Natural frequencies of meridional vibration in thin conical shells

AIAA Journal ◽  
1964 ◽  
Vol 2 (10) ◽  
pp. 1825-1827 ◽  
Author(s):  
R. E. KEEFEE
Keyword(s):  
Natural Frequencies ◽  
Conical Shells

scholarly journals Effect of Location of Delamination on Free Vibration of Cross-Ply Conical Shells

2012 ◽  
Vol 19 (4) ◽  
pp. 679-692 ◽  
Author(s):  
Sudip Dey ◽  
Amit Karmakar
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Twist Angle ◽  
Structural Instability ◽  
Numerical Results ◽  
Mode Shapes ◽  
Iteration Algorithm ◽  
Conical Shells

Location of delamination is a triggering parameter for structural instability of laminated composites. In this paper, a finite element method is employed to determine the effects of location of delamination on free vibration characteristics of graphite-epoxy cross-ply composite pre-twisted shallow conical shells. The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting Coriolis effect for moderate rotational speeds. The formulation is exercised by using an eight noded isoparametric plate bending element based on Mindlin's theory. Multi-point constraint algorithm is utilized to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The standard eigen value problem is solved by applying the QR iteration algorithm. Finite element codes are developed to obtain the numerical results concerning the effects of location of delamination, twist angle and rotational speed on the natural frequencies of cross-ply composite shallow conical shells. The mode shapes are also depicted for a typical laminate configuration. Numerical results obtained from parametric studies of both symmetric and anti-symmetric cross-ply laminates are the first known non-dimensional natural frequencies for the type of analyses carried out here.

scholarly journals Free vibration analysis of joined composite conical-cylindrical-conical shells containing fluid

2016 ◽  
Vol 38 (4) ◽  
pp. 249-265 ◽  
Author(s):  
Vu Quoc Hien ◽  
Tran Ich Thinh ◽  
Nguyen Manh Cuong
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Fluid Pressure ◽  
Free Vibration Analysis ◽  
The Finite Element Method ◽  
Fluid Interface ◽  
Governing Equations ◽  
Conical Shells ◽  
Bernoulli’S Equation

A new continuous element (CE) formulation has been presented in this paper for the vibration analysis of cross-ply composite joined conical-cylindrical-conical shells containing fluid. Governing equations are obtained using thick shell theory of Midlin, taking into account the shear deflection effects. The velocity potential, Bernoulli's equation and impermeability condition have been applied to the shell-fluid interface to obtain an explicit expression for fluid pressure. The dynamic stiffness matrix has been built from which natural frequencies have been calculated. The appropriate expressions among stress resultants and deformations are extracted as continuity conditions at the joining section. A matlab program is written using the CE formulation in order to validate our model. Numerical results on natural frequencies are compared to those obtained by the Finite Element Method and validated with the available results in other investigations. This paper emphasizes advantages of CE model, the effects of the fluid filling and shell geometries on the natural frequencies of joined composite conical-cylindrical-conical shells containing fluid.

Influence of Deformations Prior to Instability on the Dynamic Instability of Conical Shells Under Periodic Axial Load

1976 ◽  
Vol 43 (1) ◽  
pp. 87-91 ◽  
Author(s):  
J. Tani
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Axial Load ◽  
Basic Equation ◽  
Natural Frequencies ◽  
Dynamic Instability ◽  
Forced Vibrations ◽  
The Other ◽  
Conical Shells ◽  
Instability Regions

The dynamic instability of clamped, truncated conical shells under periodic axial load is studied using the Donnell-type basic equation and considering the effect of bending deformations before instability. Two principal instability regions are determined by combining Bolotin’s method and a finite-difference method. One of these belongs to double the natural frequencies of asymmetrical vibration; the other corresponds to the resonance of symmetrically forced vibrations. The effects of static axial load and end-plate mass on the principal instability regions are also investigated.

