一类变截面梁横向自由振动的精确解析解  

THE EXACT ANALYTICAL SOLUTION OF TRANSVERSE FREE VIBRATION OF A TYPE OF BEAMS WITH VARIABLE CROSS-SECTIONS

作　　者：周叮[1] 

机构地区：[1]南京理工大学

出　　处：《振动与冲击》1996年第3期12-15,共4页Journal of Vibration and Shock

摘　　要：本文研究了一类变截面梁的横向自由振动问题，半径按抛物线变化的圆形变截面梁以及高度按抛物线变化而宽度接任意次幂函数变化的矩形变截面梁是这类梁的两个典型特例。求得了其横向自由振动的精确解析解。解的形式与楔形梁完全不同，是一以幂函数表示的初等函数。本文最后给出了两个算例。This paper studies the transverse free vibration of a type of beams with variable cross-sections. The beams of circular cross-section with parabolic radius variation and the beams of rectangular cross-section with parabolic height variation power functional width variation are two special examples and their exact analytical solutions of transverse free vibration were found accordingly.The vibration mode function expressed as power function consisting of elementary function is different from that of wedge-shaped beam, expressed as Bessel function consisting of nonelementary function. Two analytical examples are given in the acticle.

关 键 词：变截面梁 振动 精确解析率 梁式结构 

分 类 号：TU323.301[建筑科学—结构工程]