased with the increase of back thickness and decrease of panel thickness, but the number of radial cracks reduced with the increase of back thickness and the decrease of panel thickness. Furthermore, the failure mechanism of the ceramic panels, including the cone and radial cracks formation mechanism was analyzed. A “composite beam” model has been established to estimate the local bending stress. The model calculation showed that the local bending stress is related to the panel thickness, back thickness and the panel/back moduli ratio.

Study on the effect of vertex angle and upstream swirl on the performance characteristics of cone flowmeter using CFD

Computational Fluid Dynamics (CFD) has emerged as a revolutionary tool for optimizing the design of any flowmeter for given conditions. The flow features obtained with CFD are more extensive compared to experiments. In the present study, CFD code ‘FLUENT” after validation has been used to investigate the effect of cone vertex angle and upstream swirl on the performance of cone flowmeter. The values of discharge coefficient ( C d ) evaluated for different vertex angles shows that the value of discharge coefficient is independent of Reynolds number and its value decreases with increase in vertex angle. In the presence of upstream disturbance in the form of swirl, the value of discharge coefficient is also independent of Reynolds number and its value is only marginally affected by the magnitude of swirl. The flow in a longitudinal plane shows the presence of a pair of contra-rotating vortices in the recirculation region just downstream of the cone. The velocity profile downstream becomes stable after a distance of about 5D.

Influence of local temperatures on the adhesion of the blank to abrasive grains

Kinetic data on the adhesion of the blank to an abrasive grain of the grinding wheel indicate that the bond between the abrasive and the metal is mainly due to capture [1]. According to current concepts regarding the bonding of materials in analogous conditions, the most important factors are the pressure, the temperature in the contact zone, and the time of exposure [2]. It is found that, in any grinding conditions, the contact surfaces of the abrasive grain with the chip and the blank include sections where the pressure exceeds the yield point of the material in the blank [3]. Experiments on metal adhesion to individual abrasive grains in microcutting (scratching) show that this process is intensified with increase in sample temperature [4]. To establish the relation between the adhesion rate and the local temperature in zones adjacent to the adhesive grain, the thermal interaction of the objects in contact during microcutting may be analyzed theoretically and investigated experimentally. In developing physical and mathematical models of the thermal process, the actual shape of the contacting objects—the blank, the abrasive grain, the chip, and the grain holder—is taken into account, as well as the location of individual sources of heat generation and their density distribution and also the temperature dependence of the thermophysical properties of the objects and the mechanical properties of the sample. In addition, the relative displacement of the contacting objects (the holder with the grain relative to the sample; and the chip relative to the grain) is taken into account. The components of the microcutting force required to calculate the power of the heat-generation sources are determined from analytical formulas [3]. It is assumed that the abrasive grain is a cone (vertex angle 2 γ ; wear length l 2 ). In other words, the grain is of the same shape as in experiments on microcutting (Fig. 1) [4]. Some of the heat from the abrasive grain passes to the holder.

Computational Investigation of Torque on Coaxial Rotating Cones

This article looks at a modification of Taylor–Couette flow, presenting a numerical investigation of the flow around a shrouded rotating cone, with and without throughflow, using the commercial computational fluid dynamics code FLUENT 6.2 and FLUENT 6.3. The effects of varying the cone vertex angle and the gap width on the torque seen by the rotating cone are considered, as well as the effect of a forced throughflow. The performance of various turbulence models are considered, as well as the ability of common wall treatments/functions to capture the near-wall behavior. Close agreement is found between the numerical predictions and previous experimental work, carried out by Yamada and Ito (1979, “Frictional Resistance of Enclosed Rotating Cones With Superposed Throughflow,” ASME J. Fluids Eng., 101, pp. 259–264; 1975, “On the Frictional Resistance of Enclosed Rotating Cones (1st Report, Frictional Moment and Observation of Flow With a Smooth Surface),” Bull. JSME, 18, pp. 1026–1034; 1976, “On the Frictional Resistance of Enclosed Rotating Cones (2nd Report, Effects of Surface Roughness),” Bull. JSME, 19, pp. 943–950). Limitations in the models are considered, and comparisons between two-dimensional axisymmetric models and three-dimensional models are made, with the three-dimensional models showing greater accuracy. The work leads to a methodology for modeling similar flow conditions to Taylor–Couette.

