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.

Comparison of Free Flexural Vibrations of Composite Plates or Panels Stiffened by a Central and a Non-Central Plate Strip

1999 ◽  
Author(s):  
U. Yuceoglu ◽  
V. Özerciyes
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Composite Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Solution Technique ◽  
Orthotropic Plates ◽  
Bending Vibration ◽  
Central Plate ◽  
Plate Strip

Abstract The natural frequencies and the corresponding mode shapes of two classes of composite base plate or panel stiffened by a central or a non-central plate strip are analyzed and compared with each other. In each case, the base plates and the single, stiffening plate strips are assumed to be dissimilar orthotropic plates connected by a very thin, yet deformable adhesive layer. The free bending vibration problems for the two cases are formulated in terms of the Mindlin Plate Theory for orthotropic plates. The governing equations are reduced to a system of first order equations. The solution technique is the “Modified Version of the Transfer Matrix Method”. The effects of the bonded central and non-central stiffening strip on the mode shapes and the natural frequencies of the composite plate or panel system are investigated. Some important conclusions are drawn from the numerical and parametric studies presented.

Free Flexural Vibrations of Orthotropic Composite Base Plates or Panels With a Bonded Noncentral (or Eccentric) Stiffening Plate Strip

2003 ◽  
Vol 125 (2) ◽  
pp. 228-243 ◽  
Author(s):  
U. Yuceoglu ◽  
V. O¨zerciyes
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Composite System ◽  
Natural Frequencies ◽  
Adhesive Layer ◽  
Base Plate ◽  
Mode Shapes ◽  
Bending Vibrations ◽  
Arbitrary Boundary ◽  
Plate Strip

The problem of the free flexural (or bending) vibrations of a rectangular, composite base plate or panel stiffened by a bonded, noncentral stiffening plate strip is considered. The lower composite base plate and the upper stiffening plate strip are assumed as dissimilar Mindlin Plates connected by a very thin and deformable adhesive layer. In the formulation, the entire composite system is considered to have simply supported edges in one direction while the other two edges may have arbitrary boundary conditions. The set of governing partial differential equations is reduced to a “special form” of a system of the first order ordinary differential equations. Then, they are integrated by the “Modified Transfer Matrix Method (with Interpolation Polynomials).” The mode shapes and the natural frequencies of the composite system are investigated and presented in detail for several boundary conditions. It was also found that the “hardness” and the “softness” of the in-between adhesive layer have significant effects on the mode shapes and the natural frequencies.

Free Flexural (or Bending) Vibrations of Orthotropic Composite Mindlin Plates With a Bonded Non-Central (or Eccentric) Lap Joint

2003 ◽  
Author(s):  
U. Yuceoglu ◽  
O¨. Gu¨vendik ◽  
V. O¨zerciyes
Keyword(s):  
Differential Equations ◽  
Natural Frequencies ◽  
Adhesive Layer ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Bending Rigidity ◽  
Lap Joint ◽  
Bending Vibrations ◽  
Theoretical Formulation ◽  
Orthotropic Composite

The present study is concerned with the “Free Flexural (or bending) Vibrations of Orthotropic Composite Mindlin Plates with a Bonded Non-Central (or Eccentric) Lap Joint”. The Mindlin plate adherends or panels of dissimilar, orthotropic material are connected by an adhesively bonded non-central (or eccentric) single lap joint. The adhesive layer is considered to be relatively very thin and linearly elastic. The theoretical formulation is based on the combination of the full set of the dynamic plate equations and the adhesive layer stress-displacement equations. Eventually, the system of equations is reduced to a set of the first order governing ordinary differential equations in the “state vector” form. The governing system of the differential equations is numerically integrated by means of the “Modified Transfer Matrix Method (with Interpolation and/or Chebyshev Polynomials)”. The effect of the non-central (or eccentric) location of the bonded lap joint is investigated and presented in detail in terms of natural frequencies and the associated mode shapes. The significant effects of the “hard” or the “soft” adhesive layer constants on the mode shapes and the natural frequencies are also investigated. Some important parametric studies such as the influences of the “Joint Length Ratio”, the “Joint Position Ratio” and the “Bending Rigidity Ratio” on the natural frequencies are computed and presented for the “hard” and the “soft” adhesive cases.

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 Bending Vibrations of Adhesively Bonded Orthotropic Plates With a Single Lap Joint

1996 ◽  
Vol 118 (1) ◽  
pp. 122-134 ◽  
Author(s):  
U. Yuceoglu ◽  
F. Toghi ◽  
O. Tekinalp
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Lap Joint ◽  
Orthotropic Plates ◽  
Adhesively Bonded ◽  
Bending Vibrations ◽  
Free Bending

This study is concerned with the free bending vibrations of two rectangular, orthotropic plates connected by an adhesively bonded lap joint. The influence of shear deformation and rotatory inertia in plates are taken into account in the equations according to the Mindlin plate theory. The effects of both thickness and shear deformations in the thin adhesive layer are included in the formulation. Plates are assumed to have simply supported boundary conditions at two opposite edges. However, any boundary conditions can be prescribed at the other two edges. First, equations of motion at the overlap region are derived. Then, a Levy-type solution for displacements and stress resultants are used to formulate the problem in terms of a system of first order ordinary differential equations. A revised version of the Transfer Matrix Method together with the boundary and continuity conditions are used to obtain the frequency equation of the system. The natural frequencies and corresponding mode shapes are obtained for identical and dissimilar adherends with different boundary conditions. The effects of some parameters on the natural frequencies are studied and plotted.

