用单自由度系统研究双模量变截面梁的冲击

研究了重物对双模量等高变截面梁的冲击问题.把被冲击的双模量等高变截面梁简化为一集中质量与无重弹簧相连接的单自由度弹性系统,使重物对梁的冲击问题转化为重物对具有集中质量单自由度弹性系统的冲击问题,然后采用动力学方程推导出了重物对梁的动载荷系数、冲击时间的函数表达式,克服了能量法仅能给出最大动载荷系数的不足.通过算例分析,指出有关文献给出的最大动载荷系数公式,仅是动力学方程推导出的动载荷系数函数式的特例.当拉压弹性模量相差较大时,不能把重物对双模量等高变截面梁的冲击问题简单处理为重物对单模量等高变截面梁的冲击问题,必须要考虑拉压弹性模量不同因素对双模量变截面梁受冲击的影响.

Study of impact problem of bimodulous beam with variable cross sections by single degree of freedom system

The problem of bimodulous beam with equal height and variable cross sections impacted, was stadied, by heavy weight. The impacted bimodulous beam of equal height and variable cross sections was simplified as a elastic system with single degree of freedom which composed by a concentrated mass and a spring without weight, thus the problem of beam impacted by heavy weight was simplified as single degree of freedom elastic system with concentrated mass impacted by heavy weight, then function expressions for factor of dynamic load and impact time were derived by dynamic equation, the defects of the energy method, which can only give the maximum factor of dynamic load, was overcome. The analysis of examples indicated that formulas for the maximum factor of dynamic load which given by related literatures is only a special case of function formula for factor of dynamic load that obtained by dynamic equations. The problem of bimodulous beam with equal height and variable cross sections impacted by heavy weight, in which have a larger difference elastic moduli in tension and compression, can not be treated simply as the problem of single-modulus beam with equal height and variable cross sections impacted by heavy weight, the influence of difference elastic moduli in tension and compression must be taken into consideration.