Multilayered Cylindrical Shells Research Articles

The Penetrated and Scattered Field Distributions in the Presence of a Non-Uniform Cold Magnetised Plasma Column Surrounded By Multiple Strips: Tm Wave Incidence

Both the penetrated and the scattered fields in the presence of a non-uniform cold magnetized plasma column are investigated in this work, and the direct integral equation is formulated for describing the currents on the surrounded multiple perfectly conducting strips on the outer boundary of plasma column due to a normally incident TMwave. In order to formulate such an integral equation, two-dimensional dyadic Green's functions in multi-layered cylindrical shells are derived at first in terms of the cylindrical vector wave functions. Furthermore, by using the Galerkin's method, the surface current of the strips is expanded in the form of a series of Chebyshev polynomials of the first kind. Parameter studies are performed to show the variation of the near- and far-zone fields with the operating frequency, the effective collision frequency, as well as the angular width and the number of surrounded strips.

Calculation of the goffered multilayered composite cylindrical shells by using the finite element method

In the present paper, the goffered multilayered composite cylindrical shells is directly calculated by finite element method. Numerical results on displacements, internal forces and moments are obtained for various kinds of external loads and different boundary conditions.

Layerwise Theory for Dynamic Buckling and Postbuckling of Laminated Composite Cylindrical Shells

A general layerwise theory for dynamic buckling and postbuckling of imperfect multilayered composite circular cylindrical shells is introduced. In contrast to the conventional displacement-based layerwise theories that are more suitable for semianalytical solutions and kinematic boundary conditions, the present method includes the displacement and stress components at the same time. Thus, the method provides an efficient formulation where both kinematic and force boundary conditions can be exactly satisfied. To use the exact expressions of strain and stress components, the full Green's strain tensor for large deflections of circular cylinders is employed. Then almost no simplification is made in the development of the governing equations. The applied loads can be composed of various mechanical loads (axial compression, external pressure, external fluid pressure, and torsion or a combination of them). Accuracy and convergence of the present theory, in comparison with the three-dimensional elasticity approaches proposed so far, are higher and more effective. Finally, a few examples of various references that have used different theories are reexamined for comparison purpose.

Natural frequency response of vertical cantilever composite shells containing fluid

An analytical investigation of the natural frequency response of multi-layered orthotropic circular cylindrical shells partially submerged in or filled with non-viscous incompressible fluid has been developed here. The typical examples could be of liquid storage tanks or vertical pipe conveying fluid or submerged in fluid. Since these shells are considered to be laminated of composite material, the effect of transverse shear deformation and rotary inertia terms have been taken into account in the analysis. Axial dependence of modal forms is assumed in the form of a simple Fourier series instead of the commonly used exponential axial dependence. A modified variational method is used here to obtain a polynomial frequency equation. This equation can be solved for an arbitrary choice of end conditions. As an illustration the important case of a vertical cantilever shell with bottom end clamped and top end free is considered and analyzed in detail. The effect of variation in the fluid height level on the frequency response is studied. The influence of axial and meridional stiffnesses of the shell on the natural frequencies is also discussed.

Vibration Control of a Multi-layer Piezoelectric Cylindrical Shell.

Equations of motion for multi-layer piezoelectric cylindrical shells and the equations of integrated piezoelectric sensors are derived. The state equation is obtained by solving the equations of motion with modal expansion method. The feedback control method, feedforward control method, and their combination as a hybrid control method are applied in the control of forced vibration of the piezoelectric cylindrical shell with integrated sensors and actuators. The simulation and experimental results show that good control effectiveness can be obtained by using the integrated piezoelectric sensors and actuators in conjunction with the hybrid control method.

Calculation of the goffered multilayered composite cylindrical shells

By using the effective modulus theory and Seydel assumptions the governing equations of the goffered multilayered composite cylindrical shell are formulated. Solution to the problem 1n term of displacements is given by the operator method, while the solution in term of stress function and deflection is obtained by Bubnov-Galerkin method in choosing appropriate forms of these quantities.

