基于振型控制的变厚度梁的优化设计研究

提出了计算梁弯曲振动的新方法。从弯曲变形的角度出发,利用有限差分的方法,建立了梁弯曲振动的计算模型,模型同时适用于等厚度梁和变厚度梁。使用不同类型的梁对模型的准确性进行了验证,结果表明模型具有较好的计算精度。同时,尝试使用该模型进行梁的振型优化设计,对模型做适当的变形后,就可以以梁的频率和振型作为目标,通过数值方法来获取最佳的厚度分布值。最后用一个实例对方法进行了验证,结果表明利用该模型进行梁的振型优化设计是可行的。

Thickness optimization of non-uniform beams based on modal shape

A new method for calculating bending vibration of a beam was proposed here.A calculating model for a non-uniform beam was established using finite difference method; the model could also be used for an uniform beam.Some examples showed that the model has good precision.Meanwhile, modal shape optimization was implemented to a non-uniform beam using the pre-established model.By changing the function's form of the model, it was possible to get the best thickness distribution to obtain an expected modal shape.An example showed that the proposed method is effective and applicable.