Rotation of Material Axes Effects on Free Bending Vibrations Response of Composite Mindlin Base Plates or Panels Stiffened by Three Bonded Plate Strips

2011 ◽  
Author(s):  
U. Yuceoglu ◽  
J. Javanshir ◽  
T. Farsadi ◽  
O¨. Gu¨vendik
Keyword(s):  
Base Plate ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Governing Equations ◽  
Bending Vibrations ◽  
Plate Elements ◽  
System 2 ◽  
Interpolation Polynomials ◽  
System 1 ◽  
Free Bending

In the present study, the rotation of material axes on the free bending vibrations response of a certain type of composite “Bonded and Stiffened System” is theoretically analyzed and numerically solved with some numerical results. The composite “Bonded and Stiffened System” is composed of a “Mindlin Base Plate or Panel” reinforced by three “Bonded Stiffening Plate Strips”. In the analysis, the 90° rotation effects of the material axes on the natural frequencies and the mode shapes of the entire “System” are investigated. The aforementioned “Bonded and Stiffened System” is considered in terms of the “System.1” and the “System.2”. In the “System.1”, the material axes of the “Base Plate” are rotated 90° (about z-axis), while there is no change in the material axes of the “Bonded Plate Strips”. In the “System.2”, there is no change in the material directions of the “Base Plate”, while the material axes of the “Bonded Plate Strips” are rotated 90° degrees. The “Base Plate or Panel” and the three “Bonded Plate Strips” are assumed to be dissimilar “Orthotropic Mindlin Plates”. The in-between, relatively very thin, linearly elastic adhesive layers are considered with different material characteristics. All “Mindlin Plate Elements” of both “Systems.1 and 2” are included in the analysis with the transverse (or bending) moments of inertia and rotary moments of inertia. The dynamic equations of the “Mindlin Plate Elements” and the in-between adhesive layer expressions (with the transverse normal and shear stresses) are combined togather. After some algebraic manipulations and combinations, they are eventually reduced to a set of the “Governing System of the First Order O.D.E’s” in compact matrix forms with the “state vectors” for each case of the “System.1” and “System.2”. The aforementioned “Governing Equations” facilitate direct application of the present method of solution that is the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. The “Governing Equations” are numerically Integrated by means of the “ (MTMM) (with Interpolation Polynomials)”. The natural frequencies and the mode shapes of the “Systems.1 and 2” are computed and graphically presented for some “Support Conditions” of the “Systems” under consideration. The comparison of the numerical results led to some important conclusions.

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.

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 Bending Vibrations of Integrally-Stiffened and/or Stepped-Thickness Rectangular Plates or Panels With a Non-Central Plate Stiffener

2007 ◽  
Author(s):  
U. Yuceoglu ◽  
N. Gemalmayan ◽  
O. Sunar
Keyword(s):  
Differential Equations ◽  
Natural Frequencies ◽  
Orthotropic Materials ◽  
Mindlin Plate ◽  
Al Alloy ◽  
Bending Vibrations ◽  
Central Plate ◽  
Plate Elements ◽  
Stress Resultant ◽  
Free Bending

The present study is primarily concerned with the “Free Bending Vibrations of Integrally-Stiffened and/or Stepped-Thickness Plates or Panels with a Non-Central Plate Stiffener”. The general theoretical formulation is based on the “Mindlin Plate Theory”. The plate elements of the system are considered to be made of dissimilar orthotropic materials with unequal thicknesses. The transverse shear deformations and the transverse and the rotary moments of inertia of plate elements are included in the analysis. The damping effects, however, are neglected. The dynamic equations of the orthotropic “Mindlin Plates” in combination with the stress resultant-displacement expressions are algebraically manipulated. They are eventually reduced to a set of the “Governing System of the First Order Ordinary Differential Equations” in the “state vectors” form. The resulting differential equations system is numerically integrated by making use of the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. The mode shapes with their dimensionless natural frequencies are presented for various support conditions in the “isotropic” Al-Alloy and in the “orthotropic” composite cases. Additionally, the effect of some of the important parameters such as (“Stiffener Position Ratio”, “Thickness Ratio”, “Stiffener Length (or Width) Ratio)” on the dimensionless natural frequencies are investigated and plotted. Based on the numerical results, some brief but important conclusions are presented.

