一种求解含振子及弹性支承圆板振动的新方法

将富里叶－贝塞尔级数引入积分方程1]，推导出一种研究含振子及弹性支承圆板振动特性的新方法，根据积分方程和富里叶－贝塞尔级数理论，首先用第一类贝塞尔函数构造圆板的格林函数，然后由叠加原理将圆板的自由振动问题转化为积分方程的特征值问题；进面将积分方程形式的特征值问题转化为无穷阶矩阵的标准特征值问题，计算时根据精度的要求，截取无穷阶矩阵的标准特征值为有限阶矩阵的标准特征值问题，采用Q－R算法，计算实践表明，本方法不仅具有运算简捷，精度高，适用性强的特点，而且能从整体上对系统的动态性加以研究，从而为这类系统的优化设计提供有;力的 工具。

Acrodynamic Optimization Design of Transonic Airfoil and Wing

A new method for predicting free vibration of circular plates with axisymmetric oscillators and/or elastic supports by combining the method of integral equation s and the Fourier series method in structure mechanics was presented. Basing on the theory of integral equation and Fourier-Bessel function, the Green's func tion of the circular plates is constructed by the Bessel function of the first k ind Then the eigenvalue problem of free vibration of circular plates is transfo rmed into the problem of integral equation by using superposition theorem. And the eigenvalue problem of integral equation is transformed into a standard eig envalue problem of a matrix with infinite order. As calculating practice, accor ding to the required precision, the Q-R algorithm is used by replacing t he matrix of infinite order with the square matrix of finite order. The advanta ges of this method are its briefness, its high precision and its extensiveness . Moreover, using this method it may be possible to consider the dynamic featu res of circular plates with additional linear system as a whole. So it can also provides a useful tool for the optimal design of systems.