scholarly journals Dynamic Response of Shear-Flexible Cylindrical Isotropic Shells with Clamped Edges

2006 ◽  
Vol 13 (2) ◽  
pp. 103-116 ◽  
Author(s):  
Zafer I. Sakka ◽  
Jamal A. Abdalla ◽  
H.R.H. Kabir
Keyword(s):  
Free Vibration ◽  
Cylindrical Shells ◽  
Shell Element ◽  
Double Fourier Series ◽  
Analytical Investigation ◽  
Fourier Series Expansion ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Bench Mark ◽  
Approximate Methods

It is fundamental to obtain the natural frequencies and the corresponding mode shapes for cylindrical shells in order to determine their response to different dynamic loading. In this paper an analytical investigation to the free vibration response of moderately-thick shear flexible isotropic cylindrical shells with all edges clamped is presented. The Sander’s kinematic relations for moderately thick cylindrical shell panels are utilized to develop the governing partial differential equations in conjunction with the boundary conditions. A recently developed generalized Navier’s approach, based on a boundary continuous double Fourier series expansion, is used as a solution methodology. A parametric study is presented with respect to various thicknesses, length and radius of curvature of the shell panel. The convergence of the solution method is established numerically for various parametric properties. The present results are compared with the results obtained from finite element method using a four-node isoparametric shell element. The results thus presented should serve as bench-mark solutions for future comparisons with numerical and approximate methods for calculation of free vibration parameters of moderately-thick isotropic cylindrical shells.

Free vibration characteristics of delaminated composite pretwisted stiffened cylindrical shell

2017 ◽  
Vol 232 (4) ◽  
pp. 595-611 ◽  
Author(s):  
Mrutyunjay Rout ◽  
Sasank Shekhara Hota ◽  
Amit Karmakar
Keyword(s):  
Free Vibration ◽  
Dynamic Equilibrium ◽  
Twist Angle ◽  
Cylindrical Shells ◽  
Shell Element ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Iteration Algorithm ◽  
Lagrange’S Equation ◽  
Benchmark Solutions

Effects of delamination on free vibration characteristics of laminated stiffened cylindrical shells with pretwist are analyzed by finite element method. The investigation is carried out using an eight-noded quadratic isoparametric shell element, which incorporates the transverse shear deformation and rotary inertia along with a three-noded beam element for the stiffener. The multipoint constraint algorithm has been included to guarantee the compatibility of deformation, equilibrium of resultant forces, and moments at delamination crack tip. The general dynamic equilibrium equation is derived from Lagrange’s equation of motion for moderate rotational speeds for which the Coriolis effect is neglected. The standard eigenvalue problem is solved utilizing QR iteration algorithm. The accuracy of the present formulation is validated with benchmark solutions is available in the literature. The present work concerns about the effects of delamination, fiber orientation, twist angle, stiffener depth-to-shell thickness ratio, and rotational speed on the fundamental frequency of shallow cylindrical shells with stiffener. Representative mode shapes for some typical case of the stiffened shell for different twist angles and rotational speeds are also presented.

FREE VIBRATION RESPONSE OF SHEAR-FLEXIBLE MODERATELY-THICK ORTHOTROPIC CYLINDRICAL SHELLS

2006 ◽  
Vol 06 (01) ◽  
pp. 121-138 ◽  
Author(s):  
Z. I. SAKKA ◽  
J. A. ABDALLA ◽  
H. R. H. KABIR
Keyword(s):  
Finite Element ◽  
Fourier Series ◽  
Analytical Solution ◽  
Free Vibration ◽  
Orthotropic Cylindrical Shell ◽  
Shell Element ◽  
Vibration Response ◽  
Fourier Series Expansion ◽  
Mode Shapes ◽  
Free Vibration Response

