Free Vibration Analysis Of Shells Research Articles

A data-driven enhanced generalized differential quadrature algorithm in free vibration analysis of shells of revolution with free-form meridian and their combined structures

A data-driven enhanced generalized differential quadrature algorithm in free vibration analysis of shells of revolution with free-form meridian and their combined structures

Free vibration analysis of sandwich FGM shells using isogeometric B spline finite strip method

This paper presents a free vibration analysis of shell panels made of functionally graded material (FGM) in the form of the ordinary and sandwich FGM and laminated shells using the isogeometric B3-spline finite strip method (IG-SFSM). B3-spline and Lagrangian interpolation are employed along the longitudinal and transverse directions respectively in this type of finite strip. The introduced finite strip formulation is based on the degenerated shell method, which provides variable thickness, arbitrary geometries, and analysis of thin or thick shells. Validity of the obtained natural frequencies by IG-SFSM is checked by comparison with results extracted from references for similar cases in different examples. These examples incorporate several geometries, materials, boundary conditions, and continuous thickness variation. A comparison of these two kinds of results and their proximity showed that the introduced IG-SFSM is a reliable tool which can be used in analysis of shells with the aforementioned properties.

Coupled thermo-mechanical analysis of one-layered and multilayered isotropic and composite shells

This work considers the fully coupled thermo-mechanical analysis of one-layered and multilayered isotropic and composite shells. The temperature is assumed a primary variable as the displacement; it is therefore directly obtained from the model and this feature permits the temperature field to be evaluated through the thickness direction. Three problems are analyzed: - static analysis of shells with imposed temperature on the external surfaces; - static analysis of shells subjected to a mechanical load, with the possibility of considering the temperature field effects; - a free vibration problem, with the evaluation of the temperature field effects. In the first problem, imposing a temperature at the top and bottom of the shells, the static response is given in terms of displacements, stresses and temperature field; the proposed method is very promising if compared to a partially coupled thermo-mechanical analysis, where the temperature is only considered as an external load, and the temperature profile must be a priori defined (considering it linear through the thickness direction or calculating it by solving the Fourier heat conduction equation). A mechanical load is applied in the second problem. The fully coupled thermo-mechanical analysis gives smaller displacement values than those obtained with the pure mechanical analysis; the temperature effect is not considered in this latter approach. The third problem is the free vibration analysis of shells. The fully coupled thermo-mechanical models permit the effect of the temperature field to be evaluated: larger frequencies are obtained with respect to the pure mechanical models. Several refined theories with orders of expansion in the thickness direction, for displacements and temperature, from linear to fourth-order are obtained in the framework of Carrera's Unified Formulation. Both equivalent single layer and layer wise approaches are considered for the multilayered shells.

Free Vibration Analysis of Cylindrical Shells Supported on Parts of the Edges

Numerical studies of the free vibration analysis of open skewed circular cylindrical shells supported only on selected segments of the straight edges are presented in this paper. The uniform thickness shell geometry is defined by the radius, subtended angle and the length, all with reference to the middle surface. The open skewed circular cylindrical shell is modeled by dividing the reference surface into few patches and introducing upon them displacement nodal points and also five degrees of freedom in accordance with the first order shear deformable shell theory are assigned to each of these nodal points. The free vibration analysis of the shell structure is performed using two types of interpolating polynomials, viz. simple high order algebraic and Bezier, respectively. The number of nodal points per patch determines the order of the displacement polynomials. As a consequence considerably high-order polynomials are used in computations for the accurately converged results. Convergence studies are carri...

Free-vibration analysis of shells via a linearly conforming radial point interpolation method (LC-RPIM)

In this paper, free-vibration analysis of shells is carried out using a linearly conforming radial point interpolation method (LC-RPIM). The present formulation is based on the first-order shear deformation shell theory. A set of arbitrarily distributed nodes in local support domains is selected to perform interpolation, and radial and polynomial basis functions are employed to construct shape functions with Delta function property. Nodal integration, which is enforced by a strain-smoothing stabilization technique, is used to restore conformability and improve the accuracy of solutions. Comparisons of current solutions are made with existing results available in literature and good agreements are obtained. Numerical examples demonstrate that the present approach provides very stable and accurate results.