High gain feedback, tolerance, and stabilization of linear systems

The problem of stabilizing linear continuous-time systems is revisited with the objective of investigating the tolerance allowed in the implementation of stabilizing feedback controllers. It is shown that, for high gain feedback, this tolerance can be described by a cone in the feedback parameter space, called the “tolerance cone”. The tolerance cone describes fractional (percentage) errors the feedback controller can tolerate without jeopardizing the internal stability of the controlled system. The larger the vertex angle of this cone, the more tolerance is available when implementing the controller. The vertex angle of the tolerance cone is determined by the proximity to singularity of a certain matrix derived from the controlled system.

Effect of residual stresses in a filament wound laminated conical shell

This paper examines the effect of residual fabrication stresses on the crushing behaviour, energy absorption, failure mechanism and failure mode of a filament wound laminated conical composite shell. The static crushing behaviour of the conical composite shell under uniform axial compressive load is investigated experimentally. The cone vertex angles were 0°, 6°, 12° and 18°. The numerical result shows that residual stresses developed have been concentrated at the small ends of cones. Experimental results obtained from this investigation show that the initial failure was dominated by interfacial and shear failure, while the delamination and eventually fibre fracture were dominated by the failure mechanism after the initial failure. It is also found that the static crushing behaviour of the conical shell is highly sensitive to the change in cone vertex angle, which strongly dominates the residual fabrication stress development. It can be deduced that as the axial residual stress increases, the initial failure load decreases.

Experimental quasi-static axial crushing of cone–tube–cone composite system

Abstract An experimental investigation was carried out to study the crashworthiness parameters of cone–tube–cone composite system. The quasi-static crushing behaviour of axially compressed cone–tube–cone composite system has been investigated experimentally. The conical parts of composed system were symmetric. The cone vertex angles used were 10 and 15°. Two arbitrary cone ratios of height-to-base-diameter ( C / D 1 ) have been explored. The tubular part heights were varied between 0 and 50 mm and between 0 and 20 mm for 1.41 and 0.69 of C / D 1 ratios, respectively. Load–displacements curves and deformation histories of typical specimens are presented and discussed. The results showed that structures with ratios (tube-height-to-total-height) vary between 0.06 and 0.11 exhibit a higher crashworthiness performance.

Crushing Behavior of Cone-Cylinder-Cone Composite System

This article examines the effect of cylindrical part length on the crushing behavior, energy absorption, failure mechanism, and failure mode of cone-cylinder-cone intersection composite shell. The static crushing behavior of a cone-cylinder-cone composite shell under uniform axial compressive load has been investigated experimentally and numerically. The conical parts of the structure were symmetric. The cone vertex angles used were 10° and 15°. The cylindrical part lengths were varied between 0 and 50 mm. Failure modes were examined using photographs taken while crushing the specimens. Numerical results show that local stress has been concentrated at the junctions between the cylinder and cones. Experimental results show that the initial failure was dominated by interfacial and shear failure, while the delamination and eventually fiber fracture dominated the failure mechanism after the initial failure. The results showed also that structure with H z2 / H Z ratios between 0.06 and 0.11 exhibit high-energy absorption capability and very high crushing load. Volume reduction was obtained and found to be significant.

Axial and lateral crushing of the filament wound laminated composite curved compound system

In this paper, experimental and numerical investigations into the crushing behaviour of the filament wound laminated curved compound system have been conducted. The structure being investigated is composed of a complete and semi-circular cone-cylinder-cone system. The conical parts of the structure were symmetric. The cone vertex angle and the cylindrical part height were 15 degrees and 10 mm, respectively. Load–displacement curves and deformation histories of typical specimens are presented and discussed. The experimental data are correlated with predictions from finite element model. Numerical results show that for curved systems under lateral load, local stress has been concentrated at the junctions between the cylinder and cones as well as the edge of the systems, while for the curved systems under axial load, the stress concentration is slightly clear at the loaded end of the curved systems. Experimental results show that the axial loaded curved systems are crushed into a progressive failure mode and exhibit high-energy absorption capability. Results also show that the debonding at the fibre–matrix interface is influenced by the load–displacement relationship for the lateral loaded curved systems. On the other hand, the fragmentation failure mode is dominated by the load–displacement relationship for the axial loaded curved systems.

