Free Flexural Vibration of Composite Plates in Different Situations Using a                High Precision Triangular Element

A high precision, thick-plate element developed by D. Sengupta has been applied to the free vibration analysis of laminated composite plates with necessary addition and modification. The effect of shear deformation has been incorporated in the formulation, taking the transverse displacement and rotations of the normal as independent field variables. These are approximated with polynomials of different orders, which has made the element free from locking in shear. The element contains internal nodes. The degrees of freedom of these nodes have been eliminated through condensation in its final form. To facilitate the condensation, an efficient mass lumping scheme has been recommended to form the mass matrix having zero mass for the internal nodes. Recommendation has also been made for the inclusion of the rotary inertia in the lumped mass matrix. Numerical examples of plates having different shapes, boundary conditions, thickness ratios, fiber orientations and number of layers have been solved. Examples of plates having internal cutout and concentrated mass have also been studied. The results obtained in all cases have been compared with those obtained from other sources to show the accuracy and range of applicability of the element.

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A High Precision Shear Flexible Triangular Element for Vibration of Composite Shells

Shock and Vibration ◽

10.1155/2004/342808 ◽

2004 ◽

Vol 11 (5-6) ◽

pp. 585-596

Author(s):

A.H. Sheikh ◽

S. Haldar ◽

D. Sengupta

Keyword(s):

High Precision ◽

Mass Matrix ◽

Free Vibration Analysis ◽

Rotary Inertia ◽

Triangular Element ◽

Future Research ◽

Lumped Mass ◽

Efficient Manner ◽

Static Condensation ◽

Wide Range

A high precision triangular shallow shell element is proposed and it is applied to free vibration analysis of composite and isotropic shells. The Mindlin's hypothesis is followed to include the effect of shear deformation. The formulation is made in an efficient manner to make the element free from shear locking problem. The element has some internal nodes, which are eliminated through static condensation technique to improve the computational elegance of the element. In the present vibration problem, the implementation of the static condensation became possible with the help of an efficient mass lumping scheme. It is quite interesting that the effect of rotary inertia can be included in the recommended scheme for lumped mass matrix. Numerical examples covering a wide range of problems are solved and the results obtained are compared with the published results in many cases, which show the precision and range of applicability of the proposed element. The performance of the proposed technique for rotary inertia is found to be excellent. Some new results are produced, which may be useful in future research.

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Experimental and Numerical Modal Analysis of Composite Laminated Shells

10.3940/rina.ijme.2019.a1.495 ◽

2019 ◽

Vol 161 (A1) ◽

Keyword(s):

Heat Dissipation ◽

Mass Matrix ◽

Experimental Studies ◽

Free Vibration Analysis ◽

Mode Shapes ◽

Radius Of Curvature ◽

Lumped Mass ◽

Auxiliary Equipment ◽

Mass Model ◽

Laminated Shells

The presence of cut outs at different positions of laminated shell component in marine and aeronautical structures facilitate heat dissipation, undertaking maintenance, fitting auxiliary equipment, access ports for mechanical and electrical systems, damage inspection and also influences the dynamic behaviour of the structures. The aim of the present study is to establish a comprehensive perspective of dynamic behavior of laminated deep shells (length to radius of curvature ratio less than one) with cut-out by experiments and numerical simulation. The glass epoxy laminated composite shell has been prepared in the laboratory by resin infusion. The experimental free vibration analysis is carried out on laminated shells with and without cut-out. The mass matrix is developed by considering rotary inertia in a lumped mass model in the numerical modeling. The results obtained from numerical and experimental studies are compared for verification and the consistency between mode shapes is established by applying modal assurance criteria.

