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.

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.

Natural Frequencies and Mode Shapes of Laminated Composite Plates: Experiments and FEA

1996 ◽  
Vol 2 (4) ◽  
pp. 381-414 ◽  
Author(s):  
T.J. Anderson ◽  
A.H. Nayfeh
Keyword(s):  
Natural Frequencies ◽  
Laminated Composite ◽  
Composite Plates ◽  
Test Methods ◽  
Mode Shapes ◽  
Boundary Condi Tions ◽  
Element Analysis ◽  
Condi Tions ◽  
Theoretical Results ◽  
Good Agreement

The natural frequencies and mode shapes of several graphite-epoxy plates were determined using experimental modal analysis and finite-element analysis. The experimental and theoretical results are com pared. The samples tested included four types of layups: ±15°, ±30°, cross-ply, and quasi-isotropic plates. Each plate was tested in three configurations: free-hanging, cantilever, and fixed-fixed for a total of twelve test configurations. The material properties of the plates and the test methods used to obtain them are in cluded. There is a very good agreement between the experimental and theoretical results for the free-hanging and cantilever configurations. The agreement for the fixed-fixed results is poor. This indicates that the clamps for the fixed-fixed configuralion are not ideal and that they introduce some uncertainty in the boundary condi tions. The free-hanging results provide accurate experimental natural frequencies of several composite plates; they can be used to validate future theoretical developments. The fixed-fixed results are used to provide pos sible explanations for the discrepancies between the measured and calculated natural frequencies previously reported in the literature.

scholarly journals Effect of Moment of Inertia of Attached Mass on Natural Frequencies of Cantilevered Symmetrically Laminated Plates

2018 ◽  
Vol 1 (2) ◽  
pp. 35-39
Author(s):  
Kenji Hosokawa
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Composite Plates ◽  
Vibration Characteristics ◽  
Laminated Plates ◽  
Moment Of Inertia ◽  
Mode Shapes ◽  
Attached Mass ◽  
Structural Applications

Since composite materials such as laminated composite plates have high specific strength and high structural efficiency, they have been usedin many structural applications. It is therefore very important to make clear the vibration characteristics of the laminated plates for the designand the structural analysis. Especially, the vibration characteristics of the laminated plates with attached mass are essential. However, wecannot find the theoretical or experimental approaches for the free vibration of laminated plates with attached mass. In the present study, theexperimental and numerical approaches are applied to the free vibration of cantilevered symmetrically laminated plates with attached mass.First, by applying the experimental modal analysis technique to the cantilevered symmetrically laminated plates with attached mass, thenatural frequencies and mode shapes of the plates are obtained. Next, the natural frequencies and mode shapes of the cantileveredsymmetrically laminated plates with attached mass are calculated by Finite Element Method (FEM). Finally, from the experimental andnumerical results, the effect of the moment of inertia of the attached mass to the natural frequencies and mode shapes of the cantileveredsymmetrically laminated plates are clarified.

scholarly journals Free Vibration Analysis of Laminated Composite Plates with General Boundary Elastic Supports Under Initial Thermal Load

2019 ◽  
Vol 15 (4) ◽  
pp. 23-32
Author(s):  
Mohammed B. Hammed ◽  
Widad I. Majeed
Keyword(s):  
Aspect Ratio ◽  
Free Vibration ◽  
Natural Frequency ◽  
Thermal Load ◽  
Ritz Method ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Design Parameters ◽  
Laminated Plate

Free vibration behavior was developed under the ratio of critical buckling temperature of laminated composite thin plates with the general elastic boundary condition. The equations of motion were found based on classical laminated plate theory (CLPT) while the solution functions consists of trigonometric function and a continuous function that is added to guarantee the sufficient smoother of the so-named remaining displacement function at the boundaries, in this research, a modified Fourier series were used, a generalized procedure solution was developed using Ritz method combined with the imaginary spring technique. The influences of many design parameters such as angles of layers, aspect ratio, thickness ratio, and ratio of initial in- plane thermal load in addition to different boundary conditions on the natural frequencies of laminated plate is analyzed. In general, the changes of fundamental natural frequency is inversely proportional with the ratio of thermal buckling load, also most parameters aspect ratio effect on the natural frequency about 35 – 40%. The present results were compared with those obtained by other researchers, and show good agreement.

Dynamic Analysis of Composite Plates

2005 ◽  
Author(s):  
Stefan Sorohan ◽  
Ioan Parausanu ◽  
Adrian Motomancea ◽  
Dumitru I. Caruntu
Keyword(s):  
Material Properties ◽  
Orthotropic Plate ◽  
Natural Frequencies ◽  
Composite Plates ◽  
Experimental Tests ◽  
Element Model ◽  
Mode Shapes ◽  
Rigid Rod ◽  
Sand Particles ◽  
Research Stage

The paper presents comparatively the measured and estimated natural frequencies and mode shapes of a rectangular orthotropic panel. The experimental tests were performed using a shaker. The plate was fixed in horizontal position directly on the shaker armature using a rigid rod. The experimental modes shapes were visualized using sand particles. The measured natural frequencies and also the modes shapes correspond to the whole system in motion. So, the analytic model of the plate must include the effect of the vibrator connected to the plates. The purpose of this experimental measurements and analytic modeling of such plates is to further developing a methodology to estimate the material properties of the composite panels. At this research stage, an orthotropic plate with unknown material properties was investigated. Using an adequate finite element model, the mechanical properties of the material were estimated. Using these properties it is possible to numerically estimate the dynamic behavior of the plate for additional sets of boundary conditions.

