Free vibration of thick orthotropic plates using trigonometric shear deformation theory

Ghugal, Yuwaraj M.; Sayyad, Atteshamuddin S.

doi:10.1590/s1679-78252011000300002

Cited by 41 publications

(28 citation statements)

References 24 publications

(49 reference statements)

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“…In this paper, a nth-order shear deformation theory developed by Xiang et al [18] is successfully extended for the cylindrical bending of laminated composite plates. The theory accounts for a parabolic variation of the transverse shear stress across the thickness and satisfies the traction free boundary conditions on the top and bottom surfaces of the plate without using problem dependent shear correction factors.…”

Section: Discussionmentioning

confidence: 99%

“…Carrera [17] studied the non-linear response of antisymmetrically laminated composite plates under cylindrical bending. Ghugal and Sayyad [18] have developed a trigonometric shear deformation theory taking into account transverse shear deformation effect as well as the transverse normal strain effect for the cylindrical bending of orthotropic plate. Recently Sayyad et al [19] developed a new trigonometric shear deformation theory for the flexural analysis of laminated composite and sandwich beams whereas Natarajan et al [20] studied the bidirectional bending and free vibration analysis of cross-ply laminated composite plates using trigonometric shear deformation theory.…”

Section: Introductionmentioning

confidence: 99%

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A nth-order shear deformation theory for composite laminates in cylindrical bending

Sayyad

Ghugal²

2015

Curved and Layered Structures

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The present study investigates whether an nthorder shear deformation theory is applicable for the composite laminates in cylindrical bending. The theory satisfies the traction free conditions at top and bottom surfaces of the plate and does not require problem dependent shear correction factor which is normally associated with the first order shear deformation theory. The well-known classical plate theory at (n = 1) and higher order shear deformation theory of Reddy at (n = 3) are the perticular cases of the present theory. The governing equations of equilibrium and boundary conditions are obtained using the principle of virtual work. A simply supported laminated composite plate infinitely long in y-direction is considered for the detail numerical study. A closed form solution for simply supported boundary conditions is obtained using Navier's technique. The displacements and stresses are obtained for different aspect ratios and modular ratios.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A nth-order shear deformation theory for composite laminates in cylindrical bending

Sayyad

Ghugal²

2015

Curved and Layered Structures

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“…The first order shear deformation theory (FSDT) developed by Mindlin (1951) is also not suitable for the analysis since it does not satisfy the zero stress conditions at top and bottom surfaces of the plate and required problem dependent shear correction factors. Therefore, many five variable and six variable plate theories have been developed for the analysis of plates (Reddy, 1984;Touratier, 1991;Soldatos, 1992;Karama et al, 2009;Sayyad and Ghugal, 2012;Sayyad, 2013;Zenkour, 2006;Sayyad and Ghugal, 2013;2014a;2014b;Ghugal and Sayyad, 2010;2013a;2013b;Metin, 2009).…”

Section: Introductionmentioning

confidence: 99%

Bending, Vibration and Buckling of Laminated Composite Plates Using a Simple Four Variable Plate Theory

Sayyad

Shinde

Ghugal³

2016

Lat. Am. j. solids struct.

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In the present study, a simple trigonometric shear deformation theory is applied for the bending, buckling and free vibration of crossply laminated composite plates. The theory involves four unknown variables which are five in first order shear deformation theory or any other higher order theories. The in-plane displacement field uses sinusoidal function in terms of thickness co-ordinate to include the shear deformation effect. The transverse displacement includes bending and shear components. The present theory satisfies the zero shear stress conditions at top and bottom surfaces of plates without using shear correction factor. Equations of motion associated with the present theory are obtained using the dynamic version of virtual work principle. A closed form solution is obtained using double trigonometric series suggested by Navier. The displacements, stresses, critical buckling loads and natural frequencies obtained using present theory are compared with previously published results and found to agree well with those.

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“…Free vibration analysis of thick orthotropic plates was performed by Ghugal et al (2011) using a trigonometric shear deformation theory. In their theory, the zero shear stress conditions on the top and bottom surfaces of the plates were satisfied.…”

Section: Introductionmentioning

confidence: 99%

Improved high order free vibration analysis of thick double curved sandwich panels with transversely flexible cores

Fard

Livani

Ghasemi

2014

Lat. Am. j. solids struct.

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This paper dealt with free vibration analysis of thick double curved composite sandwich panels with simply supported or fully clamped boundary conditions based on a new improved higher order sandwich panel theory. The formulation used the first order shear deformation theory for composite face sheets and polynomial description for the displacement field in the core layer which was based on the displacement field of Frostig's second model. The fully dynamic effects of the core layer and face sheets were also considered in this study. Using the Hamilton's principle, the governing equations were derived. Moreover, effects of some important parameters like that of boundary conditions, thickness ratio of the core to panel, radii curvatures and composite lay-up sequences were investigated on free vibration response of the panel. The results were validated by those published in the literature and with the FE results obtained by ABAQUS software. It was shown that thicker panels with a thicker core provided greater resistance to resonant vibrations. Also, effect of increasing the core thickness in general was significant decreased fundamental natural frequency values. KeywordsFree vibration, Double curved sandwich panel, Boundary conditions, Improved higher order sandwich panel theory.Improved high order free vibration analysis of thick double curved sandwich panels with transversely flexible cores INTRODUCTIONStructural efficiency is an important attribute for aircraft structures. A higher order theory approach, used by Kant and Patil (1991), replaced sandwich structure with an equivalent higher order shear deformable structure, which lacked the ability to determine local buckling modes and imperfection effects on the overall behavior. Using the three-dimensional elasticity equations, Bhimaraddi (1993) studied the static response of orthotropic doubly curved shallow shells. He assumed that the ratio of the shell thickness to its middle surface radius is negligible as compared to unity. The high- er order sandwich panel theory was developed by Frostig et al. (1994Frostig et al. ( , 2004, who considered two types of computational models in order to express governing equations of the core layer. The second model assumed a polynomial description of the displacement fields in the core that was based on displacement fields of the first model. Their theory did not impose any restrictions on distribution of the deformation through thickness of the core. Singh (1999) studied free vibration of the open deep sandwich shells made of thin layers and a moderately thick core. Rayleigh-Ritz method was also used to obtain natural frequencies. The improved higher order sandwich plate theory (IHSAPT), applying the first-order shear deformation theory for the face sheets, was introduced by Malekzadeh et al. (2005Malekzadeh et al. ( , 2006.

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Free vibration of thick orthotropic plates using trigonometric shear deformation theory

Cited by 41 publications

References 24 publications

A nth-order shear deformation theory for composite laminates in cylindrical bending

A nth-order shear deformation theory for composite laminates in cylindrical bending

Bending, Vibration and Buckling of Laminated Composite Plates Using a Simple Four Variable Plate Theory

Improved high order free vibration analysis of thick double curved sandwich panels with transversely flexible cores

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