Free Vibrations of Laminated Composite Noncircular Thin Cylindrical Shells

1994 ◽  
Vol 61 (4) ◽  
pp. 861-871 ◽  
Author(s):  
K. Suzuki ◽  
G. Shikanai ◽  
A. W. Leissa
Keyword(s):  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Power Series Expansion ◽  
Laminated Composite ◽  
Energy Functional ◽  
Solution Procedure ◽  
Free Vibrations ◽  
Layer Stacking ◽  
Kinetic Energy Functional ◽  
Energy Principles

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.

Theoretical Analysis of Free Vibrations Based on a New High Order Shell Theory for Cylindrical Shells Conveying Fluid

2017 ◽  
Author(s):  
Ming Ji ◽  
Kazuaki Inaba
Keyword(s):  
Boundary Conditions ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Fluid Pressure ◽  
Free Vibrations ◽  
High Order ◽  
Out Of Plane ◽  
Conveying Fluid

The natural frequencies of free vibrations for thick cylindrical shells with clamped-clamped ends conveying fluid are investigated. Equations of motion and boundary conditions are derived by Hamilton’s principle based on the new high order shell theory. The hydrodynamic force is derived from the linearized potential flow theory. Besides, fluid pressure acting on the shell wall is gotten by the assumption of non-penetration condition. The out-of-plane and in-plane vibrations are coupled together due to the existence of fluid-solid-interaction (FSI). Under the assumption of harmonic motion, the dispersion relationships are presented. Using the method of frequency sweeping, the natural frequencies of symmetric modes and asymmetric modes corresponding to each flow velocity are found by satisfying the dispersion relationship equations and boundary conditions. Several numerical examples with different flow velocities and thickness are presented compared with previous thin shell theory and FEM results and show reasonable agreement. The effects of thickness are discussed.

Nonlinear Natural Frequencies of Rotating Composite Thin-Walled Beam with Geometrical Nonlinear

2013 ◽  
Vol 683 ◽  
pp. 779-782 ◽  
Author(s):  
Yong Sheng Ren ◽  
Shuang Shuang Sun ◽  
Chun Jin Zhang
Keyword(s):  
Free Vibration ◽  
Nonlinear Eigenvalue Problem ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Laminated Composite ◽  
Iterative Solution ◽  
Solution Procedure ◽  
Energy Principle ◽  
Rotating Speed ◽  
Thin Walled

The nonlinear governing equations of motion for the rotating composite thin-walled beam are derived using Hamilton’s energy principle and variational-asymptotical method (VAM) on the basis of von Karman’s assumption. The nonlinear vibration of the beam is studied using Galerkin method and harmonic balance method. The large amplitude free vibration of the beam can be expressed as a nonlinear eigenvalue problem and solved using an iterative solution procedure. Numerical results are obtained for Circumferentially Uniform Stiffness (CUS )laminated composite configuration thin-walled beam. The study exhibit the effect of the fiber orientation and rotating speed on nonlinear natural frequency vs. amplitude curves. The developed model can be capable of describing nonlinear free vibration behaviors of rotating composite thin-walled beam with large deformations.

Dynamic Analysis of Anisotropic Cylindrical Shells Containing Flowing Fluid

2001 ◽  
Vol 123 (4) ◽  
pp. 454-460 ◽  
Author(s):  
M. H. Toorani ◽  
A. A. Lakis
Keyword(s):  
Transverse Shear ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Fluid Pressure ◽  
Laminated Composite ◽  
Present Theory ◽  
Curvilinear Coordinates ◽  
Structural Element ◽  
Flowing Fluid ◽  
Bernoulli’S Equation

This paper deals with the study of dynamic behavior of anisotropic cylindrical shells, based on refined shell theory, subjected simultaneously to an internal and external fluid. In the present theory, the transverse shear deformation effect is taken into account, therefore, the equations of motion are determined with displacements and transverse shear as independent variables. The solution is divided into three parts: In Section 2, the displacement functions are derived from the exact solution of refined shell equations based on orthogonal curvilinear coordinates. The mass and stiffness matrices of each structural element are derived by exact analytical integration. In Section 3, 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 which yields three forces (inertial, centrifugal, Coriolis). Numerical examples are given in Section 4 for the free vibration of laminated composite and isotropic materials for both open and closed circular cylindrical shells. Reasonable agreement is found with other theories and experiments.

