Thin Conical Shells Research Articles

An ultrasonically catalyzed conductometric metal oxide gas sensor system with machine learning-based ambient temperature compensation

The ultrasonic catalysis method provides a new means of enhancing sensing performance of some types of gas sensors. But generating the ultrasound consumes electric energy and increases the system mass. Thus, it is significant to lower the energy consumption and mass of the ultrasonic excitation structure as much as possible, while enhancing the sensing performance. In this work, a thin conical metal shell excited by a piezoelectric disk has been proposed, serving as the focusing ultrasonic transducer and protection case for a SnO2 gas sensor. The ultrasonic transducer’s total mass is only 11 g. The experiments show that the ultrasonic transducer can significantly reduce the low detection limit (LDL), and measured LDL of the sonicated sensor for H2 can be as low as 107 ppb (1/3 of the same sensing element not sonicated) with a response of 4.6%. In this case, the ultrasonic transducer’s power consumption and temperature rise is 146 mW and 3 ℃, respectively. The low temperature rise indicates that the LDL may be further decreased by increasing the ultrasonic vibration. The effect of ambient temperature change on predicted H2 concentration is compensated by two convolutional neural networks for the low (1–100 ppm) and ultralow (≤ 1 ppm) concentration ranges, and the relative error of concentration prediction in these two concentration ranges is 5.7% and 12.3%, respectively.

Nonlinear vibrations of truncated conical shells considering multiple internal resonances

The geometrically nonlinear vibration response of truncated thin conical shells is studied for the first time considering the one-to-one internal resonance, a phenomenon typically observed in symmetric structures such as conical shells. The Novozhilov nonlinear shell theory, retaining all nonlinear terms in the in-plane strain–displacement relationships of the three mid-surface displacements, is applied to study nonlinear vibrations of truncated conical shells. In-plane inertia is also taken into account, and a relatively large number of generalized coordinates, associated with the global discretization of the shell, is considered. This gives very accurate numerical solutions for simply supported, truncated thin conical shells. The effect of an exact one-to-one internal resonance, due to the axial symmetry of conical shells, is fully considered and the results are presented for different excitation levels. The numerical results show that also an almost exact one-to-one internal resonance with a mode presenting a different number of circumferential waves can also arise, which further complicates the nonlinear vibrations and leads to 1:1:1:1 internal resonance. The numerical model was augmented with additional generalized coordinates to capture this phenomenon. Pitchfork, Neimark–Sacker and period-doubling bifurcations of the forced vibration responses arising from internal resonances are detected, followed and presented, showing complex nonlinear dynamics.

Thermal-Magnetic-Elastic Effect Analysis of a Thin Current-Carrying Conical Frustum Shell*

A thermal-magnetic-elastic problem for a thin current-carrying conical frustum shell in a magnetic field is studied. The normal Cauchy form of nonlinear differential equations, which include in total eight basic unknown variables, are obtained by the variable replacement method. Using Newmark’s stable finite equidifferent formulas and the quasi-linearization method, the nonlinear partial differential equations are reduced to a sequence of quasi-linear differential equations, which can be solved by the discrete-orthogonalization method. The temperature field in a thin conical frustum shell and the integral eigenvalues are derived after considering Joule’s heat effect in an electromagnetic field and the thermal equilibrium equation. The change of stresses, displacements, and temperatures in the thin current-carrying conical frustum shell with variation of the electromagnetic parameters is discussed. It is proved that the stresses, strains, and temperatures in thin shells can be controlled by changing the electromagnetic and mechanical parameters by considering a specific example. These results are expected to be a theoretical reference for further analysis of this case.

