Numerical computation of BCOPs 1 Boundary characteristic orthogonal polynomials. 1 in two variables for solving the vibration problem of a CF-elliptical plate

摘要

Boundary characteristic orthogonal polynomials in xy -coordinates have been built up over an elliptical domain occupied by a thin elastic plate. Half of the plate boundary is taken clamped while the other half is kept free. Coefficients of these polynomials have been computed once and for all so that an orthogonal polynomial sequence is generated from a set of linearly independent functions satisfying the essential boundary conditions of the problem. Use of this sequence in Rayleigh–Ritz method for solving the free vibration problem of the plate makes it faster in convergence and leads to a simplified system whose solution is comparatively easier. Three-dimensional solution surfaces and the associated contour lines have been plotted in some selected cases. Comparison have been made with known results whenever available.