Postbuckling and vibration of shear deformable flat and curved panels on a non-linear elastic foundation

Librescu, Liviu; Lin, Whei-Min

doi:10.1016/s0020-7462(96)00057-1

Cited by 39 publications

(5 citation statements)

References 15 publications

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“…Z 0; ð2:16Þ whereJ 0 ðtÞ h ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2hm r m 0 p J 0 ðtÞ. Worthy of noting is that the governing equation (2.16) is mathematically similar to that of a plate on a fictitious, linear Winkler's foundation with negative foundation modulus (Librescu & Lin 1997). Since our interest in the present article is focused on the dynamic effect of the incident waves, in the following analysis, we will only consider the case that the values of J 0 (t) are in the subcritical buckling range, and for further simplification, it is assumed that J 0 (t)ZJ 0 Zconst., therebyJ 0 ðtÞZJ 0 Z const:…”

Section: Statement Of the Problem And Basic Equationsmentioning

confidence: 99%

Diffraction of harmonic flexural waves in a cracked elastic plate carrying electrical current

et al. 2005

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The scattering effect of harmonic flexural waves at a through crack in an elastic plate carrying electrical current is investigated. In this context, the Kirchhoffean bending plate theory is extended as to include magnetoelastic interactions. An incident wave giving rise to bending moments symmetric about the longitudinal x -axis of the crack is applied. Fourier transform technique reduces the problem to dual integral equations, which are then cast to a system of two singular integral equations. Efficient numerical computation is implemented to get the bending moment intensity factor for arbitrary frequency of the incident wave and of arbitrary electrical current intensity. The asymptotic behaviour of the bending moment intensity factor is analysed and parametric studies are conducted.

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Section: Statement Of the Problem And Basic Equationsmentioning

confidence: 99%

Diffraction of harmonic flexural waves in a cracked elastic plate carrying electrical current

et al. 2005

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“…The vibration and stability behaviors of uniform beams and columns on non-linear elastic foundation are evaluated using a finite element formulation by Rajasekhara [19]. Librescu [20] studied the vibration behavior of flat and shallow curved imperfective panels resting on a Winkler linear and non-linear elastic foundations. Padovan [21] presented a steady-state response of a plate on a non-linear foundation to the action of general traveling loads.…”

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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“…The characteristics of structure resting on a nonlinear elastic foundation were examined before [29][30][31][32][33][34]. Naidu [29] used a finite element method to study the free linear vibration and stability of beams and columns on nonlinear elastic foundations.…”

Section: Introductionmentioning

confidence: 99%

“…The mathematical model was discretized through the Galerkin procedure and its nonlinear dynamic behavior was investigated using the normal forms method. Librescu [33,34] studied the vibration behavior of flat and shallow curved imperfective Nomenclature A ij , B ij , D ij stiffiness of a plate C ij stiffness coefficients of stress-strain relations u i displacements of a plate in x, y and z directions u x ,u y , w displacements of the middle surface of a plate (z = 0) in x, y and z directions u x , u y rotations of a plate in x and y directions I 1 , I 3 inertia coefficients of a plate a, b…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration of laminated plates on a nonlinear elastic foundation

Chien¹,

Chen

2005

Composite Structures

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Postbuckling and vibration of shear deformable flat and curved panels on a non-linear elastic foundation

Cited by 39 publications

References 15 publications

Diffraction of harmonic flexural waves in a cracked elastic plate carrying electrical current

Diffraction of harmonic flexural waves in a cracked elastic plate carrying electrical current

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

Nonlinear vibration of laminated plates on a nonlinear elastic foundation

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