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Article(id=1228653709303939705, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228653708687377017, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2024.11.002, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1667664000000, receivedDateStr=2022-11-06, revisedDate=1677772800000, revisedDateStr=2023-03-03, acceptedDate=null, acceptedDateStr=null, onlineDate=1770863471579, onlineDateStr=2026-02-12, pubDate=1732723200000, pubDateStr=2024-11-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770863471579, onlineIssueDateStr=2026-02-12, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770863471579, creator=13701087609, updateTime=1770863471579, updator=13701087609, issue=Issue{id=1228653708687377017, tenantId=1146029695717560320, journalId=1225147924628267009, year='2024', volume='37', issue='11', pageStart='1803', pageEnd='1992', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770863471433, creator=13701087609, updateTime=1770863902026, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228655514792427773, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228653708687377017, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228655514792427774, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228653708687377017, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1811, endPage=1817, ext={EN=ArticleExt(id=1228653709513654907, articleId=1228653709303939705, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Vibration reduction of flexible wind turbine tower with damping cable, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Aiming at the problem of the multi-order modal vibration of flexible wind turbine tower，a self anchored damping cable is designed in this paper，which converts the angular displacement of tower bending vibration into linear displacement，and drives the damper to dissipate energy and reduce vibration. Firstly，the tower-damper-cable vibration equation is established，and the analytical solution of the additional damping ratio provided by the damper cable for the first two-order bending vibration of the wind turbine tower is obtained. Then，the relationship between the damper viscosity coefficient and the additional damping ratio provided by the damper cable for the first two-order modal vibration of the wind turbine tower is analyzed through model experiment. The results show that the damping cable can provide a large additional damping ratio for the first two-order bending vibration of the tower，and the analytical solution of the additional damping ratio is in good agreement with the experimental results. Finally，based on the theoretical calculation formula of additional damping ratio，the influence of parameters on the damping performance of damping cable is analyzed.

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针对风机柔性塔筒多阶模态振动，设计了一种自锚式阻尼索，将塔筒弯曲振动的转角位移转换为线位移，驱动阻尼器耗能减振。建立了塔筒-阻尼索振动方程，得到了阻尼索为风机塔筒前两阶弯曲振动所提供的附加阻尼比解析解，通过模型试验研究了阻尼器黏性阻尼系数与风机塔筒前两阶模态振动时阻尼索提供的附加阻尼比的关系。研究结果表明：对于塔筒前两阶弯曲振动，阻尼索都能提供较大的附加阻尼比，并且附加阻尼比解析解与试验结果相吻合。基于附加阻尼比理论计算公式，对阻尼索减振性能进行了参数影响分析。

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禹见达（1971—），男，博士，教授。 E-mail： 。

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禹见达（1971—），男，博士，教授。 E-mail： 。

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禹见达（1971—），男，博士，教授。 E-mail： 。

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Journal of Vibration and Shock， 2020，39（3）：149-154, articleTitle=Optimal design of tubular electric eddy damper and its damping force’s accurate measurement, refAbstract=null)], funds=[Fund(id=1228653736973763135, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653709303939705, awardId=52278307, language=CN, fundingSource=国家自然科学基金资助项目(52278307), fundOrder=null, country=null), Fund(id=1228653737082815045, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653709303939705, awardId=W2411050, language=CN, fundingSource=国家自然科学基金资助项目(W2411050), fundOrder=null, country=null), Fund(id=1228653737200255564, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653709303939705, awardId=2022JJ30261, language=CN, fundingSource=湖南省自然科学基金资助项目(2022JJ30261), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1228653729352712463, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653709303939705, 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caption=

Parameters of model

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参数数值
立柱截面积A/mm2444
惯性矩I/mm461812
线密度ρ/(kg·m-1)18.28
前两阶频率/Hz0.31
2.44
), ArticleFig(id=1228653736176845330, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653709303939705, language=CN, label=表1, caption=

模型参数

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参数数值
立柱截面积A/mm2444
惯性矩I/mm461812
线密度ρ/(kg·m-1)18.28
前两阶频率/Hz0.31
2.44
), ArticleFig(id=1228653736260731413, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653709303939705, language=EN, label=Tab.2, caption=

Viscous damping coefficients of eddy current dampers

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磁铁数量(级)黏性阻尼系数/（N·s·m-1）
120
249
381
4112
5145
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电涡流阻尼器黏性阻尼系数

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磁铁数量(级)黏性阻尼系数/（N·s·m-1）
120
249
381
4112
5145
), ArticleFig(id=1228653736483029538, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653709303939705, language=EN, label=Tab.3, caption=

The additional damping ratio of the first order modal vibration

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c/(N·s·m-1)%%%
00.5600
200.770.210.25
491.180.620.60
811.561.000.99
1121.911.351.38
1452.361.801.78
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第一阶模态振动附加阻尼比

