A New Solution Method for Vibration Analysis of Circular Cylindrical Thin Shells with a Circumferential Surface Crack

In this paper, we analyze the axisymmetric vibrations of a cylindrical shell of which the thickness varies in the axial direction by using the thin cylindrical shell theory and an improved thick cylindrical shell theory. We solve the equations of vibration exactly by using a series solution. As numerical examples, we obtain the natural frequencies and the mode shapes of cylindrical shells with both ends clamped, simply supported and free and examine the variations of the natural frequencies and the mode shapes for the variations of the thickness. And also, we make clear the influences of the shear deformation and the rotatory inertia upon the natural frequencies and the mode shapes.

This paper presents the study on natural frequency characteristics of a multiple layered cylindrical shell with ring support under internal pressure. The multiple layered cylindrical shell configuration is formed by three layers of isotropic materials where the inner and outer layers are stainless steel and the middle layer is aluminum. The isotropic multiple layered shell equations with ring support and internal pressure are established based on first order shear deformation theory (FSDT). The governing equations of motion were employed by using energy functional and by applying the Ritz method. The boundary conditions represented by end conditions of the multiple cylindrical shell are simply supported-simply supported (SS-SS), clamped-clamped (C-C), free-free (F-F), clamped-free (C-F), clamped-simply supported (C-SS), and free-simply supported (F-SS). The influences of internal pressure and ring support and the effect of the different boundary conditions on natural frequencies characteristics are studied. The results are validated by comparing them with those in the literature.

Numerical analysis of the creep crack constraint effects and the creep crack initiation for pressurized pipelines with circumferential surface cracks

The composite cylindrical shell pressure structure is widely used for autonomous underwater vehicle (AUV). To analyze the critical buckling problem of variable stiffness (VS) composite pressure structure of AUV, a discrete finite element (DFE) method based on the curve fiber path function is developed in this work. A design and optimization method based on the radial basis function surrogate method is proposed to optimize the critical buckling pressure for a VS composite cylindrical shell. Both the DFE and surrogate methods are verified to be valid by comparison with the experimental data from the listed references. The effects of the geometric parameter and fiber angle on the critical buckling pressure are studied for different cylindrical shell cases. The results indicate that the proposed simulation model and optimization method are accurate and efficient for the buckling analysis and optimization of a VS composite cylindrical shell. Optimization result shows that the optimum critical buckling pressure for the VS cylindrical shell is improved and is 21.1% larger than that of the constant stiffness cylindrical shell under the same geometric and boundary condition.

In this article the buckling of specially orthotropic laminated composite cylindrical shells is investigated. The nonlinear equilibrium equations based on the Sander's assumption of simplified nonlinear strain-displacement relations and the linearized stability equations for a circular cylindrical thin shell are considered. The equations include the rotations and transverse shear force. The resulting equations are improved compared to the Donnell stability equations. The mechanical and thermal buckling loads of a thin composite circular cylindrical shell based on Donnell and improved stability equations are obtained.

Circumferential Part-Through Cracks in Cylindrical Shells Under Tension

In this paper, the reliability of welded pressure pipe with circumferential surface crack was calculated by using three dimensional stochastic finite element method for A131 pipe steel. This method has overcome the shortcomings of conservative results in safety assessment with deterministic fracture mechanics method. The calculation of reliability was based on three dimensional elastic-plastic stochastic finite element programs which were developed by ourselves. The calculation results indicate that the external load has great effect on the reliability of the welded pipe. When the mean value of bending moment changes from 10000N.m to 20000N.m, the failure probability of the welded pipe will change from 3.3750×10-9 to 1.6794×10-1. When the mean value of moment is changed from10000N.m to 20000N.m, the failure probability of the welded pipe increases dramatically for the same circumferential crack opening angle, inner pressure and the crack depth. The method has put forward a new way for safety assessment of welded pipe with circumferential surface crack.

The present study aims at the investigation of free vibration analysis of thin cylindrical shells surrounded by an elastic medium, which is distributed over a particular length of the shell. The Love’s shell theory is utilized along with the Winkler foundation to obtain the governing equations of motion. An exact series expansion method of solution is employed for any arbitrary boundary conditions. The excellent accuracy of the obtained results is validated by comparing to the available literature. Moreover, several case studies are performed to provide an insight into the influence of some practically important parameters on free vibrations of circular cylindrical shells, including stiffness and length of the partial foundation. Finally, it is concluded that the proposed method can accurately determine the exact solution to the free vibration of shells partially surrounded by elastic foundations with any boundary conditions.

Based on the Donnell’s approximations of the thin shell theory, this paper presents solutions for the problem of free non-axisymmetric vibration of stepped circular cylindrical shells with cracks. The shell under consideration is sub-divided into multiple segments separated by the locations of thickness variations. It is assumed that at thejth step there exists a circumferential surface crack with uniform depthcj. The influence of circular cracks with constant depth on the vibration of the shell is prescribed with the aid of a matrix of local flexibility. The latter is related to the coefficient of the stress intensity known in the linear fracture mechanics. Numerical results are obtained for cylindrical shells of stepped thickness containing cracks at re-entrant corners of steps. Shells with various combinations of boundary conditions can be analyzed by the proposed method. Furthermore, the influences of the shell thicknesses, locations of step-wise variations of the thickness and other parameters on the natural frequencies are examined. The results can be used for the approximate evaluation of dynamic parameters of cylindrical shells with cracks and flaws.

Creep analysis of cylindrical shell by a finite difference method

The free bending vibration of single-walled carbon nanotubes (SWCNTs) is investigated in the present paper. A continuum approach based on nonlocal theory of beam bending is used for natural frequency computation. Analytical solutions of frequency equations are given for four types boundary conditions: clamped-free (C-F), simply-simply supported (S-S), clamped-simply supported (C-S) and clamped-clamped (C-C). The graphical representations of numerical results are shown for the first case of boundary conditions clamped end - free end.

Bending Vibrations of Carbon Nanotubes by Using Nonlocal Theory

Based on the viscoelastic material property of polyethylene pipe, software ANSYS was used to simulate and analyze the mechanical property of polyethylene pipe butt fusion joints with circumferential surface crack defects. The viscoelastic material creep parameters were characterized as Prony series and 1/4 node singular element was selected for meshing along the boundaries of the crack, then the stress intensity factor of polyethylene pipe butt fusion joints with circumferential surface crack was calculated under the uniform internal pressure. Through the finite element simulation, the result showed that polyethylene pipe were most likely to fracture failure when crack initiated. Thus the viscoelasticity of materials can be ignored when analyzing the stress intensity factor of circumferential surface cracks of polyethylene pipe. the main influencing factor of the circumferential crack defects was the ratio of the crack depth to the thickness of polyethylene pipe.

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

Some problems of the stability of cylindrical and conical shells