几何外形和疏密分布对弹簧有效弹性常数的影响

本文首先通过理论推导,建立了计其本身质量的旋转体弹簧所满足的波动方程,运用能量法给出振动弹簧的有效弹性常数。然后导出了弹簧本身质量忽略不计的极限情况下弹簧有效弹性常数的表达式。最后运用泛函极值原理简单讨论了在固定材料以及外形下弹簧圈的疏密如何分布,使弹簧达到最大有效弹性常数的最优化模型。

THE INFLUENCE ON THE VALID ELASTIC CONSTANT OF SPRING BY THE SHAPES AND THE DENSITY DISTRIBUTION

First,This text deduces through theories,building up the wave equation to satisfy spiral spring with accounting its quantity,then separate the variables of the equation and use the energy method to give a valid elastic constant.Next it attain the expression of the valid elastic constant under the limit circumstance of neglecting quantity of spring.End it use principle of extremum to discuss in brief about how the density of the spring coils distribute under the fixed material and shape,and to attain the mos...