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A NEW TRIANGULAR ELEMENT BASED ON HIGHER ORDER SHEAR DEFORMATION THEORY FOR FLEXURAL VIBRATION OF COMPOSITE PLATES

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455402000506 ◽

2002 ◽

Vol 02 (02) ◽

pp. 163-184 ◽

Cited By ~ 5

Author(s):

A. CHAKRABARTI ◽

A. H. SHEIKH

Keyword(s):

Shear Deformation ◽

Vibration Analysis ◽

Deformation Theory ◽

Plate Theory ◽

Plate Thickness ◽

Shear Deformation Theory ◽

Free Vibration Analysis ◽

Composite Plates ◽

Higher Order ◽

Triangular Element

A triangular element based on Reddy's higher order shear deformation theory is developed for free vibration analysis of composite plates. In the Reddy's plate theory, the transverse shear stress varies in a parabolic manner across the plate thickness and vanishes at the top and bottom surfaces of the plate. Moreover, it does not involve any additional unknowns. Thus the plate theory is quite simple and elegant. Unfortunately, such an attractive plate theory cannot be exploited as expected in finite element analysis, primarily due to the difficulties in satisfying the inter-element continuity requirement. This has inspired us to develop the present element, which has three corner nodes and three mid-side nodes with the same number of degrees of freedom. To demonstrate the performance of the element, numerical examples of isotropic and composite plates under different situations are solved. The results are compared with the analytical solutions and other published results, which show the accuracy and range of applicability of the proposed element in the problem of vibration analysis.

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A New Rectangular Plate Element for Vibration Analysis of Laminated Composites

Journal of Vibration and Acoustics ◽

10.1115/1.2893830 ◽

1998 ◽

Vol 120 (1) ◽

pp. 80-86 ◽

Cited By ~ 10

Author(s):

Guan-Liang Qian ◽

Suong V. Hoa ◽

Xinran Xiao

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Rectangular Plate ◽

Degrees Of Freedom ◽

Mass Matrix ◽

Shear Deformation Theory ◽

Composite Plates ◽

Element Model ◽

Higher Order ◽

Transverse Displacement

In this paper, a higher order rectangular plate bending element based on a Higher Order Shear Deformation Theory (HSDT) is developed. The element has 4 nodes and 20 degrees of freedom. The transverse displacement is interpolated by using an optimized interpolation function while the additional rotation degrees of freedom are approximated by linear Lagrange interpolation. The consistent element mass matrix is used. A damped element is introduced to the finite element model. The proposed FEM is used to calculate eigenfrequencies and modal damping of composite plates with various boundary conditions and different thicknesses. The results show that the present FEM gives excellent results when compared to other methods and experiment results, and is efficient and reliable for both thick and thin plates. The proposed finite element model does not lock in the thin plate situation and does not contain any spurious vibration mode, and converges rapidly. It will provide a good basis for the inverse analysis of vibration of a structure.

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Development of the Cell-based Smoothed Discrete Shear Gap Plate Element (CS-FEM-DSG3) using Three-Node Triangles

International Journal of Computational Methods ◽

10.1142/s0219876215400150 ◽

2015 ◽

Vol 12 (04) ◽

pp. 1540015 ◽

Cited By ~ 13

Author(s):

T. Nguyen-Thoi ◽

M. H. Nguyen-Thoi ◽

T. Vo-Duy ◽

N. Nguyen-Minh

Keyword(s):

Static Analysis ◽

Free Vibration Analysis ◽

Composite Plates ◽

Functionally Graded ◽

Triangular Element ◽

Plate Element ◽

Strain Smoothing ◽

Discrete Shear Gap ◽

Transverse Shear Locking ◽

Coarse Meshes

The paper presents the formulation and recent development of the cell-based smoothed discrete shear gap plate element (CS-FEM-DSG3) using three-node triangles. In the CS-FEM-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the original plate element DSG3 is used to compute the strains and to avoid the transverse shear locking. Then the cell-based strain smoothing technique (CS-FEM) is used to smooth the strains on these three sub-triangles. The numerical examples illustrate four superior properties of the CS-FEM-DSG3 including: (1) being a strong competitor to many existing three-node triangular plate elements in the static analysis; (2) giving high accurate solutions for problems with skew geometries in the static analysis; (3) giving high accurate solutions in free vibration analysis; (4) providing accurate values of high frequencies of plates by using only coarse meshes. Due to its superior and simple properties, the CS-FEM-DSG3 has been now developed for various analyses such as: flat shells, stiffened plates, functionally graded plates, composite plates, piezoelectricity composite plates, cracked plate and plates resting on the viscoelastic foundation subjected to moving loads, etc.