Higher‐order hybrid‐mixed axisymmetric thick shell element for vibration analysis

AbstractIn this study, we present free vibration analysis of shells of revolution using the hybrid‐mixed finite element. The present hybrid‐mixed element, which is based on the modified Hellinger–Reissner variational principle, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees to resolve the numerical difficulties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out by the Guyan reduction. Several numerical examples show that the present element with cubic displacement interpolation functions and consistent quadratic stress functions is highly accurate for the free vibration analysis of shells of revolution, especially for higher vibration modes. Copyright © 2001 John Wiley & Sons, Ltd.

A finite element formulation for free vibration analysis of shells of general shape

The free, undamped vibration analysis of a shell of general shape is formulated with a curved isoparametric trapezoidal finite element, including thickness shear deformations and without neglecting z R in comparison with unity and rotatory inertia effects with consistent mass matrix. The shell element with eight nodes and 40 d.f. is applicable for both thin and moderately thick shell analysis. The accuracy and efficiency of this proposed finite element are illustrated by examples and the results are compared with those obtained by other analytical and numerical methods. The comparisons show that the method yields very good results with a relatively small number of elements.

Free vibration analysis and optimisation of axisymmetric plates and shells—I. Finite element formulation

This paper deals with the free vibration analysis of shells of revolution using the finite element method. A family of variable thickness, curved C(0) Mindlin-Reissner axisymmetric finite elements is presented which include shear deformation and rotatory inertia effects. The accuracy, convergence and efficiency of these newly developed elements are explored through a series of free vibration analyses of axisymmetric shell structures and the results are compared with those obtained by other analytical and numerical methods. The comparisons show that the method yields very good results with a relatively small number of elements and that estimates for the higher modes can be obtained without any difficulties. A companion paper will consider the structural optimisation of axisymmetric shells undergoing free vibrations.

The collocation method for analyzing free vibration of shells of revolution with either internal or external fluids

A simple and effective method is developed in this paper for free vibration analysis of shells of revolution with either internal or external fluids. The fluid region is treated analytically by the use of eigenfunction expansions, and the collocation method using the roots of the orthogonal polynomial as collocation points is used to solve the integro-differential equations which describe the motion of the shell. The proposed approach is formulated in some detail. The versatility and accuracy are illustrated through several numerical examples. The method appears to be relatively easy to set up and gives satisfactory results.

On Vibrations of Shells of Revolution Using Bezier Polynomials

A very computationally efficient numerical technique for the free vibration analysis of shells of revolution is presented in this study. The generic segment of the shell structure is given in the form of a circular arc which revolves around the vertical axis. Displacement fields in each segment are represented by quintic Bezier functions which are shown in this investigation to have very desired characteristics. Accurate values of the dimensionless frequency parameter were obtained using only two to four shell segments of spherical, cylindrical, and conical shells and compared favorably with the results from the open literature. Complicated-shaped rotationally symmetric shell structures described by a series of circular arc segments tangential to each other at the juncture, can be analyzed without any approximation in geometry.

General free vibration analysis of shells of revolution using the spline finite element method

Free vibration analysis of shells of revolution using the spline finite element method is presented in this paper. The spline element, which is based on the classical thin shell theory, employs a set of B-spline shape functions for the interpolation of geometry as well as displacements. It has the merits of both the finite element method and splines interpolation. The efficiency and accuracy of the proposed element are illustrated by examples in the paper.

Use of higher order displacement functions in the free vibration analysis of shells of revolution having meridional singularities

A finite element technique in which higher order displacement functions are used in the analysis of vibration of shells of revolution with joints and poles is described. The joints typically arise where a meridional curve is made up from a number of different curves, as in the case of a cone-toroid cooling tower or a cone-cylinder chimney. A technique for overcoming the difficulties associated with the representation of the stress discontinuities at the joints when higher order displacement functions are used is discussed. A number of typical shells with joints are analysed by using this technique, and the results are found to compare very well with existing theoretical and experimental data. A pole of a shell of revolution is a point where the meridian intersects the axis of revolution, such as the apex of a spherical dome or the apex of a conical shell. It is shown that, in analysing such shells, it is not necessary to exclude the pole by introducing a small hole around it or to develop special elements. A cone-cylinder combination with an apex is analysed by using a combination of the techniques for analysing jointed shells and shells with poles. The calculated frequencies and mode shapes are shown to agree well with experimental results. It is demonstrated that the cone-cylinder combination with the apex can be idealized accurately by using a curved shell element with four nodal points. The “non-classical modes” of vibration reported in the experiment could not be predicted theoretically, even though the curved shell element was used and the value of the circumferential wave number n was not prescribed.