用于叶片减振的压电材料分布拓扑优化
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摘要
提出一种可用于实际叶盘结构的压电分支阻尼器拓扑优化方法,可以给出总质量受约束的压电材料在叶片上的最佳分布,达到尽可能大的模态阻尼比。通过理论推导说明:压电阻尼器所产生的模态阻尼比仅取决于模态机电耦合系数,且该系数只与压电材料的几何形状以及模态应力场有关。进一步结合压电本构关系,基于应力分量的线性加权给出了有限的压电材料在叶片上铺设位置"优先级"的判断指标。给出了基于叶盘结构有限元模型的压电材料拓扑优化方法,通过替换单元类型和材料参数的方式对压电材料进行布置,并给出了多模态族优化、极化方向设置、电极铺设等问题的解决方案。在一个接近真实的叶盘模型上应用了此优化方法。结果表明,仅使用质量占叶片质量10%的压电材料,就可以为多个模态提供约12%的阻尼比。
A topological optimization procedure of piezoelectric shunting damping for arbitrary full-scale bladed disks was proposed.Based on the fact that the modal electromechanical coupling factor(MEMCF)is the only parameter that affecting the level of modal damping ratios produced by piezoelectric shunting circuit.Further,it showed that MEMCF was related to modal stress field and the geometry of the piezoelectric materials only.Combining with piezoelectric constitutive relation,a linear weighting of stress components was proposed as the criterion to determine the priority of locations for piezoelectric materials.Accordingly,the topological optimization procedure was presented based on the finite element model of bladed disk,where the piezoelectric materials were introduced by modifying the type and material parameters of elements.Solutions for optimization with respect to multiple modal families,polarized direction setting,and electrode connection were also presented.The proposed procedure was applied to an empirical bladed disk.Results show that 12% damping ratio can be achieved for multiple modes using piezoelectric materials with mass of only 10%of the blade.
A topological optimization procedure of piezoelectric shunting damping for arbitrary full-scale bladed disks was proposed.Based on the fact that the modal electromechanical coupling factor(MEMCF)is the only parameter that affecting the level of modal damping ratios produced by piezoelectric shunting circuit.Further,it showed that MEMCF was related to modal stress field and the geometry of the piezoelectric materials only.Combining with piezoelectric constitutive relation,a linear weighting of stress components was proposed as the criterion to determine the priority of locations for piezoelectric materials.Accordingly,the topological optimization procedure was presented based on the finite element model of bladed disk,where the piezoelectric materials were introduced by modifying the type and material parameters of elements.Solutions for optimization with respect to multiple modal families,polarized direction setting,and electrode connection were also presented.The proposed procedure was applied to an empirical bladed disk.Results show that 12% damping ratio can be achieved for multiple modes using piezoelectric materials with mass of only 10%of the blade.
引文
[1]王建军,李其汉.航空发动机叶盘结构流体激励耦合振动[M].北京:国防工业出版社,2017.
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[11]ZHOU B.Study of piezoelectric shunt damping applied to mistuned bladed disks[D].Lyon,France:Ecole Centrale de Lyon,2012.
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[14]TANG J,WANG K.Vibration delocalization of nearly periodic strcutures using coupled piezoelectric networks[J].Journal of Vibration and Acoustics,2003,125(1):95-108.
[15]FAN Y,LI L.Vibration dissipation characteristics of symmetrical piezoelectric networks with passive branches[R].ASME Paper GT2012-69208,2012.
[16]LIU J,LI L,DENG P,et al.A comparative study on the dynamic characteristics of bladed disks with piezoelectric network and piezoelectric shunt circuit[R].ASME Paper GT2016-56794,2016.
[17]MOKRANI B,BASTAITS R,HORODINCA M,et al.Parallel piezoelectric shunt damping of rotationally periodic structures[J].Advances in Materials Science and Engineering,2015:1-12.
[18]LIU J,LI L,FAN Y,et al.Research on vibration suppression of a mistuned blisk by apiezoelectric network[J].Chinese Journal of Aeronautics,2018,31(2):285-299.
[19]DENG P,LI L,LI C.Study on vibration of mistuned bladed disk with bi-periodic piezoelectric network[J].Journal of Aerospace Engineering,2016,231(2):350-363.
[20]DUCARNE J,THOMAS O,DE J-F.Placement and dimension optimization of shunted piezoelectric patches for vibration reduction[J].Journal of Sound and Vibration,2012,331(14):3286-3303.
[21]LI Lin,YIN Shunhua,LIU Xue,et al.Enhanced electromechanical coupling of piezoelectric system for multimodal vibration[J].Mechatronics,2015,31:205-214.
[22]THOMAS O,DUCARNE J,DE J-F.Performance of piezoelectric shunts for vibration reduction[J].Smart Materials and Structures,2012,21(1):015008.1-015008.16.
