A Higher Order Theory for Free Vibration of Orthotropic, Homogeneous, and Laminated Rectangular Plates

Bhimaraddi, A.; Stevens, Leonard K.

doi:10.1115/1.3167569

Cited by 192 publications

(53 citation statements)

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“…Further, there is again very good correspondence between present results and those obtained from the literature, i.e. Bhimaraddi and Stevens [18].…”

Section: Convergence Study Veriÿcation and Parametric Studiessupporting

confidence: 92%

“…The in-plane and transverse grid point distributions implemented in this example are the same as those used for obtaining the converged results of the last example. Comparisons of present numerical results with higherorder theory results of Bhimaraddi and Stevens [18] are presented in Tables IVa and IVb. It is observed from the results that the interlaminar thickness ratios have minimal in uence on the natural frequencies, but this in uence becomes slightly more pronounced for the higher frequencies.…”

Section: Convergence Study Veriÿcation and Parametric Studiesmentioning

confidence: 78%

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Three‐dimensional theory of elasticity for free vibration analysis of composite laminates via layerwise differential quadrature modelling

Zhang

Liew

2003

Numerical Meth Engineering

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SUMMARYIn this paper, the free vibration analysis of simply-supported and clamped composite laminates, especially thick laminates, is carried out. The three-dimensional theory of elasticity is integrated into a layerwise model via di erential quadrature discretization. All physical governing equations are satisÿed, including the additional constraints of the characteristics of continuity and discontinuity of interfacial transverse and in-plane strains and stresses along the interfaces of composite laminates. E ects of plate aspect and thickness ratios on the free vibration of these laminates are examined in detail. This study demonstrates the applicability, accuracy, and stability of the present methodology, for vibration analyses of composite structures of thick laminated constitution.

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“…Further, there is again very good correspondence between present results and those obtained from the literature, i.e. Bhimaraddi and Stevens [18].…”

Section: Convergence Study Veriÿcation and Parametric Studiessupporting

confidence: 92%

Section: Convergence Study Veriÿcation and Parametric Studiesmentioning

confidence: 78%

Three‐dimensional theory of elasticity for free vibration analysis of composite laminates via layerwise differential quadrature modelling

Zhang

Liew

2003

Numerical Meth Engineering

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“…Along y"0,¸W: (7,8,10). These latter quantities can be then expressed by combining equations (19,10) in terms of the displacement and displacement gradients to obtain part of the generalized constitutive equations.…”

Section: Vibration Of Multilayered Platesmentioning

confidence: 99%

Free Vibrations of Multilayered Plates Based on a Mixed Variational Approach in Conjunction With Global Piecewise-Smooth Functions

Messina

2002

Journal of Sound and Vibration

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“…. unknowns, Lo et al [16,17] with 11 unknowns, Kant [7] with six unknowns, Bhimaraddi and Stevens [2] with five unknowns, Reddy [23] with eight unknowns, Hanna and Leissa [5] with four unknowns. Srinivas et al [27] used an exact three dimensional plate theory to study the vibration of simply supported homogenous and laminated thick rectangular plates.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of thick orthotropic plates using trigonometric shear deformation theory

Ghugal¹,

Sayyad²

2011

Lat. Am. j. solids struct.

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In this paper a trigonometric shear deformation theory is presented for the free vibration of thick orthotropic square and rectangular plates. In this displacement based theory the in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The cosine function in terms of thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. The most important feature of the theory is that the transverse shear stress can be obtained directly from the constitutive relations satisfying the shear stress free surface conditions on the top and bottom surfaces of the plate. Hence the theory obviates the need of shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Results obtained for frequency of bending mode, shear mode and thickness stretch mode of free vibration of simply supported orthotropic square and rectangular plates are compared with those of other refined theories and exact solution from theory of elasticity wherever applicable.

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A Higher Order Theory for Free Vibration of Orthotropic, Homogeneous, and Laminated Rectangular Plates

Cited by 192 publications

References 0 publications

Three‐dimensional theory of elasticity for free vibration analysis of composite laminates via layerwise differential quadrature modelling

Three‐dimensional theory of elasticity for free vibration analysis of composite laminates via layerwise differential quadrature modelling

Free Vibrations of Multilayered Plates Based on a Mixed Variational Approach in Conjunction With Global Piecewise-Smooth Functions

Free vibration of thick orthotropic plates using trigonometric shear deformation theory

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