Three-layer Cylindrical Shells Research Articles

Investigation of the influence of the elastic medium on the dynamic behavior of a three-layer elliptical cylinder under non-stationary loading

Dynamic transient processes are studied and the results of evaluating the influence of an elastic medium on the behavior of a three-layer cylindrical shell structure of elliptical cross-section under non-stationary impulse loading are given. The used model of the theory of shells and rods by S. P. Tymoshenko, taking into account independent static and kinematic hypotheses for each layer of the structure. Numerical calculations of normal deflections and normal stresses of the load-bearing layers of the structure, which determine its stress-strain state (SSS), have been performed. Variants of the structure without a polymer aggregate and with a discrete-symmetric rib-reinforced aggregate are considered. A comparative analysis of the deflections and stresses of the load-bearing layers of the structure in the absence of light aggregate and in its presence is given.Numerical results regarding the dynamics of the three-layer structure were obtained using the finite element method.

Composite cylindrical shells with auxetic core on elastic foundation: A nonlinear dynamic analysis

This paper investigated vibration analyses of a composite cylindrical shell consisting of a core with negative Poisson's ratios resting on elastic foundation subjected to pre-loaded axial compression and external excitation force. Governing equations are driven based on Donnell's improved shell theory ignoring the shallowness of cylindrical shells and, with the help of Galerkin's method, Volmir's assumption, and Runge-Kutta's fourth-order method, the dynamical analysis of shells is studied. The purpose of this article is to discuss both the linear and nonlinear aspects of the structure's vibration. Furthermore, several parametric examples are presented and discussed to show how different parameters affect the three-layer cylindrical shell oscillation. To ensure the accuracy and the precision of the numerical results, the proposed method is compared with other literature attempts.

Influence of the Contact Layer on the Stress–Strain State of a Three-Layer Cylindrical Shell

Influence of the Contact Layer on the Stress–Strain State of a Three-Layer Cylindrical Shell

Exact solution of a geometrically nonlinear problem for a long three-layer cylindrical panel of oval section

A statement is given and an exact solution of a geometrically nonlinear problem is given for a long open three-layer cylindrical shell of an oval cross-section susceptible to transverse shear under the action of a uniform surface load. The main equations are written according to the geometrically nonlinear theory of smooth shells in the quadratic approximation, in which Tymoshenko's hypotheses hold for the entire package of shell layers. The solution of the problem is obtained in a parametric form with the value of the tangential force as a parameter. For a shell with hinged longitudinal edges, the exact values of the components of the stress-strain state were obtained, the limit values of the generalized geometric parameter were determined, and a system of equations for finding the critical load was constructed. As partial cases, the obtained solution yields the corresponding results for the Kirchhoff–Leav model, the shell of a circular cross-section, and the single-layer shell. The obtained results can be a reference for approximate and numerical methods.

Analytical Calculation Method of Motor Natural Frequencies Based on Equivalent Model of Three-Layer Cylindrical Shell

Accurate calculation of natural frequencies is significant for accurate prediction and suppression of motor vibration and noise. In order to reduce the errors caused by simplified structure in the analytical method, a new analytical calculation method (ACM) of the natural frequencies of the motor is proposed in this paper. The motor enclosure, stator yoke, stator teeth and windings are equivalent to a three-layer cylindrical shell model. The motor feet are equivalent to the axial ribs on the cylindrical shell. The artificial springs are used to simulate arbitrarily complex boundary conditions between the end covers and the enclosure. The combination of zig-zag theory and first-order shear deformation theory (FSDT) is used to calculate the natural frequencies of the equivalent model of the motor proposed in this paper. According to the zig-zag theory model, the respective displacement function and energy equation are established for each cylindrical shell. The different structural dimensions and material properties between the motor enclosure, stator core and windings are considered. The first-order shear deformation theory is adopted in the displacement model of each layer of cylindrical shell, which considers transverse shear deformation, rotational inertia and orthotropy of materials. Finally, the accuracy of the analytical calculation method proposed in this paper is verified by finite element simulation (FES) and hammering method modal test (HMMT).

