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

Free vibration analysis of cylindrical shells using the Haar wavelet method

This paper focuses on an analysis of free vibration of thick rotating stiffened composite cylindrical shells with different boundary conditions. The analysis is performed on the basis of a three-dimensional theory by using the layerwise-differential quadrature method (LW-DQM). The equations of motion are derived employing Hamilton’s principle. In order to accurately allow for the thickness effects, a layerwise theory is used to discretize the equations of motion and related boundary conditions through the thickness of the shells. Then, the equations of motion and the boundary conditions are transformed into a set of algebraic equations by using the DQM in the longitudinal direction. This study demonstrates the applicability, accuracy, stability, and fast rate of convergence of the present method in free vibration analyses of rotating stiffened cylindrical shells. The presented results are compared with those of other shell theories obtained by conventional methods and with a special case where the number of stiffeners approaches zero, i.e., an nonstiffened cylindrical shell, and excellent agreements are achieved. Finally, some new results are presented, which can be used as benchmark solutions for future investigations.

Free vibration analysis of laminated closed conical, cylindrical shells and annular plates with a hole using a meshfree method

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

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

Bending analysis of a functionally graded circular plate with clamped and simply supported boundary conditions is carried out. Material properties of the plate are assumed to be functionally graded in two directions, namely in the radial direction and through the thickness of the plate, obeying exponential distribution laws. Poisson’s ratio is assumed to be constant throughout the plate. Governing equations of a circular plate with material properties varying only through the thickness of the plate, based on the third order shear deformation theory are employed. In order to carry out the bending analysis of a two directional functionally graded circular plate, the plate is divided into number of annular plates with material properties graded only through the thickness. Material properties of each annular plate are defined by the corresponding exponential grading rule and the radial position of its center, hence these properties are assumed to be constant for each annular plate but different from its adjacent plates. Imposing the overall boundary conditions and compatibility conditions of adjacent annular plates, the governing equations of all annular plates are obtained and solved simultaneously. The analytical results are compared with the results obtained by the first order shear deformation theory and finite element method which are found to be in good agreement.

Stability and free vibration analyses of double-bonded micro composite sandwich cylindrical shells conveying fluid flow

Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion

Acoustic radiation from shear deformable ring-stiffened laminated composite cylindrical shell submerged in flowing fluid

Benchmark solution for transverse vibration of annular Reddy plates

An exact solution procedure is presented for solving free vibration problems for laminated composite noncircular cylindrical shells. Based on the classical lamination theory, strain energy and kinetic energy functional are first derived for shells having arbitrary layer stacking sequences. These functional are useful for a general analysis based upon energy principles. However, in the present work equations of motion and boundary conditions are obtained from the minimum conditions of the Lagrangian (Hamilton’s principle). The equations of motion are solved exactly by using a power series expansion for symmetrically laminated, cross-ply shells having both ends freely supported. Frequencies are presented for a set of elliptical cylindrical shells, and the effects of various parameters upon them are discussed.

This paper deals with frequency optimization of symmetrically laminated angle-ply annular sector plates. The design objective is the maximization of the fundamental frequency and the design variable is the fiber orientation in the layers. The first order shear deformation theory is used for the finite element solution of laminates. Nine-node Lagrangian rectangular plate element which have five degrees of freedom per node is used for the finite element solution of the laminated annular sector plates. The modified feasible direction method is used for the optimization routine. For this purpose, a program based on FORTRAN is used. The numerical analysis is carried out to investigate the effects of annularity, boundary conditions and sector angle on the optimal designs and the results are shown in tabular and graphical forms. Finally, the obtained results are compared. It can be shown that the parameters have a key role on the optimum design of laminated annular sector plates.

A layerwise-differential quadrature method (LW-DQM) is developed for the vibration analysis of a stiffened laminated conical shell. The circumferential stiffeners (rings) and meridional stiffeners (stringers) are treated as discrete elements. The motion equations are derived by applying the Hamilton’s principle. In order to accurately account for the thickness effects and the displacement field of stiffeners, the layerwise theory is used to discretize the equations of motion and the related boundary conditions through the thickness. Then, the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equations applying the DQM in the meridional direction. The advantage of the proposed model is its applicability to thin and thick unstiffened and stiffened shells with arbitrary boundary conditions. In addition, the axial load and external pressure is applied to the shell as a ratio of the global buckling load and pressure. This study demonstrates the accuracy, stability, and the fast rate of convergence of the present method, for the buckling and vibration analyses of stiffened conical shells. The presented results are compared with those of other shell theories and a special case where the angle of conical shell approaches zero, i.e. a cylindrical shell, and excellent agreements are achieved.

Numerical investigation of functionally graded cylindrical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery

Frequency analysis of rotating truncated conical shells using the Haar wavelet method