铰支多跨梁稳态动变形的级数简易算法

Simple Series Method in Determining Steady Dynamic Deflection of Pinned Multi-Span Beam

针对全铰链支撑多跨梁稳态动变形计算问题提出正弦级数解法,动力学方程中直接包含了多余约束力,定解条件仅需考虑中间支撑处挠度为零的约束,推出了约束力满足的方程组,进而确定出多跨梁挠度幅值,利用2个算例说明了方法的可行性。本文方法不限载荷种类和数量,计算步骤简单,方法统一,收敛速度快。

A sine series method is put forward to solve the steady dynamic deflection problem of whole hinge-support multi-span beam,the redundant constraint forces are directly concluded in the formulated dynamic equations,and the zero deflection conditions of those middle supports are simply considered in the definite conditions,so the equations with which the constraint forces satisfy are obtained,and the deflection amplitude of the multi-span beam is determined.Two numerical examples are given here to illustrate the feasibility of the method.The method has no restriction on the load types and load numbers,and has advantages of simple procedure,unified approach and fast convergence.