Elastic limit load estimation including similarity approach for different end conditioned conical shells with high semi-vertex angle under axial compression

Abstract This study investigates the stability loss of thin walled conical shell structures under axial loading. More specifically, conical shells with semi-vertex angle greater than 65 ∘ ( β c > 65 ∘ ) and with different bottom edge radial stiffness were studied in order to fill the gap in existing literature. The effects of geometrical parameters of the structure on the load bearing capacity were determined. Conical shell structures with high semi-vertex angle and different boundary conditions display highly non-linear character under axial loading, hence conventional analytical approaches are not adequate to predict the limit load. Therefore, a new method was proposed in this study which can accurately predict the limit load of these structures. The deviation between the proposed method and numerical results was found to be ± 13 % , while it was one order higher (+ ~ 300%) in classical shell theory, based on the configuration. Furthermore, similarity parameters were suggested to increase the range of application of the proposed method. Similarity parameters enable researchers to work with scaled-down models which are capable of simulating the behaviour of real-time-scale models. In addition, the effect of geometrical initial imperfections on the load bearing capacity was investigated and a new reduction coefficient was identified which is much more accurate compared to the overly conservative standard counterpart. A numerical model was developed with COSMOS/M software. This model was validated with experiments, and then was used for the parametric study.

Size-dependent two-node axisymmetric shell element for buckling analysis with couple stress theory

In this paper, two-node size-dependent axisymmetric shell element formulation is developed by using thin conical shell model in the place of the beam model, which is used in previous research and using the modified couple stress theory in the place of the classical continuum theory. Since classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have become quite popular. The mass stiffness matrix and geometric stiffness matrix for axisymmetric shell element are developed in this paper, and by means of size-dependent finite element formulation it is extended to more precisely account for nanotube buckling. The results have indicated using the two-node axisymmetric shell element, where the rigidity of the nano-shell is greater than that in the classical, and the critical axial buckling loads obtained from couple stress theory are greater than that of classical, which is due to the presence of one size parameter in couple stress theory. The findings also indicate that the developed size-dependent axisymmetric shell element is able to analyze the buckling of cylindrical and conical shells and also circular plate, which is reliable for simulating micro/nanostructures and can be used for the analysis of size effect and has desirable convergence characteristic. Besides, in addition to reducing the number of elements required, using axisymmetric shell element also increases convergence speed and accuracy.

Aerodynamic Characteristics of Thin Cylindrical and Conical Shells in the Incompressible Flow

The paper presents aerodynamic characteristics of thin cylindrical and conical shells in the incompressible flow. Experimental data and results of numerical simulation in the OpenFoam software are compared. It is shown that the aerodynamic characteristics of the thin shells differ from the aerodynamic characteristics of the corresponding solid bodies and depend on the shell geometry parameters.

Evaluating actuator distributions in simply supported truncated thin conical shell with embedded piezoelectric layers

In this investigation, distributed modal actuator forces of simply supported truncated conical shell embedded by a piezoelectric layer are studied. Piezoelectric layer is distributed on the conical shell surface as actuators. Three types of distributions are considered: longitudinal, circumferential, and diagonal distributions. First, electromechanical equations of the conical shell with embedded piezoelectric actuator layer are extracted. Then modal expansion method is used to define independent modal characteristics of the conical shell. For each kind of distribution, three case studies are considered and evaluated. Results showed that in the longitudinal and diagonal distributed actuator, membrane force in the longitudinal direction is the dominant force and in the circumferential distributed actuator, the membrane force in the circumferential direction is the dominant force. The effects of cone angle, piezoelectric thickness, and piezoelectric layer segmentation on modal forces of each distributed actuator are also studied. In circumferential distributed actuator, modal forces increase as the cone angle increases. This phenomenon in the longitudinal and diagonal distributed actuator is almost reversed. The piezoelectric layer segmentation effect on the modal forces distribution is also evaluated, and it showed that this phenomenon has a critical effect on the modal forces distribution.

Экспериментальное исследование аэродинамических характеристик тонких конических и цилиндрических оболочек в дозвуковом потоке

Экспериментальное исследование аэродинамических характеристик тонких конических и цилиндрических оболочек в дозвуковом потоке

Thermal Buckling of Thin Conical Shell Subjected to Uniform Pressure and Temperature

The thermal buckling of the shell is one of the hot research fields in the field of solid mechanics. In this paper, the equation of thermal constitutive equation of isotropic material and the stability of axisymmetric conical shells were derived by tensor method. Application of thermal constitutive equation to the study of thermal buckling of conical shells, the equations of thermal stability of conical shells expressed by displacements were obtained. Considering the interaction of uniform external pressure and temperature, potential energy functional of conical shells is derived by the principle of minimum potential energy expressed in displacement, the thermal buckling of simply supported cone shell using Ritz method. The change trend of critical pressure and critical temperature caused by the change of conical shells wall thickness and base angle analysis.

