Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/153064
Title: THE DEVELOPMENT OF 2-D ORTHOGONAL POLYNOMIALS FOR VIBRATION OF PLATES
Authors: LIEW KIM MEOW
Keywords: COMPLEX SUPPORTS
COMPOSITES
FREQUENCY
LAMINATES
MODE SHAPE
ORTHOGONAL POLYNOMIALS
PLATE
RAYLEIGH-RITZ
VIBRATION
Issue Date: 1991
Citation: LIEW KIM MEOW (1991). THE DEVELOPMENT OF 2-D ORTHOGONAL POLYNOMIALS FOR VIBRATION OF PLATES. ScholarBank@NUS Repository.
Abstract: In this thesis, a computationally efficient and highly accurate numerical method is proposed for vibration analysis of plates. Using a set of 2-D orthogonal polynomials as the admissible functions in the Rayleigh-Ritz method permits the study of a wide spectrum of plate vibration problems. The displacement function of the plate is approximated by a set of 2-D orthogonal polynomials which expresses the entire plate dom1in into two implicitly related variables. The development and implementation of the 2-D orthogonal polynomials are discussed in depth. Natural frequencies and mode shapes of the plates are obtained by solving the governing eigenvalue equation which is derived by minimizing the energy functional with respect to the unknown coefficients. Several test problems to demonstrate the applicability and accuracy of the present method have been considered. The predicted solutions are verified with those reported analytically, numerically and experimentally in the open literature to validate the proposed method. Numerical results are presented both for new plate problems and for plate problems where published results are available. For plate problems having various geometrical shapes, numerical results for regular polygonal plates (square plates, hexagonal plates and octagonal plates), irregular polygonal plates (triangular plates, skew plates and trapezoidal plates) and non-polygonal plates (circular plates, elliptical plates and sectorial plates) are computed for various combinations of conventional boundary conditions. The results are also presented for plate continuous over complex suppons such as point supports, line suppons or ring suppons where these intermediate supports are arbitrarily distributed at the plate interior and the plates may have any combinations of clamped, simply supported or free boundary conditions. Finally the present method is extended further to study laminated plate problems. The effects of material, number of layers and fibre orientation upon the natural frequencies and mode shapes are also discussed.
URI: https://scholarbank.nus.edu.sg/handle/10635/153064
Appears in Collections:Ph.D Theses (Restricted)

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