Effect of Material and Geometry on Crushing Behaviour of Laminated Conical Composite Shells

This paper examines the effects of the material and structural geometry on the crushing behaviour, energy absorption, failure mechanism and failure mode of circular conical composite shell. The static crushing behaviour of circular conical composite shell under uniform axial compressive load has been investigated experimentally. The cone vertex angles used were 0, 6, 12 and 18 degrees. The cone vertical length and bottom outer diameter were kept for all the cases as 100 and 110 mm, respectively. Failure modes were examined using several photographs taken during the crushing stages for each specimen. Results obtained from this investigation showed that the initial failure was dominated by the interfacial and shear failure, while the delamination and eventually fibre fracture were dominated the failure mechanism after the initial failure. It has also found that the static crushing behaviour of the circular conical shell is very sensitive to the change in the vertex angle. Reinforcement type greatly affects the energy absorption of the circular conical and cylindrical shells.

An experimental investigation into crushing behaviour of filament-wound laminated cone–cone intersection composite shell

This paper presents the effect of cone vertex angle on the crushing behaviour, energy absorption, failure mechanism and failure mode of filament-wound laminated (FWL) cone–cone intersection composite shell. The static crushing behaviour of FWL cone–cone intersection composite shell under uniform axial load is investigated experimentally. Two types of composites were tested, namely, carbon fibre/epoxy and glass fibre/epoxy. The cones vertex angles tested are 10°, 15°, 20° and 25°. Failure modes were examined using the photographs taken during crushing the specimens. The results showed that the initial failure was dominated by interfacial and shear failure, while the delamination and eventually fibre fracture dominated the failure mechanism after the initial first failure. The results also showed that the structure with vertex angles 20° and 25° exhibited good energy absorption capability. The volume reduction is obtained and found to be significant for these sets of angles.

Vibratory behaviour of shallow conical shells by a global Ritz formulation

The development of a new approach based on the energy principle is presented to study the free vibration of shallow conical shells. In the numerical procedure, a set of orthogonally generated and kinematically oriented shape functions, which satisfies the geometric boundary conditions at the outset, is proposed to overcome the mathematical complexity in expressing the geometry and variable surface curvature of these shells. To establish the accuracy of this method, convergence and comparison studies have been carried out. In this study, the effects of various shell parameters on the fundamental and higher mode frequencies are investigated. It is found that monotonic increases in the fundamental nondimensional frequency parameter occurs when the cone vertex angle or base subtended angle is increased independently for the cantilever conical shell. The fundamental frequency parameter also becomes higher for the fully clamped conical shell with higher panel-length to cone-length ( a/ s) ratio. A set of first published vibration mode shapes is also presented.

Velocity distributions in the turbulent boundary layers on rotating cones in axial uniform flow.

An experimental study is made for the turbulent boundary layer on the rotating cone in the axial uniform stream. Measurements of the mean velocity distributions were made at various values of the surface-to-free stream velocity ratio λb for two different cone vertex angles, 0=15°and 30°. In the polar diagram of the mean velocity distributions, the profiles are not only dependent on the local velocity ratio λ but also on θ and Rw, where Rw is the Reynolds number based on the wall velocity. The distributions of the swirl flow Richardson number reveal that the destabilizing effect of the centrifugal force is considerably stronger at θ=15°than at θ=30°. Discussions of the logarithmic velocity distributions are made for the azimuthal and the meridian velocity components as well as for the resultant velocity.

2 容器内で回転する円錐体まわりの流れの遷移現象

Transition of the flow between a rotating cone and a casing is studied by using a flow visualization technique. The cone vertex angle used in the present experiment is 60°. Observations of the flow have been made for several clearance ratios s/R from 0.016 to 0.184, where s is the clearance and R is the radius of the rotating cone. Characteristics of spiral vortices which appear at first in the transition region are clarified. It is found that three different types of instabilities may occur at large clearance ratios ; one of those is a centrifugal type and the others are similar to those observed in the Ekman boundary layer. The effects of throughflow on the behavior of the spiral vortices are also investigated.

The flow around a rotating cone in a casing. For the case when the cone vertex angle is 60.DEG..

The velocity distribution around a rotating cone in a casing, and the pressure distribution on the casing wall are measured for a variety of combinations of the clearance ratio and the throughflowrate. The cone vertex angle, 2θ, used in the experiment, is 60°. The results of the velocity measurement for a large clearance ratio show the presence of a potential core in the flow field. The ratio of the angular speed of the potential core to that of the rotating cone, K, is almost the same as for the case of a rotating disk, if Cq·sinθ is kept constant (Cq is the dimensionless throughflow rate). The pressure distribution and the axial thrust coefficient are almost the same as those for a rotating disk and they are independent of the Reynolds number Re, when Cq·sinθ·Re-0.8 is kept constant.