Аэродинамические характеристики тонких конических оболочек при сверхзвуковых скоростях набегающего потока

Аэродинамические характеристики тонких конических оболочек при сверхзвуковых скоростях набегающего потока

On the origin of jets from disc-accreting magnetized stars

AbstractA brief review of the origin of jets from disc-accreting rotating magnetized stars is given. In most models, the interior of the disc is characterized by a turbulent viscosity and magnetic diffusivity (‘alpha’ discs) whereas the coronal region outside the disc is treated using ideal magnetohydrodynamics (MHD). Extensive MHD simulations have established the occurrence of long-lasting outflows in the case of both slowly and rapidly rotating stars. (1) Slowly rotating stars exhibit a new type of outflow, conical winds. Conical winds are generated when stellar magnetic flux is bunched up by the inward motion of the accretion disc. Near their region of origin, the winds have a thin conical shell shape with half opening angle of ∼30∘. At large distances, their toroidal magnetic field collimates the outflow forming current carrying, matter dominated jets. These winds are predominantly magnetically and not centrifugally driven. About 10-30% of the disc matter from the inner disc is launched in the conical wind. Conical winds may be responsible for episodic as well as long lasting outflows in different types of stars. (2) Rapidly rotating stars in the ‘propeller regime’ exhibit twocomponent outflows. One component is similar to the matter dominated conical wind, where a large fraction of the disc matter may be ejected in this regime. The second component is a high-velocity, low-density magnetically dominated axial jet where matter flows along the open polar field lines of the star. The axial jet has a mass flux of about 10% that of the conical wind, but its energy flux, due to the Poynting flux, can be as large as for the conical wind. The jet’s magnetically dominated angular momentum flux causes the star to spin down rapidly. Propeller-driven outflows may be responsible for protostellar jets and their rapid spin-down.When the artificial requirement of symmetry about the equatorial plane is dropped, the conical winds are found to come alternately from one side of the disc and then the other, even for the case where the stellar magnetic field is a centered axisymmetric dipole.Recent MHD simulations of disc accretion to rotating stars in the propeller regime have been done with no turbulent viscosity and no diffusivity. The strong turbulence observed is due to the magneto-rotational instability. This turbulence drives accretion in the disc and leads to episodic conical winds and jets.

Electromagnetic Wave Scattering By Plasma Containers

The scattering cross-section has been derived by an approximate method for a thin plasma plate and for thin spherical and conical shells. The computed results for scattering cross-section for a plate and spherical and conical shells are obtained. The results are presented in the form of scattering cross-section aspect angle plane.

Analysis of conical shells in the framework of coupled stresses theory

In this paper, the thin conical shell model is developed by using the modified couple stress theory. This non-classical formulation can incorporate size effects in nano/micro scales. For this purpose, the thin shell model is used along with the modified couple stress theory, and the equations of motion with partial differentials and classical and non-classical boundary conditions are derived by using Hamilton’s principle. Finally, the free vibrations of the single-walled carbon nanocone (SWCNC) are examined as a special case. The SWCNC is modeled as simply supported, and the Galerkin method is used to solve the vibrational problem. Results of the new formulation are compared to the classical theory. The results show that nanoshell rigidity is greater in the modified couple stress theory than in the classical theory, which leads to an increase in the natural frequencies. Also, the effect of size parameter on the vibration frequency of SWCNC in different lengths and apex angles is examined.

