A new meshless method for free vibration analysis of plates using radial basis function

Abstract

In this paper, a new meshless method for solving the eigenfrequencies of plates using the radial basis function (RBF) is proposed. By employing the imaginary-part fundamental solution as the RBF, the coefficients of influence matrices are easily determined. True eigen solutions in conjunction with spurious eigen solution are obtained for plate vibration. It is found that spurious eigen solution for the simply-supported plate using the present method is the same as the true eigensolution of the clamped case in the numerical experiments. To verify this finding, the circulant is adopted to analytically derive the true and spurious eigenequation in the discrete system of a circular plate. In order to obtain the eigenvalues and boundary modes at the same time, the singular value decomposition (SVD) technique is utilized. Two examples are demonstrated analytically and numerically to see the validity of the present method.本文是使用無網格法配合徑向基底函數來求解固定及簡支承邊界板之特徵頻率，其中影響係數矩陣可輕易的由徑向基底函數求得。利用虛部基本解當徑向基底函數求解發現假根常常會伴隨著真根產生，更有趣的是我們從中發現到固定邊界板振動問題之真根竟然是簡支承板振動問題之假根。為了同時求得特徵值及邊界模態，我們在計算的過程中運用了奇異值分解法來求解，文中我們以圓形板為例來論證我們的發現。