3D Solutions for Free Vibration of Initially Stressed Thermoelectroelastic Multilayered Cylinders

Analytic three-dimensional solutions are presented for the free vibration problems of initially stressed hybrid multilayered composite circular cylindrical shells. The shells consist of a combination of fiber-reinforced cross-ply and piezothermoelastic layers. The initial stresses are generated by either a temperature change and/or an electric field. Sensitivity coefficients are also evaluated and used to study the sensitivity of the vibrational response to variations in the different mechanical, thermal and piezoelectric material properties of the shells. Both the temperature change and the radial component of the electric field are assumed to have uniform distribution in each layer of the shells. A linear constitutive model is used, and the material properties are assumed to be independent of both the temperature and the electric field. The thermoelectroelastic response of the shell is subjected to time-varying displacements, strains, and stresses, and the free vibration response is studied. A mixed formulation is used with the fundamental unknowns consisting of the increments of the three transverse stress components and the three displacement components of the shell. Each of the fundamental unknowns is expressed in terms of a double Fourier series in the axial and circumferential surface coordinates. A state space approach is used to generate the vibrational response and to evaluate the sensitivity coefficients. A sublayer method is used for evaluating vibration frequencies and their sensitivity coefficients. Numerical results are presented showing the effects of variation in the shell thickness, and the location of the piezothermoelastic layers on the vibration frequencies and their sensitivity coefficients.

Blood vessels acoustical diagnostics at the echolocation mode

Blood vessels biomechanical models in the form of multilayered anizothropic viscoelastic cylindrical shells with viscoelastic compressible biotissue from their one side and blood flow (taken as a compressible visco-elastic fluid) from the other side have been built. The vessels’ acoustical resonant and antiresonant frequencies for middle-sized and large arteriole (veinlet), artery (vein), and aorta, both within the vacuum and within their biological medium, have been detected. Blood vessels’ models that imitate such pathologies as arteriosclerosis and diabetes are elaborated. The informative frequency range for these vessels pathologies lays within 60 Hz–6 MHz. The lower spectrum of the range deals with the large vessels, the upper one deals with middle-sized and small vessels. The most probable detected vessels’ acoustical resonances respond to the first three oscillation modes. Thanks to the fact that blood vessels have an elastic modulus less by the factor 10E3⋅⋅⋅10E6, then the well-known ‘‘metallic’’ or plastic shells’ elastic moduli, their (vessels’) dispersion characteristic as well as their modus of interaction between the moving blood column oscillations and the vessel itself, has quite a different character. This is due to the low sound propagation velocity of the longitudinal and shear waves in the vessel when compared with the velocity of the same waves within the viscoelastic blood. A diabetes case is detected by blood viscosity changes, that cause the obvious (up to 30%) vessel’s main resonance shift. Arteriosclerotic pathologies cause the appearance of an extra two or three resonances next to the main resonance of the vessel given, and they can be detected in the echosignal when compared to this vessel type anatomical standard that is filed in a computer database. Blood flow rate determination in the vessel is a trivial procedure. The suggested technique has been approved in vitro on the canina vessels’ models and is confirmed in clinical conditions (with real patients).

Three-dimensional analytical solutions for coupled thermoelectroelastic response of multilayered cylindrical shells

Analytical three-dimensional solutions are presented for the coupled thermoelectroelastic response of multilayered hybrid composite cylindrical shells. The shells consist of a combination of fiber-reinforced cross-ply and thermoelectroelastic layers. Both the thermoelectroelastic static response and its sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the response to variations in the different mechanical, thermal, and piezoelectric material properties of the shells. A linear constitutive model is used, and the material properties are assumed to be independent of the temperature and the electric field. A mixed formulation is used with the fundamental unknowns consisting of the three transverse stress components ; the three displacement components; the transverse component of the electric displacement field ; the electric potential ; the transverse heat-flux component ; and the temperature change. Each of the fundamental unknowns is expressed in terms of a double Fourier series in the surface coordinates. A state-space approach is used to generate the static response and to evaluate the sensitivity coefficients. The response and sensitivity coefficients of the shell are obtained by using a modified Frobenius method and a sublayer method. Numerical results are presented showing the effects of variation in the geometric parameters of the shells on the different response quantities and their sensitivity coefficients.

