CAJ | 학술논문

针对变截面连续梁在公路、铁路桥梁、建筑、机械结构中广泛使用的情况,为解决变截面连续梁的变系数控制微分方程无法得到解析解这一困难,提出了运用有限差分方法解此问题的方法.通过推导连续梁动力特性的振型方程,建立其差分格式,利用对称性、反对称性、边界条件,将差分方程组简化,求解振型系数行列式为0这一方程,得到自振频率,相应地求出振型,并应用到实际跨线桥的计算.结果表明,差分方解法解决连续梁的振动问题非常有效,应用步骤简洁、固定.按照此思路编制计算机专用程序能对任意多跨变截面梁进行动力分析,可适用于土木、机械、舰船等结构.
침대변절면련속량재공로、철로교량、건축、궤계결구중엄범사용적정황,위해결변절면련속량적변계수공제미분방정무법득도해석해저일곤난,제출료운용유한차분방법해차문제적방법.통과추도련속량동력특성적진형방정,건립기차분격식,이용대칭성、반대칭성、변계조건,장차분방정조간화,구해진형계수행렬식위0저일방정,득도자진빈솔,상응지구출진형,병응용도실제과선교적계산.결과표명,차분방해법해결련속량적진동문제비상유효,응용보취간길、고정.안조차사로편제계산궤전용정서능대임의다과변절면량진행동력분석,가괄용우토목、궤계、함선등결구.
In highway and railway engineering, continuous bridges are usually made up with variable section along the span in order to reduce its designed positive bending moment in the mid-span, and also to provide convenience of arranging the prestressed bars on the top of the cross section. In the paper, the vibrating mode equations were deduced at first, and then, the difference schemes of the equations were established. By utilizing the symmetry, antisymmetry, and boundary conditions, the difference equations were simplified. Based on the fact that it is impossible for all the deflections be-ing zero in each node, taking the coefficient determinant to be zero, an equation with the square of natural frequencies as unknown was generated. By solving the equation, the natural frequencies were obtained in the end.