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c/(N·s·m-1)%%%
00.5600
200.770.210.25
491.180.620.60
811.561.000.99
1121.911.351.38
1452.361.801.78
), ArticleFig(id=1228653736730493490, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653709303939705, language=EN, label=Tab.4, caption=

The additional damping ratio of the second order modal vibration

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c/(N·s·m-1)%%%
00.2200
200.850.630.68
491.821.601.66
813.042.822.73
1124.033.813.74
1454.934.714.79
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第二阶模态振动附加阻尼比

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c/(N·s·m-1)%%%
00.2200
200.850.630.68
491.821.601.66
813.042.822.73
1124.033.813.74
1454.934.714.79
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风机柔性塔筒阻尼索减振研究
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禹见达 1, 2 , 胡磊 1 , 彭文林 1
振动工程学报 | 2024,37(11): 1811-1817
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振动工程学报 | 2024, 37(11): 1811-1817
风机柔性塔筒阻尼索减振研究
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禹见达1, 2 , 胡磊1, 彭文林1
作者信息
  • 1湖南科技大学土木工程学院，湖南　湘潭　411201
  • 2湖南科技大学结构抗风与振动控制湖南省重点实验室，湖南　湘潭　411201

    • 禹见达（1971—），男，博士，教授。 E-mail： 。

Vibration reduction of flexible wind turbine tower with damping cable
Jian-da YU1, 2 , Lei HU1, Wen-lin PENG1
Affiliations
  • 1School of Civil Engineering，Hunan University of Science and Technology，Xiangtan 411201，China
  • 2Hunan Provincial Key Laboratory of Structures for Wind Resistance and Vibration Control，Hunan University of Science and Technology，Xiangtan 411201，China
出版时间: 2024-11-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.11.002
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摘要
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针对风机柔性塔筒多阶模态振动，设计了一种自锚式阻尼索，将塔筒弯曲振动的转角位移转换为线位移，驱动阻尼器耗能减振。建立了塔筒-阻尼索振动方程，得到了阻尼索为风机塔筒前两阶弯曲振动所提供的附加阻尼比解析解，通过模型试验研究了阻尼器黏性阻尼系数与风机塔筒前两阶模态振动时阻尼索提供的附加阻尼比的关系。研究结果表明：对于塔筒前两阶弯曲振动，阻尼索都能提供较大的附加阻尼比，并且附加阻尼比解析解与试验结果相吻合。基于附加阻尼比理论计算公式，对阻尼索减振性能进行了参数影响分析。

振动控制  /  风机塔筒  /  阻尼减振  /  阻尼索

Aiming at the problem of the multi-order modal vibration of flexible wind turbine tower，a self anchored damping cable is designed in this paper，which converts the angular displacement of tower bending vibration into linear displacement，and drives the damper to dissipate energy and reduce vibration. Firstly，the tower-damper-cable vibration equation is established，and the analytical solution of the additional damping ratio provided by the damper cable for the first two-order bending vibration of the wind turbine tower is obtained. Then，the relationship between the damper viscosity coefficient and the additional damping ratio provided by the damper cable for the first two-order modal vibration of the wind turbine tower is analyzed through model experiment. The results show that the damping cable can provide a large additional damping ratio for the first two-order bending vibration of the tower，and the analytical solution of the additional damping ratio is in good agreement with the experimental results. Finally，based on the theoretical calculation formula of additional damping ratio，the influence of parameters on the damping performance of damping cable is analyzed.

