考虑剪切效应时双模量梁的自由振动

摘要

Considering the shear effect,the natural vibration of a bimodulous beam was studied.The vibration differential equation of the bimodulous beam was established,the mode shapes of the bimodulous beam were derived,and the influence of shear effect on natural vibration frequencies of the bimodulous beam was analyzed.The computational results indicate that the influence of shear effect can not be ignored in some cases.The conclusion is that the odd number modal shapes of bimodulous beams are discontinuous and there are discontinuity points on the odd number type of modal waves.%研究了考虑剪切效应时双模量梁自由振动问题。利用双模量材料纯剪切应力状态单元体，推导出双模量材料剪切弹性模量表达式。在考虑剪切效应的基础上，建立双模量梁振动的微分方程，推导出了双模量梁振动问题的振型表达式，并讨论分析了剪切效应对双模量梁自由振动固有频率的影响。算例分析表明，对于某些双模量梁自由振动问题，剪切效应的影响是不能忽略的。得到了双模量梁自由振动时，奇数波型与波型振型是不连续的存在间断点的结论。