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Fourier series solution for a rectangular thick plate with free edges on an elastic foundation
Author(s) -
Henwood D. J.,
Whiteman J. R.,
Yettram A. L.
Publication year - 1982
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620181205
Subject(s) - fourier series , mathematical analysis , series (stratigraphy) , mathematics , fourier transform , boundary value problem , variable (mathematics) , eigenvalues and eigenvectors , space (punctuation) , discrete fourier series , partial differential equation , conjugate fourier series , function (biology) , fourier analysis , physics , computer science , fractional fourier transform , paleontology , short time fourier transform , quantum mechanics , biology , operating system , evolutionary biology
A Fourier series solution is presented for a system of first‐order partial differential equations which describe the linear elastic behaviour of a thick rectangular plate resting on an elastic foundation and carrying an arbitrary transverse load. The lateral edges of the plate are unstressed. A central step in the method for solving the system of equations is to combine a complementary function with a particular solution of the system in order to satisfy the boundary conditions. The complementary function is the sum of two series. The terms of the first series are products of a Fourier term in one space variable with the solution of an eigenvalue problem in the other space variable. The second series is similar and comes from reversing the roles of the space variables.