Influence of the contact layer on the stress-strain state of a three-layer cylindrical shell

The results of numerical experiments and studies of various forms of discrete filler, carried out at the Department of Building Structures (BS) and Hydraulic and Technical Structures (HTS) of the Dagestan State Technical University, are presented, which made it possible to determine the geometry of discrete fillers corresponding to the radius of the shell curve in the form of a truncated pyramid and corrugation. Keywords: three-layer structure, glue line, cylindrical shell, truncated pyramid, corrugation. hairulla213@mail.ru, yarahmedov94@mail.ru

Natural vibrations of composite cylindrical shells partially filled with fluid

The article presents the results of studies of natural vibrations of circular vertical multilayer cylindrical shells completely or partially filled with a stationary compressible fluid and subjected to hydrostatic load. The behavior of the elastic structure and the fluid medium is described using the classical shell theory and the Euler equations. The effects of sloshing on the free surface of the fluid are not considered. The linearized equations of motion for shells together with the corresponding geometric and physical relations are reduced to a system of ordinary differential equations with respect to new unknowns. The acoustic wave equation is transformed to a system of differential equations using the generalized differential quadrature method. The formulated boundary value problem is solved by Godunov’s method of orthogonal sweep. The natural frequencies of vibrations are calculated based on the combination of a stepwise procedure and subsequent refinement by the method of dividing in half. The reliability of the obtained results is verified by comparison with the known numerical solutions. The dependence of low vibration frequencies on the reinforcing angle and the level of the structure filling with a fluid for simply supported rigidly clamped and cantilevered two-layer and three-layer cylindrical shells with a fluid are analyzed in detail. It is demonstrated that the possibility of changing the frequencies and vibration modes through a suitable choice of the layer arrangement scheme and the reinforcing angle of the composite material is notably determined by a prescribed combination of boundary conditions for an elastic body.

Stability of a three-layer cylindrical shell

Problem. The article presents the results of studies of the stability of a three-layer cylindrical shell. Factors that have a significant impact on the strength and stability of the three-layer cylindrical shell were taken into account, namely the reduced modules of elasticity of the three-layer wall. Goal. The purpose of the study is to develop a methodology for calculating the stability of a three-layer cylindrical shell, which will significantly improve the calculation practice of such structures in relation to determining the critical external pressure for a three-layer cylindrical shell. Methodology. The method of variational calculation using the Euler equation of the mixed variational problem was used to determine the critical pressure. To determine the stability of the three-layer cylindrical shell, those factors that have a significant impact on its strength and stability were taken into account, namely the reduced modulus of elasticity of the three-layer wall. The bending stiffness Dh was replaced by the bending stiffness of the three-layer shell taking into account the shear deformation. Results. The current state of the issue of the stability of a three-layer cylindrical shell has been studied. Using the methods of variational calculation with the Euler equation of the mixed variational problem, the equation of the condition of equality of the internal and external forces of the orthotropic structure, which is in a state of indifferent equilibrium with radial displacement, is compiled. Accepting the previously obtained equation for radial movements and substituting it into the equation for the potential energy of the system per unit length, we obtained the equation for determining the critical pressure. The obtained analytical solution was tested for the design of the crane running wheel, which has an elastic insert. We will get pkr=1267 MPa. For crane running wheels, the allowable pressure of the wheel on the rail is taken within 250 MPa, that is, we have a reserve of stability of the rail nc=1267/250=5.1. As you can see, the margin of stability is more than sufficient. In addition, a comparison was made between the obtained method of calculating the stability of a three-layer cylindrical shell and the method described in [20]. Originality. A new method of calculating a three-layer cylindrical shell under the action of external pressure has been developed. A quantitative assessment of the critical pressure of the traveling crane wheel, which has an elastic insert, was carried out. Practical value A technique for determining the critical pressure of a three-layer cylindrical structure under the action of external pressure has been created.

Stationary stress-strain state of a three-layer viscoelastic cylindrical shell under normal loading

Multilayer viscoelastic cylindrical shells have found their wide application in construction, mechanical engineering, aircraft and rocket engineering. The aim of the work is to investigation the reaction of an infinitely long three-layer cylindrical shell to the action of a normal load moving along an axis with a constant to resonant velocity. The paper presents a mathematical formulation of the problem, developed solution methods and obtained numerical results for the problems of stationary deformation of an infinitely long three-layered cylindrical shell under normal loading. The equations of motion of the bearing layers satisfy the Kirchhoff-Love hypotheses. The solution methods are based on the joint application of the integral Fourier transform in the axial coordinate and the decomposition of all given and desired quantities into Fourier series in the angular coordinate. The outer and inner shells satisfy the Kirchhoff-Love hypotheses. The Lame viscoelasticity equation is used as a linear equation of the filler motion. An effective algorithm for solving the problem of osculations of a three-layer viscoelastic cylindrical shell under normal loading has been developed on a computer. Critical velocities of wave propagation in a three-layer shell under the influence of moving loads are found.

