Nonlinear vibrations of moderately thick orthotropic shallow spherical shells

Sathyamoorthy, M.

doi:10.1016/0045-7949(94)00585-q

Cited by 29 publications

(8 citation statements)

References 15 publications

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“…The e!ects of large vibration amplitudes on #exural vibrations of moderately thick orthotropic spherical shells, taking into account the transverse shear deformation and rotary inertia e!ects, have been studied by Sathyamoorthy [150]. He obtained a coupled set of non-linear equations which have been solved using Galerkin's method and employing the numerical Runge}Kutta integration procedure.…”

Section: Closed and Open Composite Shellsmentioning

confidence: 99%

Non-Linear Vibrations of Shell-Type Structures: A Review With Bibliography

Moussaoui¹,

Benamar²

2002

Journal of Sound and Vibration

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Section: Closed and Open Composite Shellsmentioning

confidence: 99%

Non-Linear Vibrations of Shell-Type Structures: A Review With Bibliography

Moussaoui¹,

Benamar²

2002

Journal of Sound and Vibration

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“…Some recent contributions are discussed as follows. The effects of large amplitude on the geometrically non-linear dynamic behavior of moderately thick orthotropic shallow spherical shells are obtained using shallow shell theory by Sathyamoorthy [1]. Liu and Huang [2] reported non-linear free vibration behavior of laminated plates by taking the non-linear kinematics in the von Karman sense in the framework of the FSDT under different temperature loadings.…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic Vibration Analysis of Laminated Doubly Curved Shallow Panels Using Non-Linear FEM

Mahapatra

Panda

2014

Journal of Thermal Stresses

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Non-linear vibration behavior of the laminated composite curved panel of different geometries (cylindrical, elliptical, hyperboloid, paraboloid and flat panel) under thermal environment is investigated in this article. A non-linear mathematical model is developed based on higher-order shear deformation theory by taking Green-Lagrange type of non-linear kinematics. The governing equation of the vibrated panel is obtained throughHamilton's principle and discretized using the non-linear finite element steps. The responses are obtained through direct iterative method and compared with those available in published literature. The effect of different parameters on the non-linear vibration behavior of the curved panel has been discussed in detail.

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“…To obtain more accurate values, numerical calculations should be used on the basis of the Mindlin plate theory in which both the rotary inertia and shear deformation of plates are taken into consideration. Many references in the specialized monographs by Reddy [5], Ganapathi [6], Yeh [7], Raouf [8], and Sathyamoorthy [9,10] fully attest to the phenomenon of non-linear vibration. The non-linear vibration problems have attracted considerable amount of research attention.…”

Section: Introductionmentioning

confidence: 99%

Non-linear Oscillations of Orthotropic Plates on a Non-linear Elastic Foundation

Chen

Tan

Chien

2008

Journal of Reinforced Plastics and Composites

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In this paper, the non-linear vibration response of an orthotropic plate rests on a nonlinear foundation that subjected to non-uniform initial stress is investigated. The non-linear partial differential equations of motion for an orthotropic plate are derived by Hamilton's principle. By using these derived governing equations, the large amplitude vibration of an initially stressed plate on a non-linear elastic foundation model was studied. Galerkin's approximate method was applied to the governing partial differential equations to yield ordinary differential equations. The ordinary differential equations were solved by employing a Runge—Kutta method to obtain the ratio of nonlinear to linear frequencies. The initial stress is taken to be a combination of pure bending stresses plus extensional stresses in the plane of the plate. The softening non-linear elastic foundation model is used to describe the plate—foundation interaction. Numerical example of simply supported Mindlin plates subjected to the initial stress and resting on a Winkler non-linear foundation was solved. The frequency responses of non-linear vibration are sensitive of initial stress, amplitude of vibration, material properties, linear foundation stiffness and non-linear foundation stiffness.

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Nonlinear vibrations of moderately thick orthotropic shallow spherical shells

Cited by 29 publications

References 15 publications

Non-Linear Vibrations of Shell-Type Structures: A Review With Bibliography

Non-Linear Vibrations of Shell-Type Structures: A Review With Bibliography

Thermoelastic Vibration Analysis of Laminated Doubly Curved Shallow Panels Using Non-Linear FEM

Non-linear Oscillations of Orthotropic Plates on a Non-linear Elastic Foundation

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