Effects of Rotation of Material Axes on Free Flexural Vibrations of Centrally Bonded Symmetric Double Doubler Joint in Composite Mindlin Plates or Panels

2011 ◽  
Author(s):  
U. Yuceoglu ◽  
O. Gu¨vendik
Keyword(s):  
Boundary Value Problem ◽  
Dynamic Equations ◽  
Moments Of Inertia ◽  
Adhesive Layers ◽  
Plate Elements ◽  
System 2 ◽  
Support Conditions ◽  
Effects Of Rotation ◽  
Interpolation Polynomials ◽  
System 1

The present study investigates the serious effects of rotation of material axes on the free dynamic response of composite plates or panels with “Bonded Double Doubler Joint Systems”. The “Plate Adherends” and the “Upper and Lower Doubler Plates” are connected through the relatively very thin adhesive layers. The “Bonded Double Doubler Joint System” is considered in terms of the “System.1” and the “System.2”. In the “System.1”, the material directions of “Plate Adherends” are rotated 90° (about z-axis) while there is no change in the material axes of the “Double Doubler Plates”. In the “System.2”, the material directions of the “Double Doubler Plates” are rotated 90° (about z-axis), while there is no change in the material axes of the “Plate Adherends”. All plate elemnts of the “System.1” and the “System.2” are assumed to be dissimilar “Orthotropic Mindlin Plates” with the transverse shear deformations and the transverse (or bending) moments of inertia and the rotary moments of inertia. The upper and lower adhesive layers are linearly elastic continua with dissimilar material properties and with unequal thicknesses. The damping effects in all plate elements and also in adhesive layers are neglected. The entire theoretical analysis for both “Systems.1 and 2” is based on the “Orthotropic Mindlin Plate Theory”. For this purpose, the dynamic equations of the left and the right “Plate adherends” and of the “Upper and Lower Doubler Plates” and the equations of the adhesive layers are combined to-gather with the stress resultant – displacement expressions of the plate elements. Then, after some algebric manipulations and combinations, and with the “Classical Levy’s Solutions” the original dynamic equations are finally reduced into the two new sets of the “Governing System of the First Order O.D.E’s” in compact matrix forms with the “state vectors” for the “System.1” and “System.2”, respectively. In this way, the original “Initial and Boundary Value Problem” (or the free vibrations problem) is converted to the “Multi–Point Boundary Value Problem” of Mechanics and Physiscs. In the case of both “Systems.1 and 2”, these results facilitate the direct application of the present method of solution that is the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. The aforementioned “Governing Equations” for both “Systems.1 and 2” are numerically integreted by making use of the “ (MTMM) (with Interpolation Polynomials)”. Thus, the natural frequencies and the mode shapes of the “Systems.1” and the “System.2” are graphically presented for the same “Support Conditions”. The comparison of the numerical results corresponding to each “System.1” and “System.2” for the same “Support Conditions” is considered leading to some very important conclusions.

Free Bending Vibrations of a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint) With a Gap in Mindlin Plates or Panels

2007 ◽  
Author(s):  
U. Yuceoglu ◽  
O. Gu¨vendik ◽  
V. O¨zerciyes
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Shear Stresses ◽  
Lap Joint ◽  
Bending Vibrations ◽  
Joint System ◽  
Adhesive Layers ◽  
Bonded Joint ◽  
Free Bending

In this present study, the “Free Bending Vibrations of a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint) with a Gap in Mindlin Plates or Panels” are theoretically analyzed and are numerically solved in some detail. The “plate adherends” and the upper and lower “doubler plates” of the “Bonded Joint” system are considered as dissimilar, orthotropic “Mindlin Plates” joined through the dissimilar upper and lower very thin adhesive layers. There is a symmetrically and centrally located “Gap” between the “plate adherends” of the joint system. In the “adherends” and the “doublers” of the “Bonded Joint” assembly, the transverse shear deformations and the transverse and rotary moments of inertia are included in the analysis. The relatively very thin adhesive layers are assumed to be linearly elastic continua with transverse normal and shear stresses. The “damping effects” in the entire “Bonded Joint” system are neglected. The sets of the dynamic “Mindlin Plate” equations of the “plate adherends”, the “double doubler plates” and the thin adhesive layers are combined together with the orthotropic stress resultant-displacement expressions in a “special form”. This system of equations, after some further manipulations, is eventually reduced to a set of the “Governing System of the First Order Ordinary Differential Equations” in terms of the “state vectors” of the problem. Hence, the final set of the aforementioned “Governing Systems of Equations” together with the “Continuity Conditions” and the “Boundary conditions” facilitate the present solution procedure. This is the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials). The present theoretical formulation and the method of solution are applied to a typical “Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint) with a Gap”. The effects of the relatively stiff (or “hard”) and the relatively flexible (or “soft”) adhesive properties, on the natural frequencies and mode shapes are considered in detail. The very interesting mode shapes with their dimensionless natural frequencies are presented for various sets of boundary conditions. Also, several parametric studies of the dimensionless natural frequencies of the entire system are graphically presented. From the numerical results obtained, some important conclusions are drawn for the “Bonded Joint System” studied here.