Electroelastic modeling of thin-laminated composite plates with surface-bonded piezo-patches using Rayleigh–Ritz method

2018 ◽  
Vol 29 (10) ◽  
pp. 2192-2205 ◽  
Author(s):  
Mehmet Murat Gozum ◽  
Amirreza Aghakhani ◽  
Gokhan Serhat ◽  
Ipek Basdogan
Keyword(s):  
Modal Analysis ◽  
Vibration Analysis ◽  
Composite Structures ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
System Level ◽  
Laminated Composite Plates ◽  
Modeling Tools ◽  
Analysis And Design

Laminated composite panels are extensively used in various engineering applications. Piezoelectric transducers can be integrated into such composite structures for a variety of vibration control and energy harvesting applications. Analyzing the structural dynamics of such electromechanical systems requires precise modeling tools which properly consider the coupling between the piezoelectric elements and the laminates. Although previous analytical models in the literature cover vibration analysis of laminated composite plates with fully covered piezoelectric layers, they do not provide a formulation for modeling the piezoelectric patches that partially cover the plate surface. In this study, a methodology for vibration analysis of laminated composite plates with surface-bonded piezo-patches is developed. Rayleigh–Ritz method is used for solving the modal analysis and obtaining the frequency response functions. The developed model includes mass and stiffness contribution of the piezo-patches as well as the two-way electromechanical coupling effect. Moreover, an accelerated method is developed for reducing the computation time of the modal analysis solution. For validations, system-level finite element simulations are performed in ANSYS software. The results show that the developed analytical model can be utilized for accurate and efficient analysis and design of laminated composite plates with surface-bonded piezo-patches.

scholarly journals Free vibration analysis of isotopic rectangular plate with one edge free of support (CSCF and SCFC plate)

2014 ◽  
Vol 3 (1) ◽  
pp. 30 ◽  
Author(s):  
Stanley I Ebirim ◽  
J C Ezeh ◽  
M Owus Ibearugbulem
Keyword(s):  
Aspect Ratio ◽  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Shape Function ◽  
Ritz Method ◽  
Dimensional Parameter ◽  
Fundamental Natural Frequency ◽  
Aspect Ratios ◽  
Significant Difference

The paper presents a theoretical formulation based on Ibearugbulems shape function and application of Ritz method. In this study, the free vibration of simply supported plate with one free edge was analyzed. The Ibearugbulems shape function derived was substituted into the potential energy functional, which was minimized to obtain the fundamental natural frequency. Aspect ratios from 0.1 to 2.0 with 0.1 increments were considered. The values of fundamental natural frequencies of the first mode were determined for different aspect ratio. For aspect ratio of 1.0, the value of non-dimensional parameter of fundamental natural frequency obtained was 23.86. Comparison was made for values of non-dimensional parameter of fundamental natural frequencies obtained in this study with those of previous research works. It was seen that there is no significant difference between values obtained in this study with those of previous studies. Keywords: fundamental natural frequency; Ibearugbulems shape function; CSCF plate; Ritz method; SCFC plate.

Vibration-based delamination evaluation in GFRP composite beams using ANN

2021 ◽  
pp. 096739112110033
Author(s):  
TG Sreekanth ◽  
M Senthilkumar ◽  
S Manikanta Reddy
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Composite Structures ◽  
Composite Beams ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Aviation Industry ◽  
Frequency Data ◽  
Fiber Reinforced ◽  
Back Propagation Algorithm

Delamination is definitely an important topic in the area of composite structures as it progressively worsens the mechanical performance of fiber-reinforced polymer composite structures in its service period. The detection and severity analysis of delaminations in engineering areas like the aviation industry is vital for safety and economic considerations. The existence of delaminations varies the vibration characteristics such as natural frequencies, mode shapes, etc. of composites and hence this indication can be effectively used for locating and quantifying the delaminations. The changes in vibration characteristics are considered as inputs for the inverse problem to determine the location and size of delaminations. In this paper Artificial Neural Network (ANN) is used for delamination evaluationof glass fiber-reinforced composite beams using natural frequency as typical vibration parameter. The Finite Element Analysis is used for generating the required dataset for ANN. The frequency-based delamination prediction technique is validated by finite element models and experimental modal analysis. The results indicate that the ANN-based back propagation algorithm can predict the location and size of delaminations in composites with good accuracy for numerical natural frequency data but the accuracy is comparitivelyless for experimental natural frequency data.

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