Asymmetric Free Vibrations of Layered Conical Shells

1982 ◽  
Vol 104 (2) ◽  
pp. 453-462 ◽  
Author(s):  
K. Chandrasekaran ◽  
V. Ramamurti
Keyword(s):  
Natural Frequencies ◽  
Middle Surface ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Orthotropic Materials ◽  
Conical Shells ◽  
Shell Models ◽  
Theoretical Predictions ◽  
Parametric Studies ◽  
Ritz Procedure

Asymmetric free vibrations of layered truncated conical shells are studied. Individual layers made of special orthotropic materials and both symmetric and asymmetric stacking with respect to the middle surface are considered. An energy-method based on the Rayleigh-Ritz procedure is employed. The influence of layer arrangements and that of the coupling between bending and stretching on the natural frequencies and mode-shapes are analyzed. Experimental results from tests on two shell models are provided for comparison with theoretical predictions. Numerical results based on extensive parametric studies are presented.

Investigation of the Free Vibrations of Composite Anisogrid Lattice Conical Shells Formed by Geodesically Spiral and Circumferential Ribs

2017 ◽  
Vol 09 (04) ◽  
pp. 1750047 ◽  
Author(s):  
Siamak E. Khadem ◽  
Reza Nezamoleslami
Keyword(s):  
Conical Shell ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Wave Number ◽  
Vertex Angle ◽  
Conical Shells ◽  
Outer Skin ◽  
Special Cases ◽  
Composite Lattice ◽  
Lattice Part

This paper focuses on the dynamic behavior of composite anisogrid lattice conical shells. Lattice composite conical shell consists of composite helical and circumferential ribs and thin outer skin. The free vibration analysis of anisogrid composite lattice conical shell is presented. A smeared method is employed to calculate the variable coefficients of stiffness of conical shell and more close to the realistic applications. The lattice part of conical shell is modeled as a beam, so in addition to the axial loads, ribs endure shear loads and bending moments. The first-order shear deformation shell theory is used to account for the effects of transverse shear deformations and rotary inertia. The current results are verified with 3D finite element model of conical shell by ANSYS Software and those reported in the literature. Some special cases as influences of geometric parameters of lattice part of shell, effects of boundary conditions and circumferential wave number on natural frequencies of the shell are discussed. It was concluded that employment of the smear method could be recommended for determining the coefficients of stiffness of the composite lattice conical shells with outer skin. Also increasing the vertex angle of cone increases the natural frequencies of conical shell.

Natural frequencies of truncated conical shells

1984 ◽  
Vol 92 (3) ◽  
pp. 447-453 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
K. Tanaka
Keyword(s):  
Natural Frequencies ◽  
Conical Shells

scholarly journals FREE VIBRATION ANALYSIS OF JOINED COMPOSITE CONICAL-CONICAL-CONICAL SHELLS CONTAINING FLUID

2016 ◽  
Vol 54 (5) ◽  
pp. 650 ◽  
Author(s):  
Vu Quoc Hien ◽  
Tran Ich Thinh ◽  
Nguyen Manh Cuong ◽  
Pham Ngoc Thanh
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
The Finite Element Method ◽  
Fluid Interface ◽  
Governing Equations ◽  
Conical Shells ◽  
Bernoulli’S Equation ◽  
Matlab Program

ABSTRACT A new continuous element (CE) formulation has been presented in this paper for the vibration analysis of three joined cross-ply composite conical shells containing fluid. The three joined cross-ply composite conical shells containing fluid can be considered as the general case for joined conical-cylindrical-conical, joined cylindrical-conical-cylindrical, joined cylindrical-conical-conical and joined conical-conical-cylindrical shells containing fluid. Governing equations are obtained using thick shell theory of Midlin, taking into account the shear deflection effects. The velocity potential, Bernoulli’s equation and impermeability condition have been applied to the shell-fluid interface to obtain an explicit expression for fuild pressure. The dynamic stiffness matrix has been built from which natural frequencies have been calculated. The appropriate expressions among stress resultants and deformations are extracted as continuity conditions at the joining section. A matlab program is written using the CE formulation in order to validate our model. Numerical results on natural frequencies are compared to those obtained by the finite element method (FEM) and validated with the available results in other investigations. This paper emphasizes advantages of CE model and the effects of the fluid level, semi-vertex angles and lamination sequences on the natural frequencies of joined composite conical-conical-conical shells.

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