Free vibration response of multilayered orthotropic fluid-filled circular cylindrical shells

A theoretical analysis for the free vibration of multilayered orthotropic circular cylindrical shells filled with non-viscous, incompressible fluid has been developed. Transverse shear and rotary inertia terms are included in the thin shell theory used herein. Axial dependence of modal forms is taken in the form of simple Fourier series instead of exponential axial dependence which is more commonly used. The approximate method adopted here yields a polynomial equation in the frequency parameter which can then be solved to study the influence of boundary conditions on the vibration characteristics. Some results in the case of a simply-supported fluid-filled shell are given here. The effect of the frequency response due to variations in the fluid height is studied. The effect on the natural frequencies of variation in the axial and meridional stiffness of the shell is also analysed.

A refined theory of the vibrations of a cylindrical shell based on an expansion in series of the normal displacement

A refined theory of vibrations of a multilayer orthotropic cylindrical shell based on the method of hypotheses [1, 2] and an expansion of the normal displacement in series in terms of the thickness of the shell [3] is considered. The fact that the results are intended to be used in practical structures determines the set of selected hypotheses.

Scattering from an advanced composite cylindrical shell

With advanced composite materials forming parts of the aircraft skins, the study of their electromagnetic effects, such as the shielding properties of the composite shield, the antenna characteristics with the composite ground, and the scattering phenomena due to the composite scatterer, becomes an important issue in electromagnetic compatibility. A field analysis of scattering from an advanced composite cylindrical shell is given. Based on a theory used to describe the electromagnetic field in an anisotropic, multilayered, and lossy cylindrical shell structure, numerical results regarding monostatic and bistatic echo widths are presented for graphite/epoxy and boron/epoxy fiber-reinforced composite ones. Particularly, the parameters to influence the scattering characteristics, such as material property, cylinder radius, fiber orientation pattern, polarization (TE or TM), and frequency of incident wave are investigated in detail.

Analysis of free damped vibrations of laminated composite cylindrical shells

Damped free vibrations of multilayered composite cylindrical shells are investigated. Vibration and damping analysis of cylindrical shells is performed by using the first-order shear deformation theory (FOSDT). Based on other researchers' works, two damping models are developed, i.e., the energy method (EM), and the method of complex eigenvalues (MCE). Several numerical examples of the damped free vibration problem of laminated composite cylindrical shells have been solved and comparison has been made with the results of other authors.

EFFECTS OF BOUNDARY CONDITIONS ON FREQUENCIES OF A MULTI-LAYERED CYLINDRICAL SHELL

A formulation based on Love's first approximation theory and with beam functions used as axial modal functions in the Ritz procedure is used to study the effects of boundary conditions on the free vibration characteristics for a multi-layered cylindrical shell. Altogether, nine different boundary conditions are considered. Four of the boundary conditions are with ends having the same end conditions: clamped–clamped, free–free, simply supported–simple supported and sliding–sliding. The other five boundary conditions are with ends having different end conditions: clamped–free, clamped–simply supported, clamped–sliding, free–simply supported and free-sliding. Mode shapes for the fundamental frequencies of nine boundary conditions are also presented. To validate the analysis, comparisons of frequency parameters with those from exact three-dimensional linear elasticity analysis, Flügge theory, higher order displacement analysis and shear deformation theory in the literature are made; very good agreement is achieved by using the present method with results available in the literature.

A three-dimensional asymptotic analysis of anisotropic inhomogeneous and laminated cylindrical shells

An asymptotic for anisotropic inhomogeneous cylindrical shells is formulated on the basis of three-dimensional elasticity withouta priori assumptions. The inhomogeneities are considered varying in the radial direction, thus including the important case of laminated composite shells in which the material properties are piecewisely constant through the thickness. Reformulation and nondimensionalization of the basic three-dimensional elasticity equations reveal that the problem can be treated by means of asymptotic expansion. By using asymptotic expansion and successive integration, we show in a natural and consistent manner that the asymptotic theory gives rise to two-dimensional shell equations, in forms similar to those in the classical laminated shell theory (CST), at each level of approximation. Thus the three-dimensional asymptotic solution for the problem is no more difficult to obtain than that based on CST. The asymptotic solution can be improved by determining the higher-order modifications in a systematic way. Various through-thickness effects can be accounted for hierarchically. The performance of the theory is illustrated by comparing the asymptotic solutions with the available numerical results for a homogeneous and for a multilayered cross-ply cylindrical shell under lateral loads.

