摘要
旨在为结构抗振设计奠定一定基础,研究结构动力学优化问题。从阻尼结构基层、阻尼层和约束层的力学本构出发,依据Hamilton原理,推导出阻尼板振动方程。构建以阻尼单元存在状态为设计变量,模态阻尼比最大为目标,阻尼材料体积以及结构频率为约束的优化数学模型。推导了结构的阻尼比灵敏度及频率约束灵敏度计算式。选定矩形阻尼板为分析对象并引入渐近法实现了矩形板优化模型求解。仿真显示:矩形板优化后,模态阻尼比有较大幅增加且频率变动较小,但若按阻尼单元编号顺序依次删减阻尼材料,则不仅使模态阻尼比下降且使频率产生较大变动;此外,当对矩形板单一阶次模态进行优化时,则该阶模态振幅明显下降,而对多阶模态进行复合优化时则使板获得良好的综合抗振效果。研究表明,约束阻尼结构的多模态复合阻尼比最大化拓扑渐进动力学优化,在抗振动设计中具有广泛的应用前景。
To lay foundations of anti-vibration design of structure,the optimization of constrained damping plates is studied. Based on mechanics constitutive relation of constrained damping structure and Hamilton principle,a differential dynamical equation for the constrained damping plates is derived. A mathematical model is built to maximize modal damping ratio with least damping material volume and structure modal frequency as constraint condition. Structural modal damping ratio formula is derived to give iteration direction for structural optimization. The sensitivity equation in frequency constraints is introduced. To verify evolutionary optimization algorithm for the model,a rectangular plate of numerical example is provided. After optimization,structural modal damping ratio of the plate increases,the modal frequency varies little,and according to the element number deleting damping materials of optimization methods,the damping ratio can show a trend of decline,the frequency increases dramatically. For single order modal optimization,specific order response peak are decreased. However,the composite vibration damping structure effect is better when the structure of compound multimodal optimization. The research shows that better comprehensive vibration effect can be obtained when maximizing structure composite modal damping ratio during the damping structural optimization iteration process.
出处
《南昌航空大学学报（自然科学版）》
CAS
2016年第1期1-9,共9页
Journal of Nanchang Hangkong University(Natural Sciences)
基金
国家自然科学基金(51265040)
关键词
阻尼板
抗振动
模态阻尼比
频率约束
多模态优化
damped plates
anti-vibration
modal damping ratio
frequency constraint
multimodal optimization