[23]NEUBAUER M,WALLASCHEK J.Vibration damping with shunted piezoceramics:fundamentals and technical applications[J].Mechanical System and Signal Processing,2013,36(1):36-52.
[2]LAXALDE D,THOUVEREZ F,LOMBARD J P,Foreced response analysis of integrally bladed disks with friction ring dampers[J].Journal of Vibration and Acoustics,2010,132(1):011013.1-011013.9.
[3]ZHOU B,THOUVEREZ F,LENOIR D.An adaptive control strategy based on passive piezoelectric shunt techniques applied to mistuned bladed disk[J].Journal of Computation and Applied Mathematics,2013,246(5):289-300.
[4]HAGOOD N W,VON FLOTOW A.Damping of structural vibrations with piezoelectric materials and passive electrical networks[J].Journal of Sound Vibration,1991,146(2):243-268.
[5]PREUMONT A.Dynamics of electromechanical and piezoelectric systems[M].Netherlands:Springer,2006.
[6]李琳,宋志强,易凯军.压电网络复合板的波动特性与隔声性能分析[J].声学学报,2017(2):95-102.LI Lin,SONG Zhiqiang,YI Kaijun.Wave propagation and insulation performance of the plate with piezoelectric network[J].Acta Acustica,2017(2):95-102.(in Chinese)
[7]易凯军,李琳.压电网络板的振动控制原理与控制效果[J].北京航空航天大学学报,2014,40(11):1629-1636.YI Kaijun,LI Lin.Vibration-controlling mechanism and controlling effectiveness of plate with piezoelectric network[J].Journal of Beijing University of Aeronautics and Astronautics,2014,40(11):1629-1636.(in Chinese)
[8]王建军,李其汉.具有分支电路的可控压电阻尼减振技术[J].力学进展,2003,33(3):389-403.WANG Jianjun,LI Qihan.Viobration reduction of controllable piezoelectric damping with shunting circult[J].Advances in Mechanics,2003,33(3):389-403.(in Chinese)
[9]安德波蒙,李琳,范雨,等.机电耦合系统和压电系统动力学[M].北京:北京航空航天大学出版社,2014.
[10]MIN J B,DUFFY K P,CHOI B B,et al.Numerical modeling methodology and experimental study for piezoelectric vibration damping control of rotating composite fan blades[J].Computer and Structures,2013,128:230-242.
[11]ZHOU B.Study of piezoelectric shunt damping applied to mistuned bladed disks[D].Lyon,France:Ecole Centrale de Lyon,2012.
[12]LIU J,LI L,HUANG X,et al.Dynamic characteristics of the blisk with synchronized switch damping based on negative capacitor[J].Mechanical System and Signal Processing,2017,95(1):425-445.
[13]YU H,WANG K W.Piezoelectric networks for vibration suppression of mistuned bladed disks[J].Journal of Vibration and Acoustics,2007,129(5):559-566.
[14]TANG J,WANG K.Vibration delocalization of nearly periodic strcutures using coupled piezoelectric networks[J].Journal of Vibration and Acoustics,2003,125(1):95-108.
[15]FAN Y,LI L.Vibration dissipation characteristics of symmetrical piezoelectric networks with passive branches[R].ASME Paper GT2012-69208,2012.
[16]LIU J,LI L,DENG P,et al.A comparative study on the dynamic characteristics of bladed disks with piezoelectric network and piezoelectric shunt circuit[R].ASME Paper GT2016-56794,2016.
[17]MOKRANI B,BASTAITS R,HORODINCA M,et al.Parallel piezoelectric shunt damping of rotationally periodic structures[J].Advances in Materials Science and Engineering,2015:1-12.
[18]LIU J,LI L,FAN Y,et al.Research on vibration suppression of a mistuned blisk by apiezoelectric network[J].Chinese Journal of Aeronautics,2018,31(2):285-299.
[19]DENG P,LI L,LI C.Study on vibration of mistuned bladed disk with bi-periodic piezoelectric network[J].Journal of Aerospace Engineering,2016,231(2):350-363.
[20]DUCARNE J,THOMAS O,DE J-F.Placement and dimension optimization of shunted piezoelectric patches for vibration reduction[J].Journal of Sound and Vibration,2012,331(14):3286-3303.
[21]LI Lin,YIN Shunhua,LIU Xue,et al.Enhanced electromechanical coupling of piezoelectric system for multimodal vibration[J].Mechatronics,2015,31:205-214.
[22]THOMAS O,DUCARNE J,DE J-F.Performance of piezoelectric shunts for vibration reduction[J].Smart Materials and Structures,2012,21(1):015008.1-015008.16.
[23]NEUBAUER M,WALLASCHEK J.Vibration damping with shunted piezoceramics:fundamentals and technical applications[J].Mechanical System and Signal Processing,2013,36(1):36-52.