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.

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.

Effects of Variable Non-Central Locations of Bonded Double Doubler Joint System on Free Flexural Vibrations of Orthotropic Composite Mindlin Plate or Panel Adherents

2012 ◽  
Author(s):  
U. Yuceoglu ◽  
Ö. Güvendik
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Central Position ◽  
Joint Region ◽  
Joint System ◽  
Adhesive Layers ◽  
Governing System ◽  
Plate Elements ◽  
Interpolation Polynomials

This study investigates the “Effects of Variable Non-Central Locations of Bonded Double Doubler Joint System on Free Flexural Vibrations of Orthotropic Composite Mindlin Plate or Panel Adherents”. The problem is theoretically analyzed and is numerically solved in terms of the natural frequencies and the corresponding mode shapes of the entire “System”. The “Bonded Double Doubler Joint System” and the “Plate of Panel Adherents” are considered as dissimilar “Orthotropic Mindlin Plates”. In all plate elements, the transverse shear deformations and the transverse and rotary moments of inertia are included in the analysis. The relatively very thin adhesive layers in the “Bounded Joint Region” are assumed to be linearly elastic continua with transverse normal and shear deformations. The “damping effects” in the adhesive layers and in all plate elements of the “System” are neglected. The sets of the “Dynamic Mindlin Equations” of both upper and lower “Doubler Plates” and the “Plate or Panel Adherents” and the adhesive layer equations are combined together with the orthotropic stress resultant-displacement expressions resulting in a set of “Governing System of PDE’s” in a “special form”. By making use of the “Classical Levy’s Solutions”, in aforementioned “Governing PDE’s” and following some algebraic manipulations and combinations, the “Governing System of the First Order Ordinary Differential Equations” are obtained in compact “state vector” forms. Thus, the “Initial and Boundary Value Problem” at the beginning is finally converted into a “Multi-Point Boundary Value Problem” of Mechanics (and Physics). These analytical results developed facilitate the present method of solution that is the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. The final set of the “Governing System of ODE’s” is numerically integrated by means of the “MTMM with Interpolation Polynomials”. In this way, the natural frequencies and the mode shapes of the “Bonded System”, depending on the variable non-central location of the “Bonded Double Doubler Joint System” are computed for several sets of the far left and the far right “Boundary Conditions” of the “Orthotropic Plate or Panel Adherents”. It was observed that, based on the numerical results, the mode shapes and their natural frequencies are very much affected by the variable position (or location) of the “Bonded Double Doubler Joint” in the “System”. It was also found that as the “Bonded Double Doubler Joint” moves from the central position in the “System” towards the increasingly non-central position, the natural frequencies (in comparison with those of the central position) changes, respectively. The highly-stiff “Bonded Double Doubler Joint Region” becomes “almost stationary” in all modes in “Hard” Adhesive cases.

Development of an Analytical Model for Beams With Two Dimples in Opposing Direction

2017 ◽  
Author(s):  
Mofareh Ghazwani ◽  
Kyle Myers ◽  
Koorosh Naghshineh
Keyword(s):  
Differential Equations ◽  
Opposite Direction ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Modal Strain Energy ◽  
Noise And Vibration ◽  
Various Boundary Conditions ◽  
Strategic Approach ◽  
Value Model ◽  
Good Agreement

Structures such as beams and plates can produce unwanted noise and vibration. An emerging technique can reduce noise and vibration without any additional weight or cost. This method focuses on creating two dimples in the same and opposite direction on a beam’s surface where the effect of dimples on its natural frequencies is the problem of interest. The change in the natural frequency between both cases have a different trend. The strategic approach to calculate natural frequencies is as follows: first, a boundary value model (BVM) is developed for a beam with two dimples and subject to various boundary conditions using Hamilton’s Variational Principle. Differential equations describing the motion of each segment are presented. Beam natural frequencies and mode shapes are obtained using a numerical solution of the differential equations. A finite element method (FEM) is used to model the dimpled beam and verify the natural frequencies of the BVM. Both methods are also validated experimentally. The experimental results show a good agreement with the BVM and FEM results. A fixed-fixed beam with two dimples in the same and opposite direction is considered as an example in order to compute its natural frequencies and mode shapes. The effect of dimple locations and angles on the natural frequencies are investigated. The natural frequencies of each case represent a greater sensitivity to change in dimple angle for dimples placed at high modal strain energy regions of a uniform beam.

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.

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