On the existence of weak solutions of anisotropic generally restrained plates

This paper presents investigations of free vibration of anisotropic plates of different geometrical shapes and generally restrained boundaries. The existence and uniqueness of weak solutions of boundary value problems and eigenvalue problems which correspond to the statical and dynamical behaviour o...

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Bibliographic Details
Published inApplied mathematical modelling Vol. 32; no. 11; pp. 2254 - 2273
Main Authors Grossi, Ricardo Oscar, Nallim, Liz Graciela
Format Journal Article
LanguageEnglish
Published New York, NY Elsevier Inc 01.11.2008
Elsevier Science
Subjects
Composite material
Elastically restrained edges
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
Structural and continuum mechanics
Vibration analysis
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
Weak solutions
Weak solutions
Elastically restrained edges
Composite material
Vibration analysis
Solution uniqueness
Geometrical shape
Free boundary
Stratified material
Circular plate
Existence theorem
Existence of solution
Free vibration
Anisotropic material
Polynomial method
Modeling
Uniqueness theorem
Ellipticity
Boundary value problem
Weak solution
Elliptic plate
Eigenvalue problem
Ritz method
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Summary:This paper presents investigations of free vibration of anisotropic plates of different geometrical shapes and generally restrained boundaries. The existence and uniqueness of weak solutions of boundary value problems and eigenvalue problems which correspond to the statical and dynamical behaviour of the mentioned plates is demonstrated. It is determined that when the plates have corner points formed by the intersection of edges free or elastically restrained against translation, the corresponding bilinear forms maintain the V – ellipticity property. Also, an analytical formulation, based on the Ritz method and polynomial expressions as approximate functions for analysing the free vibrations of laminated plates with smooth and non-smooth boundary with non-classical edge supports is presented. Numerical results are presented for circular, elliptical and trapezoidal plates for different boundary conditions and material properties.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0307-904X
DOI:10.1016/j.apm.2007.07.015