Wave interpretation of numerical results for the vibration in thin conical shells

The dynamic behaviour of thin conical shells can be analysed using a number of numerical methods. Although the overall vibration response of shells has been thoroughly studied using such methods, their physical insight is limited. The purpose of this paper is to interpret some of these numerical results in terms of waves, using the wave finite element, WFE, method. The forced response of a thin conical shell at different frequencies is first calculated using the dynamic stiffness matrix method. Then, a wave finite element analysis is used to calculate the wave properties of the shell, in terms of wave type and wavenumber, as a function of position along it. By decomposing the overall results from the dynamic stiffness matrix analysis, the responses of the shell can then be interpreted in terms of wave propagation. A simplified theoretical analysis of the waves in the thin conical shell is also presented in terms of the spatially-varying ring frequency, which provides a straightforward interpretation of the wave approach. The WFE method provides a way to study the types of wave that travel in thin conical shell structures and to decompose the response of the numerical models into the components due to each of these waves. In this way the insight provided by the wave approach allows us to analyse the significance of different waves in the overall response and study how they interact, in particular illustrating the conversion of one wave type into another along the length of the conical shell.

Experiments to investigate the effects of radiative cooling on plasma jet collimation

Preliminary experiments have been performed to investigate the effects of radiative cooling on plasma jets. Thin (3 μm–5 μm) conical shells were irradiated with an intense laser, driving jets with velocities >100 km s−1. Through the use of different targets materials – aluminium, copper and gold – the degree of radiative losses was altered, and their importance for jet collimation investigated. A number of temporally-resolved optical diagnostics was used, providing information about the jet evolution. Gold jets were seen to be narrower than those from copper targets, while aluminium targets produced the least collimated flows.

Elastoplastic deformation of conical shells with two circular holes

The elastoplastic state of thin conical shells with two circular holes is analyzed. The stress distribution in the stress-concentration zone is examined using a proposed technique. The stress–strain state around the two circular holes in shells under internal pressure is analyzed taking plastic strains into account. Numerical results are presented in a table

A numerical solution for the coupled dynamic thermoelasticity of axisymmetric thin conical shells

The problem of an axisymmetric thin conical shell under general thermal and mechanical shock is considered. Governing equations have been obtained using coupled dynamic thermoelastic equation and the energy equation with parabolic approximation of temperature distribution through thickness of the shell. The governing equations have been solved using the Galerkin finite element method with Kantrovich approximation for space and time domains. An illustrative example was solved using the present method. Displacement, force, moments, and stress fields have been extracted for the illustrative example.

Numerical Simulation on Drop Test of the Conical Shell

The drop test for the thin 2A12 conical shells was developed on a drop hammer. The dynamical responses, typical deformation histories and failure mode of the shells were presented. The drop impact response of the thin conical shells were numerically simulated and analyzed in detail by using the explicit, nonlinear transient dynamic code, LS-DYNA. In the calculation, the material plastic behavior of the conical shells was described by Johnson-Cook constitutive relationship, which includes the effects of the strain rate, strains harden and temperatures soften. The deformation and failure model of the conical shell obtained from the numerical simulation were consistent well with the experiment. It was shown that the calculation method, material model and the failure criterion were available. The test and numerical simulation results were all shown that the failure mode was different because of the different drop height.

Natural vibrations of thin conical panels of variable thickness

A numerical analytical approach is proposed to study the natural vibrations of thin isotropic conical shells with varying thickness. The approach is based on the spline-approximation of unknown functions. Open shells (panels) with different boundary conditions are considered. The effect of variable thickness on the dynamic characteristics is analyzed

The buckling of FGM truncated conical shells subjected to combined axial tension and hydrostatic pressure

Abstract The purpose of this paper is to investigate the elastic buckling of FGM truncated thin conical shells under combined axial tension and hydrostatic pressure. Here axial tensions are separately applied to small and large bases of the truncated conical shell, respectively. It is assumed that the cone is a mixture of metal and ceramic, and that its properties changes as the power and exponential functions of the shell thickness. After giving the fundamental relations, the stability and compatibility equations of an FGM truncated conical shell, subject to combined axial tension and hydrostatic pressure, have been derived. Applying Galerkin’s method general formulas have been obtained for the critical combined and separate loads of FGM conical shells. The appropriate formulas for homogenous and FGM cylindrical shells are found as a special case. Effects of changing shell characteristics, material composition and volume fraction of constituent materials on the critical combined and separate loads of FGM shells with simply supported edges are also investigated. The results obtained for homogeneous cases are compared with their counterparts in the literature.