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A new finite element for free vibration analysis of stiffened composite plates

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/29/4/5603 ◽

2007 ◽

Vol 29 (4) ◽

pp. 529-538 ◽

Cited By ~ 1

Author(s):

Tran Ich Thinh ◽

Ngo Nhu Khoa

Keyword(s):

Finite Element ◽

Free Vibration ◽

Vibration Analysis ◽

Plate Theory ◽

Free Vibration Analysis ◽

Composite Plates ◽

Laminated Plates ◽

Triangular Element ◽

Plate Element ◽

Stiffened Plate

A new 6-noded stiffened triangular plate element for the analysis of stiffened composite plates based on Mindlins deformation plate theory has been developed. The stiffened plate element is a combination of basic triangular element and bar component. The element can accommodate any number of arbitrarily oriented stiffeners and obviates the use of mesh lines along the stiffeners. Free vibration analyses of stiffened laminated plates have been carried out with this element and the results are compared with those published. The finite element results show very good matching with the experimental ones.

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A Hermite Spline Layerwise Time Domain Spectral Finite Element for Guided Wave Prediction in Laminated Composite and Sandwich Plates

Journal of Vibration and Acoustics ◽

10.1115/1.4035702 ◽

2017 ◽

Vol 139 (3) ◽

Cited By ~ 11

Author(s):

C. S. Rekatsinas ◽

D. A. Saravanos

Keyword(s):

Finite Element ◽

Time Domain ◽

Guided Waves ◽

Mass Matrix ◽

Time Integration ◽

Laminated Composite ◽

Guided Wave ◽

Sandwich Plates ◽

Transverse Displacement ◽

Lumped Mass

A new time domain spectral plate finite element (FE) is developed to provide fast numerical calculations of guided waves and transient phenomena in laminated composite and sandwich plates. A new multifield layerwise laminate theory provides the basis for the FE, which incorporates cubic Hermite polynomial splines for the approximation of the in-plane and transverse displacement fields through the thickness of the plate, enabling the modeling of symmetric and antisymmetric wave modes. The time domain spectral FE with multi-degrees-of-freedom (DOF) per node is subsequently formulated, which uses integration points collocated with the nodes to yield consistent diagonal lumped mass matrix which expedites the explicit time integration process. Numerical simulations of wave propagation in aluminum, laminated carbon/epoxy and thick sandwich plates are presented and validated with an analytical solution and a three-dimensional (3D) solid element; moreover, the capability to accurately and rapidly predict antisymmetric and symmetric guided waves is demonstrated.

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EXPERIMENTAL AND NUMERICAL MODAL ANALYSIS OF COMPOSITE LAMINATED SHELLS WITH CUT-OUT

The International Journal of Maritime Engineering ◽

10.5750/ijme.v161ia1.1077 ◽

2021 ◽

Vol 161 (A1) ◽

Author(s):

A Mandal ◽

C Ray ◽

S Haldar

Keyword(s):

Heat Dissipation ◽

Mass Matrix ◽

Experimental Studies ◽

Free Vibration Analysis ◽

Mode Shapes ◽

Radius Of Curvature ◽

Lumped Mass ◽

Auxiliary Equipment ◽

Mass Model ◽

Laminated Shells

The presence of cutouts at different positions of laminated shell component in marine and aeronautical structures facilitate heat dissipation, undertaking maintenance, fitting auxiliary equipment, access ports for mechanical and electrical systems, damage inspection and also influences the dynamic behaviour of the structures. The aim of the present study is to establish a comprehensive perspective of dynamic behavior of laminated deep shells (length to radius of curvature ratio less than one) with cut-out by experiments and numerical simulation. The glass epoxy laminated composite shell has been prepared in the laboratory by resin infusion. The experimental free vibration analysis is carried out on laminated shells with and without cut-out. The mass matrix is developed by considering rotary inertia in a lumped mass model in the numerical modeling. The results obtained from numerical and experimental studies are compared for verification and the consistency between mode shapes is established by applying modal assurance criteria.

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