The free vibration response of shear-flexible moderately-thick orthotropic cylindrical shell panels, with fixed edges, is investigated using an analytical approach. The governing partial differential equations are developed based on Sander's kinematics and are solved using generalized Navier's with a boundary continuous double Fourier series expansion. The frequencies and mode shapes from the analytical solution for various parametric ratios, including degree of orthotropy (stiffness ratio), radius-to-segment ratio and segment-to-thickness ratio are compared with the finite element solutions that are based on an eight-node 48 degrees of freedom shell element. The rate of convergence of the analytical solution method with respect to the number of Fourier series terms, for various parametric ratios, is presented. The results of the analytical solution are very comparable to that of the finite element solution. It is clear that the presented analytical solution can be used as a benchmark to calibrate and validate numerical and finite element solutions that usually involve approximation to shell theories.

Free vibration analysis of pretwisted delaminated composite stiffened shallow shells: A finite element approach

2017 ◽  
Vol 36 (8) ◽  
pp. 619-636 ◽  
Author(s):  
Mrutyunjay Rout ◽  
Tanmoy Bandyopadhyay ◽  
Amit Karmakar
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Dynamic Equilibrium ◽  
Twist Angle ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Shell Element ◽  
Mode Shapes ◽  
Shallow Shells

This paper presents the effect of stiffeners on the free vibration response of delaminated composite shallow cylindrical shells employing the finite element method. An eight-noded isoparametric shell element based on the first-order shear deformation theory is combined with a three-noded isoparametric curved beam element in the present formulation. The stiffeners follow the nodal lines of the shell wherein the stiffness and mass of the stiffeners are lumped at the corresponding nodal points of the shell elements considering curvature and eccentricity. The generalized dynamic equilibrium equation is derived from Lagrange’s equation of motion, wherein Coriolis effect for moderate rotational speeds is neglected. The multi-point constraint algorithm has been used to model delamination at the desired locations wherein the compatibility of deformation and equilibrium of stress resultants are ensured at the delamination crack front. Numerical results are presented for cantilevered long, intermediate and short cylindrical shells as defined by Aas-Jakobsen’s parameters, and the influence of important parameters like location of delamination, twist angle, rotational speed, number of layers and eccentricity of the stiffeners is studied. The mode shapes for a typical composite un-stiffened and stiffened long cylindrical shell at different rotational speeds and twist angles are also presented.

Free Vibrations of Longitudinally Stiffened Cylindrical Shells

1974 ◽  
Vol 41 (4) ◽  
pp. 1087-1093 ◽  
Author(s):  
J. T. S. Wang ◽  
S. A. Rinehart
Keyword(s):  
Experimental Data ◽  
Free Vibration ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Structural System ◽  
Isotropic Cylinder ◽  
Simply Supported ◽  
Thin Walled ◽  
Stiffened Cylindrical Shells

This study is concerned with the free-vibration characteristics of thin cylindrical shells reinforced by longitudinal stringers for any edge boundary conditions. The structural system is treated as an isotropic cylinder interacting with a set of discrete thin-walled stringers. Frequencies of simply supported shells obtained according to the present analysis compare favorably with Ritz solution and existing experimental data. For mode shapes, the present analysis often yields much better results than Ritz solution. Numerical results for frequencies and mode shapes for clamped-clamped cylindrical shells are included, and frequencies of a shell with very flexible stiffeners compare favorably with frequencies of an unstiffened shell.

Analytical Study on the Buckling of Cylindrical Shells With Arbitrary Thickness Imperfections Under Axial Compression

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Guowei Cao ◽  
Zhiping Chen ◽  
Licai Yang ◽  
Haigui Fan ◽  
Fan Zhou
Keyword(s):  
Radial Displacement ◽  
Analytical Study ◽  
Arbitrary Order ◽  
Cylindrical Shells ◽  
Analytical Investigation ◽  
Fourier Series Expansion ◽  
Buckling Loads ◽  
Buckling Modes ◽  
Arbitrary Thickness ◽  
Unified Method