Free vibrations of a rotating multi-layered cylindrical shell

In this paper parametric studies on the frequency properties of a rotating multi-layered cylindrical shell are undertaken. The equations of motion for the rotating multi-layered shell, which consider the effects of centrifugal, Coriolis and the initial hoop tension, are formulated using Love's first approximation theory. The analysis is carried out using closed-form solutions for the simply supported cylindrical shell. Results are presented for the frequency characteristics at different modes, geometric properties and different layered configurations of the rotating cylindrical shell. Effects of centrifugal and Coriolis influence on the frequencies and vibratory displacement are also considered. The present method is found to be accurate when compared with results available in the literature.

Plane-wave shielding properties of anisotropic laminated composite cylindrical shells

The plane-wave shielding properties of advanced composite cylindrical shells are analyzed. Based on a rigorous theory that clearly displays the propagating nature of the electromagnetic field in an anisotropic, multi-layered, and lossy cylindrical shell structure. In this study, numerical results are presented for graphite/epoxg fiber-reinforced composite shells. In particular, the parameters that influence the shielding effectiveness, such as material properties, cylinder configuration, fiber orientation, and incident wave polarization, are investigated in detail. For design purposes, an empirical formula is also proposed to estimate the shielding effectiveness in the lower frequency range. Finally, a sharp reduction of shielding performance due to resonance is also examined.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An asymptotic theory for dynamic response of anisotropic inhomogeneous and laminated cylindrical shells

An asymptotic theory is developed for dynamic response of anisotropic inhomogeneous and laminated cylindrical shells. The formulation is based on three-dimensional elasticity without a priori assumption. By means of asymptotic expansion with multiple time scales, the basic equations are decomposed into differential equations of various orders which can be integrated successively. It is shown that the three-dimensional asymptotic solution to the problem can be determined hierarchically by solving the two-dimensional equations in the classical laminated shell theory. Modifications to the solution are obtained in a systematic way by treating the higher-order equations and eliminating the secular terms. Various thickness effects, such as transverse shear and rotary inertia, can be accounted for in a natural and consistent manner. It is demonstrated along the way that a uniform expansion that yields asymptotic solution valid regardless of the time span is obtained with the use of multiple time scales, whereas a straightforward expansion fails to produce valid results for long times. The theory is illustrated by determining the vibration characteristics of a multilayered cross-ply cylindrical shell.

Interaction between buckling modes of imperfect cylindrical composite shells

The problem of the postbuckling behavior and sensitivity to initial geometrical imperfections of multilayered composite cylindrical shells is solved with allowance for the interaction of different buckling modes. The solution is based on the Byskov-Hutchinson asymptotic method and nonlinear equations of a Timoshenko-type shell theory. Boroaluminum, boron fiber-reinforced plastic, and glass fiber-reinforced plastic shells with imperfections in the form of five superimposed modes of similar structure and geometry are investigated. Snapping loads with and without the interaction of buckling modes are calculated and compared. The evolution of the mode amplitudes in the prebuckling and postbuckling states and their ratio at the limit point is demonstrated. 13 refs., 3 figs., 1 tab.

Scattering from a multi-layered cylindrical shell containing a bulkhead

A multi-layered cylindrical shell is modeled with the direct global matrix approach (DGM). The DGM approach allows the shell to have multiple viscoelastic layers, which are modeled with the full 3-D equations of elastodynamics. The DGM formulation is numerically stable for the wave types of interest (membrane compression, membrane shear, and flexural waves). The shell also contains a thin elastic bulkhead, which is modeled with the Mindlin thin plate theory. This coupled system is excited by obliquely incident plane waves in a fluid medium that surrounds the shell. The scattering caused by the bulkhead is computed. The effects of viscoelastic layers are investigated. [Work supported by ONR.]