Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Non-Central Shell Segment

2005 ◽  
Author(s):  
V. O¨zerciyes ◽  
U. Yuceoglu
Keyword(s):  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Adhesive Layer ◽  
Solution Procedure ◽  
Mode Shapes ◽  
Orthotropic Materials ◽  
First Order ◽  
Present Solution ◽  
Circular Cylindrical Shells

In this study, the “Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by A Bonded Non-Central Shell Segment” are analyzed and investigated in some detail. The “full” circular cylindrical “base” shell and the non-centrally bonded circular cylindrical shell “stiffener” are assumed to be made of dissimilar orthotropic materials. The “base” shell and the “stiffening” shell segment are adhesively bonded by an in-between, relatively very thin, yet linearly elastic adhesive layer. In the theoretical analysis, for both shell elements, a “First Order Shear Deformation Shell Theory (FSDST)” such as “Timoshenko-Mindlin -(and Reissner)” type is employed. The damping effects in the entire system are neglected. The sets of dynamic equations of both “base” shell and “stiffening” shell segment and the adhesive layer are combined together, manipulated and are, finally, reduced to a “Governing System of First Order Ordinary Differential Equations” in Forms of the “state vectors” of the problem. This result constitutes a so-called “Two-Point Boundary Value Problem” for the entire composite shell system, which facilitates the present solution procedure. The final system of equations is numerically integrated by means of the “Modified Transfer Matrix Method (MTMM) (with Chebyshev Polynomials)”. The typical mode shapes with their natural frequencies are presented for several sets of support conditions. The very significant effect of the “hard” and the “soft” adhesive layer on the mode shapes and the natural frequencies are demonstrated. Some important parametric studies (such as the “Joint Length Ratio”, etc.) are also presented.

Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment

2004 ◽  
Author(s):  
U. Yuceoglu ◽  
V. O¨zerciyes
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Adhesive Layer ◽  
Shear Stresses ◽  
First Order ◽  
Stress Resultant ◽  
Circular Cylindrical Shells

This study is concerned with the “Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment.” The base shell is made of an orthotropic “full” circular cylindrical shell reinforced and/or stiffened by an adhesively bonded dissimilar, orthotropic “full” circular cylindrical shell segment. The stiffening shell segment is located at the mid-center of the composite system. The theoretical analysis is based on the “Timoshenko-Mindlin-(and Reissner) Shell Theory” which is a “First Order Shear Deformation Shell Theory (FSDST).” Thus, in both “base (or lower) shell” and in the “upper shell” segment, the transverse shear deformations and the extensional, translational and the rotary moments of inertia are taken into account in the formulation. In the very thin and linearly elastic adhesive layer, the transverse normal and shear stresses are accounted for. The sets of the dynamic equations, stress-resultant-displacement equations for both shells and the in-between adhesive layer are combined and manipulated and are finally reduced into a ”Governing System of the First Order Ordinary Differential Equations” in the “state-vector” form. This system is integrated by the “Modified Transfer Matrix Method (with Chebyshev Polynomials).” Some asymmetric mode shapes and the corresponding natural frequencies showing the effect of the “hard” and the “soft” adhesive cases are presented. Also, the parametric study of the “overlap length” (or the bonded joint length) on the natural frequencies in several modes is considered and plotted.

Free Vibrations of Composite Shallow Circular Cylindrical Shell Panels With a Bonded Central Stiffening Shell Strip

2001 ◽  
Author(s):  
U. Yuceoglu ◽  
V. Özerciyes
Keyword(s):  
Shallow Shell ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Adhesive Layer ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Order System ◽  
Theoretical Formulation ◽  
First Order ◽  
Stress Resultant

Abstract This study is concerned with the “Free Vibrations of Composite Shallow Circular Cylindrical Shells or Shell Panels with a Central Stiffening Shell Strip”. The upper and lower shell elements of the stiffened composite system are considered as dissimilar, orthotropic shallow shells. The upper relatively narrow stiffening shell strip is centrally located and adhesively bonded to the lower main shell element In the theoretical formulation, a “First Order Shear Deformation Shell Theory (FSDST)” is employed. The complete set of the shallow shell dynamic equations (including the stress resultant-displacement and the constitutive equations) and the equations of the thin flexible, adhesive layer are first reduced to a set of first order system of ordinary differential equations. This final set forms the governing equations of the problem. Then, they are integrated by means of the “Modified Transfer Matrix Method”. In the adhesive layer, the “hard” and the “soft” adhesive effects are considered. It was found that the material characteristics of the adhesive layer influence the mode shapes and the corresponding natural frequencies of the composite shallow shell panel system. Additionally, some parametric studies on the natural frequencies are presented.

Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells With a Bonded Central Lap Joint

2003 ◽  
Author(s):  
V. O¨zerciyes ◽  
U. Yuceoglu
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Adhesive Layer ◽  
Lap Joint ◽  
First Order ◽  
Single Lap Joint ◽  
Circular Cylindrical Shells

In this study, the problem of the free asymmetric vibrations of composite “full” circular cylindrical shells with a bonded single lap joint is considered. The “full” circular cylindrical shell adherends to be made of dissimilar and orthotropic materials are connected by relatively very thin, yet flexible and linearly elastic adhesive layer. The bonded single lap joint is a centrally located in the composite shell system. The analysis is based on a “Timoshenko-Mindlin (and Reissner) Type Shell Theory” which is a “First Order Shear Deformation Shell Theory (FSDST)”. In the formulation, the set of governing differential equations is reduced to a system of first order ordinary differential equations in the “state vector” form. Then, they are integrated by means of a numerical procedure, that is, the “Modified Transfer Matrix Method (with Chebyshev Polynomials)”. The mode shapes and the natural frequencies of the “full” cylindrical shell lap joint system are investigated for various boundary conditions. Also, the effects, on the modes and natural frequencies, of the “hard” (or rather relatively stiff) and the “soft” (or relatively very flexible) adhesive layer cases are considered and presented. Some of the numerical results of the important parametric studies are computed and plotted.

Sudden Drop Phenomena in Natural Frequencies of Composite Plates or Panels With a Non-Central (or Eccentric) Stiffening Plate Strip

2000 ◽  
Author(s):  
U. Yuceoglu ◽  
V. Özerciyes
Keyword(s):  
Differential Equations ◽  
Composite Plate ◽  
Natural Frequencies ◽  
Adhesive Layer ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Orthotropic Plates ◽  
Sudden Drop ◽  
First Order ◽  
Plate Strip

Abstract In this study the free bending vibrations of compsite base plates or panels reinforced by a non-central (or eccentric) stiffening plate strip are considered. The base plate and the stiffening plate strip are dissimilar orthotropic plates. They are connected by a very thin and flexible adhesive layer. The dynamic equations of the entire composite plate system are obtained from the “Mindlin Plate Theory” for orthotropic plates. The set of the governing partial differential equations of the composite plate or panel system are reduced to a set of first order ordinary differential equations by the elimination of the time variable and one of the space variables. This final system of the first order differential equations in one space variable is integrated by the “Modified Version of the Transfer Matrix Method”. It was shown that the natural frequencies, at any mode, of the plate or panel system gradually increase at first with the increasing “Bending Cross Stiffness Ratio”. After then, for certain values of this “Ratio”, the natural frequencies for each mode, suddenly drop to a lower value and subsequently start to go up, although slowly, regardless of the support conditions. This unusual “Sudden Drop Phenomena” is explained in detail and, also, the mode shapes corresponding to the sudden drop are presented. The effect of the “hard” and the “soft” adhesive layer on the “Phenomena” are also shown.

Free Flexural Vibrations Response of Composite Mindlin Plates or Panels With a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint)

2005 ◽  
Author(s):  
U. Yuceoglu ◽  
O. Gu¨vendik ◽  
V. O¨zerciyes
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Solution Technique ◽  
Shear Stresses ◽  
Lap Joint ◽  
Adhesive Layers ◽  
Present Solution ◽  
Flexural Vibrations ◽  
Support Conditions ◽  
Interpolation Polynomials

The present study is concerned with the “Free Flexural Vibrations Response of Composite Mindlin Plates or Panels with a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint). The plate “adherends” and the plate “doublers” are considered as dissimilar, orthotropic “Mindlin Plates” with the transverse and the rotary moments of inertia. The relatively, very thin adhesive layers are taken into account in terms of their transverse normal and shear stresses. The mid-center of the bonded region of the joint is at the mid-center of the entire system. In order to facilitate the present solution technique, the dynamic equations of the plate “adherends” and the plate “doublers” with those of the adhesive layers are reduced to a set of the “Governing System of First Order ordinary Differential Equations” in terms of the “state vectors” of the problem. This reduced set establishes a “Two-Point Boundary Value Problem” which can be numerically integrated by making use of the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. In the adhesive layers, the “hard” and the “soft” adhesive cases are accounted for. It was found that the adhesive elastic constants drastically influence the mode shapes and their natural frequencies. Also, the numerical results of some parametric studies regarding the effects of the “Position Ratio” and the “Joint Length Ratio” on the natural frequencies for various sets of support conditions are presented.

Free Vibration of a Circular Cylindrical Shell Elastically Restrained by Axially Spaced Springs

1983 ◽  
Vol 50 (3) ◽  
pp. 544-548 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
Y. Muramoto
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Circular Cylindrical Shell ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Governing Equations ◽  
Structure Matrix ◽  
The Matrix ◽  
Circular Cylindrical Shells ◽  
Elastically Restrained

An analysis is presented for the free vibration of a circular cylindrical shell restrained by axially spaced elastic springs. The governing equations of vibration of a circular cylindrical shell are written as a coupled set of first-order differential equations by using the transfer matrix of the shell. Once the matrix has been determined, the entire structure matrix is obtained by the product of the transfer matrices and the point matrices at the springs, and the frequency equation is derived with terms of the elements of the structure matrix under the boundary conditions. The method is applied to circular cylindrical shells supported by axially equispaced springs of the same stiffness, and the natural frequencies and the mode shapes of vibration are calculated numerically.

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