Annular Plate Structures Research Articles

Vibration of bolted composite cylindrical-cylindrical flanged shells considering contact characteristics

A semi-analytical model for bolted composite cylindrical-cylindrical flanged shells (BCCFS) considering the influence of the flange and the connection characteristics of the bolted flange joint is established. In the model, flanges are treated as annular plate structures and modeled using Kirchhoff plate theory. To simulate the connectivity performance of the bolted flange joint, a surface-spring model considering the pressure distribution characteristics is developed and applied to the model of the bolted structure. A method based on fractal contact theory is proposed to identify stiffness-related parameters of the surface-spring model, which avoids additional tensile experiments of the bolted joint. Sufficient modal tests are performed to validate the accuracy of the model. Furthermore, the effects of flange thickness, length ratio of two shells, and quantity of bolts on the free vibration characteristics of the structure are studied. The frequency veering phenomenon with the variation of size parameters is found and analyzed in depth.

A unified spectral-geometric model of FGM double conical/cylindrical/spherical shell coupled with annular plates

This paper presents the analysis of the free and force vibration characteristics of FGM double layered cylindrical/conical/spherical shell and annular plate coupled structures under various boundary conditions and coupled connection conditions. The spectral geometry method is utilized to represent the displacement variable for FGM shell and annular plate structures in the uniform form, which overcomes the discontinuity or jump phenomenon at the boundary. To simulate the boundary conditions and coupling connection relationship between the FGM plate and shell substructures, the artificial virtual spring technique is implemented by adjusting the stiffness values of linear or rotational springs. Based on the Rayleigh-Ritz procedure, the unified dynamic equations of the FGM double layered cylindrical/conical/spherical shell and annular plate coupled structures are derived. Numerical examples are provided to demonstrate the convergence of the proposed model, and the accuracy and correctness of the proposed analytical model are verified by comparing the results with the vibration results obtained by the finite element method. Furthermore, parametric analysis is conducted to investigate the effect of material parameters, geometric parameters, and position parameters on the inherent characteristics and steady-state response of the FGM double layered coupled structure under various boundary conditions. Overall, this paper contributes to the understanding of the dynamic behavior of FGM double layered coupled structures and provides a useful analytical tool for the design and optimization of such structures.

Natural frequency analysis of imperfect GNPRN conical shell, cylindrical shell, and annular plate structures resting on Winkler-Pasternak Foundations under arbitrary boundary conditions

The goal of the present research is to examine the Natural Frequencies (NFs) of perfect and imperfect Graphene Nanoplatelet Reinforced Nanocomposite (GNPRN) structures of revolution (conical and cylindrical shells and annular plate structures) resting on elastic foundations under general boundary conditions (BCs). The graphene nanoplatelet material is implemented to compose the nanocomposite enhanced by a polymeric matrix including porosities. The springs technique is applied to define the general BCs of GNPRN structures of revolution. Elastic foundations are described by two parameters, i.e., Winkler-Pasternak Foundations (WPFs). Additionally, Donnell's hypothesis and first-order shear deformation theory (FSDT) are employed to figure out the primary formulations associated with the GNPRN structures of revolution. In contrast, the equations of motion are found using Hamilton's principle. Then the equations of motion are then discretized using the well-known Generalized Differential Quadrature Method (GDQM). Next, the standard eigenvalue solution is assigned to obtain the NFs of the perfect/imperfect GNPRN structures of revolution. Finally, various benchmarks are addressed to verify the approach suggested for evaluating the NFs of the perfect/imperfect GNPRN structures of revolution. Furthermore, several novel examples highlight the effects of the change in geometrical and material properties, arbitrary boundary conditions, and WPFs on the NFs of the perfect/imperfect GNPRN structures of revolution.