Investigation of the dynamic behavior of three-layer cylindrical shells of elliptical form under internal axisymmetric pulse loading

The results of the assessment of the dynamic behavior of three-layer cylindrical shells of circular and elliptical cross-sections under internal impulse loading are given. The finite-element method was used to calculate the indicators of the stress-strain state (SSS) of such structures by the NASTRAN software complex. The values normal deflections and normal stresses of circular and three elliptical forms of intersection of cylindrical structures are determined. A comparative analysis of the values of these indicators with the results of the dynamic behavior of uneven cylindrical shells was performed.
 The shape and curvature of the cross section of three-layer cylindrical thin-walled composite shells significantly affect their SSS under dynamic impulse loading.
 Replacing the circular shape of the cross section of a cylindrical structure with an elliptical one and increasing the ratio of the semiaxes of the elliptical section leads to an increase in normal deflections and normal stresses of the middle surface of the structure.

Parametric Resonance of a Three-Layer Cylindrical Composite Shell Supported by Longitudinal Ribs and a Cylinder under Action of Time-Varying Axial Force

Parametric Resonance of a Three-Layer Cylindrical Composite Shell Supported by Longitudinal Ribs and a Cylinder under Action of Time-Varying Axial Force

Determination of the stability of a three-layer shell of a traveling wheel with light filler

Purpose. Development of a calculation methodology for three-layer cylindrical shell stability, which will significantly improve the calculation practice for these structures regarding the determination of critical external pressure. Methodology. When determining the critical external pressure, the method of variational calculation using the Euler equation of the mixed variational problem was used. To determine three-layer cylindrical shell stability, the factors of significant influence on its strength and stability were taken into consideration, namely the reduced modulus of a three-layer wall elasticity. Bending stiffness Dh was substituted with flexural stiffness of three-layer shell with account for the shear deformation. Findings. The current situation of the three-layer cylindrical shell stability issue is investigated. Using the variational calculation methods via the Euler equation of the mixed variational problem an equation is composed of equality condition of inner and external force action of an orthotropic structure, which is under the state of neutral equilibrium with radial displacement. The previously obtained equation for radial displacements having been taken and applied to the system potential energy per unit of length equation, an equation for the critical pressure determination is determined. The analytical solution obtained was proposed for the structure of the crane travelling wheel with an elastic insert. Pcr 1267MPa was obtained. The allowable wheel pressure on rail for the crane travelling wheels is adopted to be within 250 MPa, i.e. the available stability margin is nc 1267/250 5.1. As we can see, the stability margin is more than sufficient. Originality. A new methodology for the three-layer cylindrical shell under external pressure calculation is developed. A quantitative assessment of the crane travelling wheel with flexible insert critical pressure is carried out. Practical value. A determination methodology for critical pressure of a three-layer cylindrical structure under external pressure is created.

Higher-order hygro-magneto-electro-thermomechanical analysis of FG-GNPs-reinforced composite cylindrical shells embedded in PEM layers

Sandwich structures are applicable in different industries due to their high strength-to-weight ratio. So, the current work aims to present the study about vibrational behavior of three-layered cylindrical shells with graphene nanoplatelets (GNPs)-reinforced composite core and piezo-electro-magnetic (PEM) face sheets. The whole structure rests on the visco-Pasternak foundation, and it is also exposed to hygro-magneto-electro-thermal (HMET) loads. Epoxy has been selected as matrix and GNPs as reinforcing phases of the core, and based on the rule of the mixture and Halpin-Tsai micromechanical models, its effective values for hygro-thermo-mechanical properties are gained. Third-order shells theory which accounts the shear deformation effects is utilized to describe displacements. Employing extended Hamilton's principle for dynamic systems, the motion equations are attained. By ensuring the results' correctness after validating them with previously published papers, the effects of different parameters on the results are interpreted. The results depict that GNPs' dispersion patterns and their weight fraction play crucial roles in the vibrational response of the under consideration model. This work's findings may help design and manufacture more efficient engineering structures such as pressure vessels.

Vibrations of a Cylindrical Sandwich Shell with a Honeycomb Core Made Using FDM technology

