弹性地基扇形权弯曲问题的复Bessel函数级数解

A SERIES SOLUTION OF COMPLEX BESSEL FUNCTIONS FOR BENDING PROBLEM OF SECTOR PLATES ON ELASTIC FOUNDATION

本文对于在Winkler型弹性地基上的扇形板弯曲问题给出了一种级数解法。对于沿径向简单支撑的扇形板，在周向采用正弦三角函数展开后，将关于径向待定函数的Bessel方程用复Bessel函数表示其解。然后，将其变换成实解形式，从而得到原问题齐次方程的实通解。在此基础上，对于扇形板受集中力或沿周向线分布载荷作用下的弯曲解给出了一般计算方法以及任意横向载荷作用下挠曲函数的表达式，并给出了沿径向和周向都为简单支撑情形的算例。

A series solution of complex Bessel functions is proposed in this paper to solve the bending problem of sector Plates on the elastic foundation of Winkler type For the sector Plate with simple supports along the radial direction, after the solution of the problem is expanded by a sine series along circumferential direction, we use the complex Bessel functions to express the solution to the deduced Bessel equation on the unknown function varying in radial direction Thenwe transform the complex solution into the real general solution of the homogeneous equation of the problem. Consequently, the solutions of deflection for the sector plate under a concentrated load, line distributed load along circumferential direction, and arbitrary destributed load in the transverse direction are obtained. Finally, some numerical examples for the sector plate with simple supports are given to show the feasibility of the present solutions.