Three-dimensional vibration analysis of thick functionally graded conical, cylindrical shell and annular plate structures with arbitrary elastic restraints

In the present work, a three-dimensional vibration analysis of thick functionally graded conical, cylindrical shell and annular plate structures with arbitrary elastic restraints is presented. The last two structures are obtained as special cases of the conical shell. The effective material properties of functionally graded structures vary continuously in the thickness direction according the general four-parameter power law distributions in terms of volume fraction of constituents, and are estimated by Voigt’s rule of mixture. The exact solution is obtained by means of variational principle in conjunction with modified Fourier series which is composed of a standard Fourier series and some auxiliary functions. Validity and accuracy of the current method are demonstrated by comparing the present solutions with existing results. Numerous new results are given for functionally graded conical, cylindrical shells and annular plates with various boundary conditions including classical and elastic boundary conditions. Parametric investigations are carried out to study the effects of geometrical parameter, boundary conditions and material profiles on free vibration of functionally graded structures.

A numerical solution for vibration analysis of composite laminated conical, cylindrical shell and annular plate structures

This paper focuses on the free vibration analysis of composite laminated conical, cylindrical shells and annular plates with various boundary conditions based on the first order shear deformation theory, using the Haar wavelet discretization method. The equations of motion are derived by applying the Hamilton’s principle. The displacement and rotation fields are expressed as products of Fourier series for the circumferential direction and Haar wavelet series and their integral along the meridional direction. The constants appearing from the integrating process are determined by boundary conditions, and thus the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equations. Then natural frequencies of the laminated shells are obtained by solving algebraic equations. Accuracy, stability and reliability of the current method are validated by comparing the present results with those in the literature and very good agreement is observed. Effects of some geometrical and material parameters on the natural frequencies of composite shells are discussed and some representative mode shapes are given for illustrative purposes. Some new results for laminated shells are presented, which may serve as benchmark solutions.

A Gas Switch Triggered by a Microhollow Cathode Discharge (MHCD) Array With Lower Trigger Energy

A microhollow cathode discharge (MHCD) array was operated at atmospheric pressure with a pulse voltage of 2.5 kV supplied by a trigger circuit. Triggered by this MHCD array, a gas switch with an annular plate structure operated under a voltage of 27 kV with a fall time of 30 ns and a current of 400 A with a rise time of 15 ns was investigated. It is used for discharging the charge stored in a capacitor of 4 nF through a resistor of 50 Ω. The advantages of the switch are obvious: a compact trigger with lower trigger voltage. An electrical model including MHCD capacitance is built, and the simulation results agree well with the experimental results.

2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures

This paper focuses on the dynamic behavior of functionally graded conical, cylindrical shells and annular plates. The last two structures are obtained as special cases of the conical shell formulation. The first-order shear deformation theory (FSDT) is used to analyze the above moderately thick structural elements. The treatment is developed within the theory of linear elasticity, when materials are assumed to be isotropic and inhomogeneous through the thickness direction. The two-constituent functionally graded shell consists of ceramic and metal that are graded through the thickness, from one surface of the shell to the other. Two different power-law distributions are considered for the ceramic volume fraction. The homogeneous isotropic material is inferred as a special case of functionally graded materials (FGM). The governing equations of motion, expressed as functions of five kinematic parameters, are discretized by means of the generalized differential quadrature (GDQ) method. The discretization of the system leads to a standard linear eigenvalue problem, where two independent variables are involved without using the Fourier modal expansion methodology. For the homogeneous isotropic special case, numerical solutions are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Nastran, Straus, Pro/Mechanica. Very good agreement is observed. Furthermore, the convergence rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good. Different typologies of non-uniform grid point distributions are considered. Finally, for the functionally graded material case numerical results illustrate the influence of the power-law exponent and of the power-law distribution choice on the mechanical behavior of shell structures.

Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution

Based on the First-order Shear Deformation Theory (FSDT) this paper focuses on the dynamic behavior of moderately thick functionally graded conical, cylindrical shells and annular plates. The last two structures are obtained as special cases of the conical shell formulation. The treatment is developed within the theory of linear elasticity, when materials are assumed to be isotropic and inhomogeneous through the thickness direction. The two-constituent functionally graded shell consists of ceramic and metal. These constituents are graded through the thickness, from one surface of the shell to the other. A generalization of the power-law distribution presented in literature is proposed. Two different four-parameter power-law distributions are considered for the ceramic volume fraction. Some material profiles through the functionally graded shell thickness are illustrated by varying the four parameters of power-law distributions. For the first power-law distribution, the bottom surface of the structure is ceramic rich, whereas the top surface can be metal rich, ceramic rich or made of a mixture of the two constituents and on the contrary for the second one. Symmetric and asymmetric volume fraction profiles are presented in this paper. The homogeneous isotropic material can be inferred as a special case of functionally graded materials (FGM). The governing equations of motion are expressed as functions of five kinematic parameters, by using the constitutive and kinematic relationships. The solution is given in terms of generalized displacement components of the points lying on the middle surface of the shell. The discretization of the system equations by means of the Generalized Differential Quadrature (GDQ) method leads to a standard linear eigenvalue problem, where two independent variables are involved without using the Fourier modal expansion methodology. Numerical results concerning six types of shell structures illustrate the influence of the power-law exponent, of the power-law distribution and of the choice of the four parameters on the mechanical behaviour of shell structures considered.

Dynamic Relaxation Nonlinear Viscoelastic Analysis of Annular Sector Composite Plate

The geometrically nonlinear laminated annular plate structure with nonlinear viscoelastic orthotropic composite is considered using the dynamic relaxation (DR) method for the first time in the present study. The DR technique in conjunction with the finite difference discretization is used to study the behavior of a Mindlin plate. The plate is made of nonlinear viscoelastic orthotropic material expressed by the Schapery single integral model. A recursive-iterative formulation is implemented for the hereditary integral of the material. Under uniform lateral pressure and clamped and hinged edged constraints, the unsymmetrical laminated sector plate deformation is predicted in different times. The present results are compared with the elastic finite element (FE) generated numerical results. The correlations are very satisfactory. The load-center deflections for linear and nonlinear viscoelastic material plate along the symmetrical radial line for elastic and viscoelastic plate are illustrated. The dimensionless deflection results for up to 480min are predicted to show the creep behavior of the material. Finally, the dimensionless stress couple results are obtained after 8 h creep time for a graphite/epoxy composite plate.

Nonlinear buckling of microfabricated thin annular plates

Annular plate structures are commonly used in MEMS devices, particularly in pumps and valves. In MEMS applications, large nonlinear deflections are routinely achieved. In this paper, the nonlinear buckling of a thin elastic annular plate under a compressive radial force acting in the plane of the plate is considered. Although the critical loads at which buckling starts can be determined by solving a linear eigenvalue problem, the large deflection behavior of a buckled plate beyond the critical loads can be described by the nonlinear theory proposed by von Kármán. The buckling loads of the annular plate for various boundary conditions are calculated and the post-buckling behaviors are examined. Interestingly, the buckling of an annular plate exhibits a supercritical pitchfork bifurcation. Thus, the post-buckling behavior is stable and will not collapse catastrophically. Several design implications for microfabricated structures, in particular microvalves, are also given.

COUPLED FREQUENCIES OF A FRICTIONLESS LIQUID IN A CIRCULAR CYLINDRICAL TANK WITH AN ELASTIC PARTIAL SURFACE COVER

If the free liquid surface in a circular cylindrical container is partially covered by a structural element, the natural frequencies of the liquid are exhibiting increased magnitude. In addition, a much calmer liquid motion results from such coverages. In order to save structural weight, such devices may exhibit elastic behavior. The following investigation treats the hydroelastic problem of the interaction of liquid sloshing with an elastic annular plate structure attached to the cylindrical sidewall. It was found that decreasing rigidity of the annular plate exhibits less increase of the natural frequencies than that of a rigid plate. The increase of the plate width and a decrease of the Bond number increases the natural frequency drastically.