结构频带激励下的整体动响应优化

结合频响函数的性质，采用目标频带内各模态峰值响应的 -范数作为整体响应水平的衡量指标，将等效目标函数的灵敏度表示为固有频率和振型灵敏度的函数，进而采用基于梯度的迭代方法求解，实现结构在宽频激励下的整体动响应优化，该方法适合于多频带的响应控制。此外，在频带响应优化模型的基础上，提出了通过增加频率约束，使之能应用于密集频率结构，避免迭代过程中的密频和重频现象。最后通过桁架截面优化和形状优化的数值算例，表明了本文提出方法的合理性和有效性。

Structural frequency response optimization under bandwidth excitation

A structural dynamics response optimization under bandwidth frequency excitation was considered.A differentiable q-norm form of response function’s peak value was introduced according to properties of frequency response function.This equivalent objective function can be used in multiple-bandwidth situation.Sensitivities of equivalent objective function then were derived from structure’s eigen-sensitivity.Besides,frequency constraints were introduced for prohibiting clustered or repeated frequencies during optimization.Illustrated examples of truss sizing and shape optimization were presented for verification and further application of the proposed method.