多变量单元结构共振解耦动力优化设计方法

针对截面多变量单元结构的动力优化问题，建立了带频率约束的结构动力优化设计模型，对隐式非线性频率约束函数进行Taylor近似展开，给出了截面多变量单元频率梯度函数显式表达式，基于Kuhn-Tucker条件构建迭代算法，其中拉格朗日乘子通过建立联合方程组求解，形成了含多变量单元共振解耦优化设计方法。以矩形截面单元结构为算例的结果表明，所给单元多变量算法具有良好的准确性；截面变量对频率的贡献存在主次之分，区分指标可采用梯度值；次要变量的修正因子迭代中可采用定值，且其下限应尽可能降低，利于节约成本。本文工作对多变量复杂截面结构动力优化设计可提供理论指导，提高结构动力优化方法的适用性。

Optimal method of resonance decoupling design for multivariable cross-sectional structure

Dynamic optimization design model for multivariable cross-sectional structures with frequency constraints is studied.The implicit nonlinear frequency constraint function is approximately obtained by Taylor''s expansion formulation,and the explicit expression of the gradient function of frequency to cross-sectional design variables is given.Based on the Kuhn-Tucker condition,an iteration algorithm consisting of the constraints and the objective function gradient and Lagrange multipliers is derived by solving a set of simultaneous equations is deduced,which constitutes the optimization method of resonance decoupling design for multivariable cross-sectional structures.The results show that the accuracy of the algorithm is satisfied in terms of calculation of rectangular section structure.It is found that the contribution of cross-sectional variables to frequency is different,frequency gradient values can be taken as an indicator to distinguish dominant and inferior variables.The modified factors of inferior variables may be constant in the iteration solution,and its lower limit should be reduced as much as possible,which is good for cost savings.The work done here can provide theoretical guidance and improve applicability for structural dynamic optimization design of complex cross sections.