A High-Order Theory for Dynamic Buckling and Postbuckling Analysis of Laminated Cylindrical Shells

1999 ◽  
Vol 121 (1) ◽  
pp. 94-102 ◽  
Author(s):  
M. R. Eslami ◽  
M. Shariyat
Keyword(s):  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Strain Tensor ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Order Theory ◽  
High Order ◽  
Nonlinear Equations Of Motion ◽  
Laminated Composite Shells ◽  
Made In

Using a high-order Reisner-Mindlin-type shear deformation theory in a power series form, the general large deformation form of the Green strain tensor for imperfect cylindrical shells is introduced. Then, based on Hamilton’s principle, the equations of motion are derived for laminated composite shells. Related constitutive equations are also proposed. In this formulation, temperature dependency of material properties is considered, too. No simplifications are made in solving the coupled nonlinear equations of motion. Finally, few examples of the well-known references are reconsidered for comparison purposes.

scholarly journals The Liu-Parr power series expansion of the Pauli kinetic energy functional with the incorporation of shell-inducing traits: Atoms

2018 ◽  
Vol 118 (14) ◽  
pp. e25601 ◽  
Author(s):  
Eduardo V. Ludeña ◽  
Edison X. Salazar ◽  
Mauricio H. Cornejo ◽  
Darío E. Arroyo ◽  
Valentin V. Karasiev
Keyword(s):  
Kinetic Energy ◽  
Power Series ◽  
Series Expansion ◽  
Power Series Expansion ◽  
Energy Functional ◽  
Kinetic Energy Functional

scholarly journals Behavior of Uniform Anisotropic Beams of Rectangular Section under Transverse Impact of a Mass

1997 ◽  
Vol 4 (2) ◽  
pp. 125-141 ◽  
Author(s):  
Lu Chun ◽  
K. Y. Lam
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Solution Procedure ◽  
Beam Deflection ◽  
Transverse Impact ◽  
Lagrange Principle ◽  
Arbitrary Boundary ◽  
Force Contact ◽  
Laminated Composite Beam

A numerical method is presented to investigate the dynamic response of uniform orthotropic beams subjected to an impact of a mass. Higher order shear deformation and rotary inertia are included in the analysis of the beams. The impactor and laminated composite beam are treated as a system. The nonlinear differential governing equations of motion are then derived based on the Lagrange principle and modified nonlinear contact law, and solved numerically. The solution procedure is applicable to arbitrary boundary conditions. Numerical results are compared with those available in the literature to demonstrate the validity of the method, and very good agreement is achieved. The effects of boundary conditions on the contact force, contact duration, stress distributions, and beam deflection are discussed.

Vibration and Buckling of Rotating, Pretwisted, Preconed Beams Including Coriolis Effects

1986 ◽  
Vol 108 (2) ◽  
pp. 140-149 ◽  
Author(s):  
K. B. Subrahmanyam ◽  
K. R. V. Kaza
Keyword(s):  
Equations Of Motion ◽  
Energy Functional ◽  
Solution Procedure ◽  
Thickness Ratio ◽  
The Other ◽  
Collective Effects ◽  
Coriolis Forces ◽  
Coriolis Effects ◽  
Axis Of Rotation ◽  
Setting Angle

The effects of pretwist, precone, setting angle and Coriolis forces on the vibration and buckling behavior of rotating, torsionally rigid, cantilevered beams are studied in this investigation. The beam is considered to be clamped on the axis of rotation in one case, and off the axis of rotation in the other. Two methods are employed for the solution of the vibration problem: one based upon a finite-difference approach using second-order central differences for solution of the equations of motion, and the other based upon the minimum of the total potential energy functional with a Ritz type of solution procedure making use of complex forms of shape functions for the dependent variables. Numerical results obtained by using these methods are compared to those existing in the literature for specialized simple cases. Results indicating the individual and collective effects of pretwist, precone, setting angle, thickness ratio, and Coriolis forces on the natural frequencies and the buckling boundaries are presented and discussed. Furthermore, it is shown that the inclusion of Coriolis effects is necessary for blades of moderate-to-large thickness ratios while these effects are not so important for small thickness ratio blades. Finally, the results show the possibility of buckling due to centrifugal softening terms for large values of precone and rotation.

3-D Vibration Analysis of Fiber Reinforced Composite Laminated Cylindrical Shells

1997 ◽  
Vol 119 (1) ◽  
pp. 46-51 ◽  
Author(s):  
Jiang Xiaoyu
Keyword(s):  
Vibration Analysis ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Shear Stresses ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
Transverse Normal Stress ◽  
Transverse Shear Stresses ◽  
Laminated Cylindrical Shells

In this paper, 3-D solutions of free vibrations are presented for isotropic and composite laminated cylindrical shells. The perturbation method and a variational principle are used to obtain the solutions which satisfy the 3-D differential equations of motion, the strain-displacement relations, the stress-strain relations, the boundary conditions and the continuity conditions at layer interfaces. The distributions of displacements and stresses in the shells are shown in figures. The free vibration frequencies are listed in tables. In the thickness direction of the shells, continuous displacements and stresses are obtained. And the importance of transverse shear stresses and transverse normal stress is analyzed.

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