Presented is a model of the dynamic deformation of a three-layer cylindrical shell with a honeycomb core, manufactured by fused deposition modeling (FDM), and skins reinforced with oriented carbon nano-tubes (CNT). A ULTEM 9085 thermoplastic-based honeycomb core is considered. To analyze the stress-strain state of the honeycomb core, a finite element homogenization procedure was used. As a result of this procedure, the dynamic response of the honeycomb core is modeled by a homogeneous orthotropic material, whose mechanical properties correspond to those of the core. The proposed model is based on the high-order theory, extended for the analysis of sandwich structures. The skin displacement projections are expanded along the transverse coordinate up to quadratic terms. The honeycomb core displacement projections are expanded along the transverse coordinate up to cubic terms. To ensure the integrity of the structure, shell displacement continuity conditions at the junction of the layers are used. The investigation of linear vibrations of the shell is carried out using the Rayleigh-Ritz method. For its application, the potential and kinetic energies of the structure are derived. Considered are the natural frequencies and modes of vibrations of a one-side clamped cylindrical sandwich shell. The dependence of the forms and frequencies of vibrations on the honeycomb core thickness and the direction of reinforcement of the shell skins have been investigated. It was found that the eigenforms of a sandwich shell are characterized by a smaller number of waves in the circumferential direction, as well as a much earlier appearance of axisymmetric forms. This means that when analyzing the resonant vibrations of a sandwich shell, it is necessary to take into account axisymmetric shapes. Changing the direction of reinforcement of the skins with CNTs makes it possible to significantly influence the frequencies of the natural vibrations of the shell, which are characterized by a nonzero number of waves in the circumferential direction. It was found that this parameter does not affect the frequencies of the axisymmetric shapes of the shell under consideration.

Impact of engineering/technology factors and transient loads on the stress - strain state of a three-layer cylindrical shell

An issue of a stress-strain state of a three-layer cylindrical shell under variable loads has been considered. Assessment results of a three-layer cylindrical shell stress-strain state with regard to the physical and mechanical characteristics of an aggregate polymer filler and its reinforcement intensity by means of the stiffening rings rigidly connected to the shell coating are presented in the article. Calculations have been performed using the software Nastran. Values of displacements and stresses have been calculated by applying the direct transient dynamic process algorithm. The time interval was 0.0000025 sec, and the total number of steps was 200. Choice of the three-dimensional finite element type was conditioned by the need of acquiring more detailed and accurate calculation results. The finite element model included 8000 three-dimensional solid finite elements and 9360 nodes. Impact of the physical and mechanical characteristics’ parameters of integral polymeric filler through the stiffening rings on the shell’s stress-strain state under the axisymmetric inner impulse load has been investigated. Numerous results concerning dynamics of the three-layer structure, which have been obtained by the finite elements method, allow distinguishing the stress-strain state of a three-layered cylinder-type elastic structure at any moment within an analyzed time interval. Optimization of the shell design is recommended. Intensity of the polymeric filler reinforcement impacts considerably the stress-strain state of the shell, as well as its performance characteristics. Increasing the intensity of the shell’s polymeric layer reinforcement decreases considerably the deformation of the shell’s bearing layers. Comparison of the obtained results to the impact of other factors indicates the credibility of the approach used and that the unbiased information was received.

Block-Layer Approach for the Analysis of the Stress–Strain State of Three-Layer Irregular Cylindrical Shells of Rotation

Block-Layer Approach for the Analysis of the Stress–Strain State of Three-Layer Irregular Cylindrical Shells of Rotation

Propagation of Own Non- Axisymmetric Waves in Viscoelastic Three-Layered Cylindrical Shells

Propagation of Own Non- Axisymmetric Waves in Viscoelastic Three-Layered Cylindrical Shells

Stress–Strain State of Three-Layer Cylindrical Shells with Reinforced Light Core Under Nonstationary Loading*

Stress–Strain State of Three-Layer Cylindrical Shells with Reinforced Light Core Under Nonstationary Loading*

Vibration analysis of a sandwich cylindrical shell in hygrothermal environment

Abstract The sandwich structures are three- or multilayered structures such that their mechanical properties are better than each single layer. In the current research, a three-layered cylindrical shell including a functionally graded porous core and two reinforced nanocomposite face sheets resting on the Pasternak foundation is used as model to provide a comprehensive understanding of vibrational behavior of such structures. The core is made of limestone, while the epoxy is utilized as the top and bottom layers’ matrix phase and also it is reinforced by the graphene nanoplatelets (GNPs). The pattern of the GNPs dispersion and the pores distribution play a crucial role at the continuous change of the layers’ properties. The sinusoidal shear deformation shells theory and the Hamilton’s principle are employed to derive the equations of motion for the mentioned cylindrical sandwich shell. Ultimately, the impacts of the model’s geometry, foundation moduli, mode number, and deviatory radius on the vibrational behavior are investigated and discussed. It is revealed that the natural frequency and rotation angle of the sandwich shell are directly related. Moreover, mid-radius to thickness ratio enhancement results in the natural frequency reduction. The results of this study can be helpful for the future investigations in such a broad context. Furthermore, for the pipe factories current study can be effective at their designing procedure.

Dynamic Stability of a Three-Layer Cylindrical Shell Reinforced by Ring Ribs and a Hollow Cylinder under the Action of External Pulsing Pressure

Dynamic Stability of a Three-Layer Cylindrical Shell Reinforced by Ring Ribs and a Hollow Cylinder under the Action of External Pulsing Pressure