Exact 3D piezoelasticity solution of hybrid cross–ply plates with damping under harmonic electro-mechanical loads

Kapuria, S.; Achary, G.G.S.

doi:10.1016/j.jsv.2004.03.030

Cited by 30 publications

(12 citation statements)

References 22 publications

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“…The formulation and very limited results for the exact 3D elasticity solution for natural frequencies of simply supported rectangular laminated plates were presented by Srinivas and Rao [41]. Kapuria and Achary [18] have extended it to present an exact 3D piezoelasticity solution for the dynamic response of rectangular multi-layered piezoelectric plates. In this study, the exact 3D elasticity results for ω n in Tables 3, 5, 6 and 10 have been obtained as special case of the piezoelasticity solution, using the computer program developed in the work of [18].…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…Kapuria and Achary [18] have extended it to present an exact 3D piezoelasticity solution for the dynamic response of rectangular multi-layered piezoelectric plates. In this study, the exact 3D elasticity results for ω n in Tables 3, 5, 6 and 10 have been obtained as special case of the piezoelasticity solution, using the computer program developed in the work of [18]. These results have been validated with those of [41].…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

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Free vibration analysis of composite and sandwich plates using an improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory

2008

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The new improved discrete Kirchhoff quadrilateral element based on the third-order zigzag theory developed earlier by the present authors for the static analysis of composite and sandwich plates is extended for dynamics and assessed for its performance for the free vibration response. The element is free from the shear locking. The finite element formulation is validated by comparing the results for simply supported plates with the analytical Navier solution of the zigzag theory. Comparison of the present results for the natural frequencies with those of a recently developed triangular element based on the zigzag theory, for composite and sandwich plates, establishes the superiority of the present element in respect of simplicity, accuracy and computational efficiency. The accuracy of the zigzag theory is assessed for composite and sandwich plates with various boundary conditions and aspect ratio by comparing the finite element results with the 3D elasticity analytical and finite element solutions.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Numerical Results and Discussionmentioning

confidence: 99%

Free vibration analysis of composite and sandwich plates using an improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory

2008

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“…The exact 3D results for free vibration response have been obtained by using the methodology presented by Heyliger and Saravanos [1] after validating the results and those for forced vibration have been obtained from Ref. [4]. Since TOT has the same number of displacement variables as the present theory and does not require an arbitrary shear correction factor, results are also compared with the coupled TOT [16].…”

Section: Results and Assessmentmentioning

confidence: 99%

“…Three-dimensional solutions [4] reveal that, for moderately thick plates under electric potential load, w has significant variation across the thickness due to the much greater electrical contribution to ε z than that of σ x , σ y . This is also confirmed by the distributions of w across the elastic and piezo layers presented later in Figs.…”

Section: Displacement and Potential Field Approximationsmentioning

confidence: 99%

“…The theory can model both open and closed circuit electric boundary conditions. The accuracy of the theory is assessed by direct comparison with the analytical coupled 3D piezoelasticity solutions [1,4] for free vibration and the forced time-harmonic damped response of simply supported hybrid plates. The results are also compared with coupled mixed-field TOT [16] in which zero transverse shear strain conditions are imposed at the top and bottom surfaces.…”

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A coupled zigzag theory for the dynamics of piezoelectric hybrid cross-ply plates

Kapuria

Achary

2005

Arch Appl Mech

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A recently developed coupled third-order zigzag theory for the statics of piezoelectric hybrid crossply plates is extended to dynamics. The theory combines a third-order zigzag approximation for the in-plane displacements and a sub-layerwise linear approximation for the electric potential, considering all components of the electric field. The nonuniform variation of the transverse displacement due to the piezoelectric field is accounted for. The conditions for the absence of shear traction at the top and bottom surfaces and continuity of transverse shear stresses in the presence of electromechanical loading are satisfied exactly, thereby reducing the number of displacement variables to five, which is the same as in a first-or third-order equivalent single-layer theory. The governing equations of motion are derived from the extended Hamilton's principle. The theory is assessed by comparing the Navier solutions for the free and forced harmonic vibration response of simply supported plates with the exact three-dimensional piezoelasticity solutions. Comparisons for hybrid test, composite and sandwich plates establish that the present theory is quite accurate for the dynamic response of moderately thick plates.

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Free Vibration Analysis of Levy-Type Smart Hybrid Plates Using Three-Dimensional Extended Kantorovich Method

Behera

Kumari

2019

Lecture Notes in Mechanical Engineering

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Exact 3D piezoelasticity solution of hybrid cross–ply plates with damping under harmonic electro-mechanical loads

Cited by 30 publications

References 22 publications

Free vibration analysis of composite and sandwich plates using an improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory

Free vibration analysis of composite and sandwich plates using an improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory

A coupled zigzag theory for the dynamics of piezoelectric hybrid cross-ply plates

Free Vibration Analysis of Levy-Type Smart Hybrid Plates Using Three-Dimensional Extended Kantorovich Method

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