This paper presents an analytical study on the buckling of axially compressed cylindrical shells with arbitrary thickness imperfections (nonaxisymmetric and axisymmetric). First, the basic governing partial differential equations, which consider thickness imperfections, are obtained. Second, a unified method that combines the perturbation method and Fourier series expansion is developed to derive buckling load, radial displacement and stress function, that are expressed by triple series in terms of thickness imperfection parameter and buckling modes up to arbitrary order. Third, two patterns of nonaxisymmetric thickness imperfections, which are modal and exponential, are, respectively, investigated. These results are absolutely new to literature. When modal thickness imperfection becomes axisymmetric, the buckling loads degenerate to the known results. In addition to the analytical investigation, analyses and comparisons are also carried out.

Free Vibrations of Noncircular Cylindrical Shells Having Circumferentially Varying Thickness

1985 ◽  
Vol 52 (1) ◽  
pp. 149-154 ◽  
Author(s):  
K. Suzuki ◽  
A. W. Leissa
Keyword(s):  
Power Series ◽  
Free Vibration ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Thickness Variation ◽  
Series Expansions ◽  
Varying Thickness ◽  
Power Series Expansions ◽  
Vibration Problems

An exact method using power series expansions is presented for solving free vibration problems for noncircular cylindrical shells having circumferential thickness variation. The method is used to obtain the first known results for this class of problems. Frequencies and mode shapes are presented for a set of elliptical cylindrical shells having second degree thickness variation in each quadrant.

Natural Frequencies and Mode Shapes of Laminated Composite Skew Hypar Shells with Complicated Boundary Conditions Using Finite Element Method

2012 ◽  
Vol 585 ◽  
pp. 44-48 ◽  
Author(s):  
Ajay Kumar ◽  
Pradeep Bhargava ◽  
Anupam Chakrabarti
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Higher Order ◽  
Finite Element Formulation ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Element Formulation

In the present investigation, free vibration behaviour is studied for the laminated composite skew hypar shells having twist radius of curvature. A higher-order shear deformation theory is employed in the C0 finite element formulation. Higher-order terms in the Taylor’s series expansion are used to represent the higher-order transverse cross sectional deformation modes. The formulation includes Sanders’ approximation for doubly curved shells considering the effect of transverse shear. The structural system is considered to be undamped. The correctness of the formulation is established by comparing the present results of problems with those available in the published literature. The effects of different parameters are studied on the free vibration aspects of laminated composite skew hypar shells. Effect of cross curvature is included in the formulation. The C0 finite element formulation has been done quite efficiently to overcome the problem of C1 continuity associated with the HSDT. The isoparametric FE used in the present model consists of nine nodes with seven nodal unknowns per node. Since there is no result available in the literature based on HSDT on the problem of free vibration of laminated composite skew hypar shells, new results are presented by varying geometry, boundary conditions, ply orientations and skew angles which will serve as benchmark for future researchers.

Free Vibration Analysis of Arbitrarily Shaped Plates With Smoothly Varying Free Edges Using NDIF Method

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
S. W. Kang ◽  
I. S. Kim ◽  
J. M. Lee
Keyword(s):  
Boundary Condition ◽  
Free Boundary ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Free Boundary Condition ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Polar Coordinate System ◽  
Boundary Node

The so-called non-dimensional influence function method that was developed by the authors is extended to free vibration analysis of arbitrarily shaped plates with the free boundary condition. A method proposed in this paper can be applied to plates with only smoothly varying boundary shapes. In the proposed method, a local polar coordinate system has been employed at each boundary node to effectively consider the free boundary condition, which is much more complex than the simply supported or clamped boundary condition. The local coordinates system devised allowed us to successfully deal with the radius of curvature involved in the free boundary condition, and, as a result, the accuracy of the proposed method has been reinforced. Finally, verification examples showed that the natural frequency and mode shapes obtained by the proposed method agree excellently with those given by other analytical or numerical methods.

Sign in / Sign up

Export Citation Format

Share Document