The Effect of Boundary Conditions on Nonlinear Vibration and Flutter of Laminated Cylindrical Shells

2004 ◽  
Author(s):  
E. L. Jansen
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Vibration ◽  
Cylindrical Shells ◽  
Perturbation Expansion ◽  
Present Theory ◽  
Dependent Variables ◽  
Different Types ◽  
Lamination Theory ◽  
Initial Geometric Imperfections ◽  
Nonlinear Static

A nonlinear vibration analysis of cylindrical shells is presented, in which the specified boundary conditions at the shell edges can be satisfied rigorously. The method is based on a perturbation expansion for both the frequency parameter and the dependent variables. The present theory includes the effects of finite vibration amplitudes, initial geometric imperfections and a nonlinear static deformation. Nonlinear Donnell-type equations formulated in terms of the radial displacement W and an Airy stress function F are used, and classical lamination theory is employed. Further, an extension of the theory is presented to analyze linearized flutter in supersonic flow, based on piston theory. The effect of different types of boundary conditions on the nonlinear vibration and linearized flutter behavior of cylindrical shells is illustrated for several characteristic cases.

Effect of Boundary Conditions on Nonlinear Vibration and Flutter of Laminated Cylindrical Shells

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
E. L. Jansen
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Vibration ◽  
Cylindrical Shells ◽  
Perturbation Expansion ◽  
Present Theory ◽  
Dependent Variables ◽  
Lamination Theory ◽  
Initial Geometric Imperfections ◽  
Nonlinear Static ◽  
Laminated Cylindrical Shells

A nonlinear vibration analysis of laminated cylindrical shells is presented in which the effect of the specified boundary conditions at the shell edges, including nonlinear fundamental state deformations, can be accurately taken into account. The method is based on a perturbation expansion for both the frequency parameter and the dependent variables. The present theory includes the effects of finite vibration amplitudes, initial geometric imperfections, and a nonlinear static deformation. Nonlinear Donnell-type equations formulated in terms of the radial displacement W and an Airy stress function F are used, and classical lamination theory is employed. Furthermore, an extension of the theory is presented to analyze linearized flutter in supersonic flow, based on piston theory. The effect of different types of boundary conditions on the nonlinear vibration and linearized flutter behavior of cylindrical shells is illustrated for several characteristic cases.

scholarly journals Exact Free Vibration Analysis for Plate Built-Up Structures under Comprehensive Combinations of Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Xiang Liu ◽  
Chen Xie ◽  
Han-cheng Dan
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Present Theory ◽  
Plate Elements ◽  
Stiffness Model ◽  
Different Types ◽  
Support Conditions

In this research, an exact dynamic stiffness model for spatial plate built-up structures under comprehensive combinations of different boundary conditions is newly proposed. Dynamic stiffness formulations for plate elements with 16 different types of supported opposite edges and arbitrarily supported boundary conditions along other edges are developed, which makes the dynamic stiffness method (DSM) more applicable to engineering problems compared to existing works. The Wittrick–Williams algorithm of the DSM is applied with the explicit expressions of the J0 count for plate elements under all above support conditions. In return, there is no need to refine the element in the DSM, and thus, it becomes immensely efficient. Moreover, the present theory is applied for exact free vibration analysis within the whole frequency range of three built-up structures which are commonly encountered in engineering. The results show that the DSM gives exact results with as much as 100-fold computational efficiency advantage over the commercial finite element method. Besides, benchmark results are also provided.

A Method for Obtaining Stresses and Displacements in Thick Cylindrical Shells Under Arbitrary Boundary Conditions

1973 ◽  
Vol 40 (1) ◽  
pp. 221-226 ◽  
Author(s):  
E. B. Golub ◽  
F. Romano
Keyword(s):  
Stress State ◽  
Variational Principle ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Present Theory ◽  
Bending Stress ◽  
Arbitrary Boundary ◽  
Elasticity Solutions ◽  
Circular Cylindrical Shells

This paper presents a means for obtaining both the stress and displacement states which appear in thick, circular, cylindrical shells under arbitrary load and boundary conditions. The governing differential equations and the associated boundary conditions are obtained by utilizing Reissner’s variational principle [6], the assumed form of the stress state containing, in addition to terms corresponding to conventional membrane and bending stress resultants, supplementary sets of self-equilibrating stress resultants. Comparison of results obtained from known elasticity solutions shows that the present theory accurately yields solutions for shells with radius-thickness ratios of the order of 3.0. Numerically computed here, for comparison purposes, is the axisymmetric, periodically spaced, band load problem of Klosner and Levine.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

The study of the nonlinear vibration of S-S and C-C laminated composite conical shells on elastic foundations through an approximate method

2021 ◽  
pp. 095440622110214
Author(s):  
Shahin Mohammadrezazadeh ◽  
Ali Asghar Jafari
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Vibration ◽  
Approximate Method ◽  
Laminated Composite ◽  
Vertex Angle ◽  
Nonlinear Frequency ◽  
Conical Shells ◽  
Elastic Foundations ◽  
Vibration Responses ◽  
Comparison Of The Results

This paper investigates the nonlinear vibration responses of laminated composite conical shells surrounded by elastic foundations under S-S and C-C boundary conditions via an approximate approach. The laminated composite conical shells are modeled based on classical shell theory of Love employing von Karman nonlinear theory. Nonlinear vibration equation of the conical shells is extracted by handling Lagrange method. The linear and nonlinear vibration responses are obtained via an approximate method which combines Lindstedt-Poincare method with modal analysis. The validation of this study is carried out through the comparison of the results of this study with results of published literature. The effects of several parameters including the constants of elastic foundations, boundary conditions, total thickness, length, large edge radius and semi-vertex angle on the values of fundamental linear frequency and curves of amplitude parameter versus nonlinear frequency ratio for laminated composite conical shells with both S-S and C-C boundary conditions are investigated.

Sign in / Sign up

Export Citation Format

Share Document