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 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.

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.

Frequency Response of a Three-Node Finite Element for Composite Thin and Thick Plates

2004 ◽  
Author(s):  
A. V. S. Ravi Shastry ◽  
Pramod Kumar
Keyword(s):  
Finite Element ◽  
Frequency Response ◽  
Plate Theory ◽  
Composite Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Integration Scheme ◽  
Shear Locking ◽  
Triangular Finite Element ◽  
Strain Components

A shear-locking free isoparametric three-node triangular finite element is considered for the study of frequency response of moderately thick and thin composite plates. The strain displacement relationship is based on Reissner-Mindlin plate theory that accounts for transverse shear deformations into the plate formulation to circumvent the shear locking effect. The element is developed with full integration scheme; hence the element remains kinematically stable. The performance of the element for the case of static load response using the shear correction terms to shear strain components applied to a composite plate has been studied. The natural frequencies and mode shapes in accordance with varying mode numbers, are deduced and the results are compared with the available analytical and finite element solutions in literature.

Analytical Solution for Free Vibration of Annular Mindlin Plate with a Circumferential Open Crack

2019 ◽  
Vol 24 (3) ◽  
pp. 494-503
Author(s):  
Eshagh Derakhshan ◽  
Mahboobeh Fakhrzarei ◽  
Shahram Derakhshan
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Crack Depth ◽  
Current Method ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Open Crack ◽  
Element Analysis ◽  
Radial Location

Mindlin plate theory is employed to obtain the free vibration response of an annular moderately thick plate with a circumferential open crack with fixed-free boundary conditions. To model the crack, a set of continuously distributed rotational springs are employed at the crack location. The corresponding spring stiffness value is a function of the crack depth and is given as a closed-form function. To obtain the vibration behaviour, the eigenvalue problem is solved to obtain the natural frequencies and mode shapes. The current method is verified by comparing the results with those obtained from finite element analysis. Through a parametric study, the effects of the crack depth and its radial location on the natural frequencies and mode shapes are investigated. The results show that for a constant crack depth, the reduction in natural frequency is a strong function of the radial location of the crack.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

Effect of Delamination on Natural Frequencies of E-glass and S-glass Epoxy Composite Plates

2021 ◽  
Author(s):  
P. K. Karsh ◽  
Bindi Thakkar ◽  
R. R. Kumar ◽  
Abhijeet Kumar ◽  
Sudip Dey
Keyword(s):  
Natural Frequencies ◽  
Epoxy Composite ◽  
Orientation Angle ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Transverse Shear Deformation ◽  
The Finite Element Method ◽  
Modes Of Failure ◽  
Ply Orientation

The delamination is one of the major modes of failure occurring in the laminated composite due to insufficient bonding between the layers. In this paper, the natural frequencies of delaminated S-glass and E-glass epoxy cantilever composite plates are presented by employing the finite element method (FEM) approach. The rotary inertia and transverse shear deformation are considered in the present study. The effect of parameters such as the location of delamination along the length, across the thickness, the percentage of delamination, and ply-orientation angle on first three natural frequencies of the cantilever plates are presented for S-glass and E-glass epoxy composites. The standard eigenvalue problem is solved to obtain the natural frequencies and corresponding mode shapes. First three mode shape of S-Glass and E-Glass epoxy laminated composites are portrayed corresponding to different ply angle of lamina.

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 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.

Maximizing the Fundamental Natural Frequency of Triangular Composite Plates

1996 ◽  
Vol 118 (2) ◽  
pp. 141-146 ◽  
Author(s):  
S. Abrate
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Composite Structures ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Fundamental Natural Frequency ◽  
Wide Range

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

In-Plane Vibration Modes of Arbitrarily Thick Disks

1997 ◽  
Author(s):  
Kevin I. Tzou ◽  
Jonathan A. Wickert ◽  
Adnan Akay
Keyword(s):  
Natural Frequencies ◽  
Arbitrary Dimension ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Three Dimensional Model ◽  
Bending Vibration ◽  
Annular Disk ◽  
Out Of Plane ◽  
Plane Bending

Abstract The three-dimensional vibration of an arbitrarily thick annular disk is investigated for two classes of boundary conditions: all surfaces traction-free, and all free except for the clamped inner radius. These two models represent limiting cases of such common engineering components as automotive and aircraft disk brakes, for which existing models focus on out-of-plane bending vibration. For a disk of significant thickness, vibration modes in which motion occurs within the disk’s equilibrium plane can play a substantial role in setting its dynamic response. Laboratory experiments demonstrate that in-plane modes exist at frequencies comparable to those of out-of-plane bending even for thickness-to-diameter ratios as small as 10−1. The equations for three-dimensional motion are discretized through the Ritz technique, yielding natural frequencies and mode shapes for coupled axial, radial, and circumferential deformations. This treatment is applicable to “disks” of arbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings, and shells. The solutions so obtained converge in the limiting cases to the values expected from the classical theories, and to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the technologically-important range, the natural frequencies of certain in- and out-of-plane modes can be close to one another, or even identically repeated.

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