基于MO-RAMP插值模型的阻尼板GCMOC法拓扑减振优化

Topology dynamic optimization of damping plates using GCMOC method based on MO-RAMP

为了有效实现板件的抗振性动力学设计,研究约束阻尼板拓扑动力学优化方法。建立约束阻尼板有限元动力学分析模型,推导出模态损耗因子计算公式;建立了基于模态损耗因子最大化目标,以阻尼层单元相对密度为拓扑变量,以阻尼材料使用量及结构频率作为控制的阻尼板优化数学模型;利用序列凸规划理论而对传统优化准则法进行改进,采用改进准则法GCMOC(global extreme point converged by method of optimization criterion)解算优化模型以求取全域性优化解,推导出面向GCMOC的拓扑变量迭代式;考虑到多阶次RAMP(rational approxination of material properties)函数的形状具有较理想的可控下凹几何特征,提出在优化迭代中采用多阶次RAMP材料插值模型(MO-RAMP)对拓扑变量集合进行惩罚以实现其快速的0,1二值化,并尽量减少处于0.3~0.7的中间拓扑变量值出现;编制了面向约束阻尼板的拓扑动力学优化程序,实现了基于MO-RAMP的约束阻尼板GCMOC法变密度式减振拓扑动力学优化过程。算例分析表明,MO-RAMP与GCMOC复合的算法用于阻尼板拓扑迭代时,可将阻尼单元密度值快速地推向逼近0或1的值。它能得到清晰的阻尼单元优化密度云并有利于优化构型的实现;能在大幅减少阻尼材料用量条件下充分发挥其黏弹耗能效应,能在保证阻尼板动力学特性基本稳定的前提下使结构获得更好的减振效果。

Here,to effectively realize anti-vibration dynamic design of plates,the topological dynamic optimization method of constrained damping plates was studied.The finite element dynamic analysis model of a constrained damping plate was established,and the calculation formula of modal loss factor was derived.Based on the maximization objective of modal loss factor,taking relative densities of damping layer elements as topological variables and the use amount of damping material and structural frequency as control variables,the optimization mathematical model of damping plate was established.The traditional optimization criterion method was improved using the sequential convex programming theory.The improved criterion method GCMOC was used to solve the optimization model and obtain the global optimization solution,and the iterative formula of topology variables facing to GCMOC(global extreme point converged by method of optimization criterion)was derived.Considering the shape of multi-order ramp function has more ideal controllable concave geometric characteristics,a multi-order rational approxination of material properties(MO-RAMP)was proposed to punish the topological variables set in optimization iteration,realize its fast 0 and 1 binarization,and minimize the occurrence of intermediate topological variables in the range of 0.3-0.7.The topological dynamic optimization program facing to constrained damping plate was compiled,and the variable density type topological dynamic optimization for constrained damping plate was realized using GCMOC method based on MO-RAMP.Example analysis showed that when the composite algorithm of MO-RAMP and GCMOC is used in topology iteration of damping plate,the damping element relative density can be quickly pushed to the value close to 0 or 1 to get a clear density cloud of damping element optimization,and be helpful to realizing the optimal configuration;adopting the proposed method can make full use of damping material’s viscoelastic energy-dissipating effect under the condition of greatly reducing the amount of damping material,and make the structure obtain better vibration reduction effect on the premise of ensuring basic stability of dynamic characteristics of damping plate.