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 Vibrations of Bonded and Centrally Doubly Stiffened Composite Orthotropic Base Plates or Panels

Aerospace ◽  
2004 ◽  
Author(s):  
U. Yuceoglu ◽  
V. O¨zerciyes ◽  
K. C¸il
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Base Plate ◽  
Mode Shapes ◽  
Shear Stresses ◽  
Adhesive Layers ◽  
First Order ◽  
Flexural Vibrations ◽  
Interpolation Polynomials ◽  
Base Plates

The problem of the “Free Flexural Vibrations of Bonded and Centrally Doubly Stiffened Composite Orthotropic Base Plates or Panels” is formulated and investigated. The composite plate or panel system is made up of an orthtropic base plate reinforced or doubly stiffened by the upper and lower stiffening orthotropic plate strips. The stiffening plate strips are at the mid-center and are adhesively bonded to the base plate. The base plate and the stiffening plate strips are considered as dissimilar orthotropic Mindlin plates. Thus, the analysis is based on a “First Order Shear Deformation Plate Theory (FSDPT)” of Mindlin type. In the very thin, linearly elastic adhesive layers, the transverse normal and shear stresses are included. The sets of the dynamic equations and other equations of plates and adhesive layers are finally reduced to a “Governing System of the First Order Ordinary Differential Equations.” Then, this system is integrated by means of the “Modified Transfer Matrix Method (with Interpolation Polynomials and/or Chebyshev Polynomials).” The mode shapes and the associated natural frequencies are calculated and some parametric studies are presented. Also, the influences of the “hard” and the “soft” adhesive layers on the natural frequencies and the mode shapes are shown.

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.

scholarly journals Milk Production, Body Weight, Body Condition Score, Activity, and Rumination of Organic Dairy Cattle Grazing Two Different Pasture Systems Incorporating Cool- and Warm-Season Forages

Animals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 264
Author(s):  
Kathryn E. Ritz ◽  
Bradley J. Heins ◽  
Roger D. Moon ◽  
Craig C. Sheaffer ◽  
Sharon L. Weyers
Keyword(s):  
Body Weight ◽  
Milk Production ◽  
Body Condition Score ◽  
Warm Season ◽  
Cool Season ◽  
Organic Dairy ◽  
Condition Score ◽  
Annual Grasses ◽  
System 2 ◽  
System 1

Organic dairy cows were used to evaluate the effect of two organic pasture production systems (temperate grass species and warm-season annual grasses and cool-season annuals compared with temperate grasses only) across two grazing seasons (May to October of 2014 and 2015) on milk production, milk components (fat, protein, milk urea nitrogen (MUN), somatic cell score (SCS)), body weight, body condition score (BCS), and activity and rumination (min/day). Cows were assigned to two pasture systems across the grazing season at an organic research dairy in Morris, Minnesota. Pasture System 1 was cool-season perennials (CSP) and Pasture System 2 was a combination of System 1 and warm-season grasses and cool-season annuals. System 1 and System 2 cows had similar milk production (14.7 and 14.8 kg d−1), fat percentage (3.92% vs. 3.80%), protein percentage (3.21% vs. 3.17%), MUN (12.5 and 11.5 mg dL−1), and SCS (4.05 and 4.07), respectively. Cows in System 1 had greater daily rumination (530 min/day) compared to cows in System 2 (470 min/day). In summary, warm-season annual grasses may be incorporated into grazing systems for pastured dairy cattle.

scholarly journals Comparison of Three Fungicide Spray Advisories for Lettuce Downy Mildew

Plant Disease ◽  
2001 ◽  
Vol 85 (8) ◽  
pp. 895-900 ◽  
Author(s):  
B. M. Wu ◽  
K. V. Subbarao ◽  
A. H. C. van Bruggen ◽  
S. T. Koike
Keyword(s):  
Downy Mildew ◽  
Drip Irrigation ◽  
Leaf Wetness ◽  
Lettuce Downy Mildew ◽  
Advisory System ◽  
System 2 ◽  
Forecasting System ◽  
Low Incidence ◽  
System 1 ◽  
First Time

Lettuce growers in coastal California have relied mainly on protective fungicide sprays to control downy mildew. Thus, timing of sprays before infection is critical for optimal results. A leaf-wetness-driven, infection-based advisory system, previously developed, did not always perform satisfactorily. In this study, the advisory system was modified by incorporating a pathogen survival component (system 1) or both survival and sporulation components (system 2). These systems were then evaluated in commercial lettuce fields in coastal California during 1996-1998. Three or four treatments were carried out in each field: (i) no spray; (ii) sprays as scheduled by the growers; (iii) sprays following modified system 1; and (iv) sprays following the original advisory system (1996) or modified system 2 (1998). Downy mildew incidence was evaluated every 2 to 9 days. In fields with drip irrigation, the number of fungicide applications was reduced by one or two regardless of the advisory system used compared to the grower's calendar-based schedule, although one unnecessary spray was recommended in 1996 at Soledad and 1997 at Salinas. Under all three systems, disease levels were low (incidence <25% and about 1 lesion per plant) for fields with drip irrigation, but not for fields with sprinklers (incidence up to 100% and 5 to 10 lesions per plant). For the first time, we established that survival and sporulation components are not needed for a lettuce downy mildew forecasting system. Instead, a threshold with a shorter period of morning leaf wetness and high temperatures were found to have potential for improving forecasting efficiency.

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