Abstract
Abstract
The present paper deals with the determination of the boundary and eigenvalue problems that describe the static and dynamic behaviour of anisotropic tapered plates with edges elastically restrained against rotation and translation and nonsmooth boundaries. It is demonstrated that this type of boundary restrictions leads to unstable boundary conditions and that the presence of corner points when the boundary is elastically restrained against translation generates additional boundary conditions. This is particularly interesting in the case of triangular plates.
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References
1.
Guelfand I.
Fomin S.
Calculus of variations , 1963 (Prentice Hall , Englewood Cliffs, New Jersey ).
2.
Dym C.
Shames I.
Solid Mechanics: A Variational Approach , 1973 (McGraw Hill Book Company , New York ).
3.
Timoshenko S.
Krieger W.
Theory of Plates and Shells , 1959 (McGraw Hill , New York ).
4.
Kantorovich L.
Krylov V.
Approximate Methods of Higher Analysis , 1964 (Interscience Publishers , New York ).
5.
Hildebrand F.
Methods of Applied Mathematics , 1965 (Prentice Hall , New Jersey ).
6.
Weinstock R.
Calculus of Variations with Applications to Physics and Engineering , 1974 (Dover Publications , New York ).
7.
Troutman J. L.
Variational Calculus and Optimal Control , 1996 (Springer-Verlag , New York ).
8.
Szilard R.
Theory and Analysis of Plates , 1974 (Prentice Hall , New Jersey ).
9.
Mikhlin S.
Variational Methods of Mathematical Physics , 1964 (MacMillan Co. , New York ).
10.
Rektorys K.
Variational Methods in Mathematics, Science and Engineering , D. 1980 (Reidel Co. ).
11.
Lekhnitskii S. G.
Anisotropic Plates , 1968 (Gordon and Breach Science Publishers , New York ).
12.
Whitney J. M.
Structural Analysis of Laminated Anisotropic Plates , 1987 (Technomic Publishing Co. Inc. , Pennsylvania ).
13.
Reddy J. N.
Mechanics of Laminated Anisotropic Plates: Theory and Analysis , 1997 (CRC Press , Boca Raton, Florida ).
14.
Vinson J. R.
Sierakowski R. L.
The Behavior of Structures Composed of Composite Materials , 2002 (Kluwer Academic Publishers , Dordrecht, Boston, London ).
15.
Jones R. M.
Mechanics of Composite Materials , 1999 (Taylor and Francis , Virginia, USA ).
16.
Grossi R. O.
Lebedev L.
Static and dynamic analyses of anisotropic plates with corner points J. Sound and Vibration , 2001 , 243 , 947 –958 .
17.
Nallim L. G.
Luccioni B. M.
Grossi R. O.
A Rayleigh-Ritz approach to transverse vibration of isotropic polygonal plates with variable thickness Proc. Instn Mech. Engrs, Part K: J. Multi-body Dynamics , 2002 , 216 (3 ), 213 –222 .
18.
Kim C. S.
Dickinson S. M.
The free flexural vibration of right triangular isotropic and orthotropic plates J. Sound and Vibration , 1990 , 141 (2 ), 291 –311 .
19.
Grossi R. O.
Albarracin C.
Some observations on the application of the Rayleigh-Ritz method Appl. Acoustics , 2001 , 62 , 1171 –1182 .