vibration control  /  wind turbine tower  /  damping and vibration reduction  /  damping cable
禹见达, 胡磊, 彭文林. 风机柔性塔筒阻尼索减振研究. 振动工程学报, 2024 , 37 (11) : 1811 -1817 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.11.002
Jian-da YU, Lei HU, Wen-lin PENG. Vibration reduction of flexible wind turbine tower with damping cable[J]. Journal of Vibration Engineering, 2024 , 37 (11) : 1811 -1817 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.11.002
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引言
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风能是一种可再生能源，其储存量大、分布广，据估算仅地面风力的1%就能满足全球发电能量的需求［1］，中国可利用的风能资源储量在10亿千瓦以上［2］，丰富的资源和对绿色能源的需求为风电产业的发展带来了机遇与挑战。常见的风力发电系统由风轮、机舱、塔筒和基础组成。塔筒属于高耸结构，其中，全钢柔性塔筒更加高耸、轻柔、低阻尼，极易在风荷载作用下发生大幅涡激振动，最常见的是第二阶模态弯曲振动，也有第一阶模态弯曲振动的发生。塔筒弯曲振动时，其周期性变化的惯性力使得塔筒承受巨大的交变应力，导致连接螺栓松动，基础环与混凝土基础之间的穿孔钢筋被剪断［3］，加速塔筒结构疲劳破坏，在遇到极端天气时易发生倒塌［4-5］。因此，风机塔筒因外部荷载作用导致的大幅振动必须得到控制。
现有风机塔筒振动控制措施主要有两种，一是在主体结构上加装控制装置，被动或主动地施加一组控制力；二是增大主体结构的刚度［6］，小幅增加塔筒结构刚度不能起到对塔筒的减振效果，而大幅增大塔筒刚度的方法显然会显著增加塔筒的成本。
目前调谐质量阻尼器（TMD）是塔式结构振动控制中研究最多的一种控制装置。陈鑫等［7］针对自立式高耸结构安装环形TMD，通过数值模拟及模型试验发现，附加TMD后试验模型阻尼比增加了0.02。对于1.5 MW的小功率风机，陈俊岭等［8］测得质量比为1%的颗粒调谐质量阻尼器能将塔筒第一阶弯曲模态阻尼比由0.494%增加到0.862%。SUN等［9］认为，若振动导致风机基础破损，机舱和塔架的响应将显著增加，固有频率显著降低，被动TMD失去控制效果。黄智文等［10］研究表明，多重调谐质量阻尼器（MTMD）可进一步提高TMD减振的鲁棒性，但MTMD增加了系统的安装和维护成本［11］，即使经过优化设计，频率差同样会显著降低其减振效果［12］。FITZGERALD等［13］研究认为主动调谐质量阻尼器（ATMD）可以提高TMD对塔筒减振的可靠性。主动控制需外加能源，并需检测振动结构响应，结构装置复杂，存在响应延时与可靠性差的缺点［14-15］。
由于现有的调谐减振措施并不能完全抑制塔筒的大幅振动，CHEN等［16］提出了通过叶片的“熔断”机制防止塔架倒塌，从而保护昂贵的发电机组的安全措施。但是叶片“熔断”机制并不能作为一种常规措施来实施，因此，亟需寻找一种高效率、低成本的减振措施。
黏滞阻尼器是一种性能优良的被动振动控制装置，利用结构大幅的局部变形驱动阻尼器耗能，可以快速消耗结构振动的机械能，在结构抗振方面得到了广泛应用［17-18］。对于以弯曲变形为主的风机柔性塔筒振动，虽然塔筒整体变形大，但局部变形小，无法驱动小尺度的阻尼器大幅往复运动耗能。针对在塔筒减振中如何充分利用黏滞阻尼器良好的耗能能力，DAI等［19］提出了一种将塔筒第一阶弯曲变形转化为拉索端部刚性运动驱动阻尼器耗能减振的阻尼索，该阻尼索理论上可以很好地抑制塔筒第一阶弯曲模态振动，但对于塔筒的高阶振动很难有抑制效果。禹见达等［20］提出了一种复合阻尼索减振技术，阻尼索安装于高耸结构与地面之间，利用其相对于地面的运动驱动阻尼器运动，实现对高耸结构的耗能减振，可以获得很好的减振效果。但复合阻尼索因跨度大，需要占用周边土地而在实际应用中受限。为此，本文设计了一种自锚式阻尼索，将塔筒一定高度处的大转角转化为其与塔筒基础的相对线位移，进而利用其驱动阻尼器耗能减振，并通过理论分析和模型试验分析了阻尼索对塔筒结构的减振效果。
1　风机塔筒-自锚式阻尼索系统
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针对柔性风机塔筒，自锚式减振阻尼索结构示意图如图1所示。在塔筒合适高度处沿周向安装三根横梁，阻尼索上端连接塔筒，下端依次连接横梁外端部和塔筒基础混凝土外缘，形成三套阻尼索系统，抑制塔筒任意方向的弯曲振动。阻尼索由阻尼器和复位弹簧并联后再与拉索串联而成，复位弹簧预先张拉，并保证弹簧弹性力大于阻尼器阻尼力，这样就能使阻尼索时刻处于拉紧状态。
当风机塔筒沿某一方向发生前两阶模态弯曲振动时，塔筒与阻尼索变形如图2所示。将塔筒视为悬臂立柱，塔筒顶部机舱及叶片模拟为顶部集中质量M，设塔筒的抗弯刚度为EI，塔筒高度为，单位长度质量为，复位弹簧刚度为，拉索刚度为，横梁安装高度为，横梁长度为，阻尼器质量为，阻尼器黏性阻尼系数为，外加激励为F。
系统的拉格朗日方程为：
式中　 分别为振动系统的广义坐标与广义速度；T为系统的动能；U为系统的势能；为系统的耗散能；为对应于广义坐标的除有势力以外的其他非有势力的广义力。
假设立柱在任意时刻t的挠度为，其中，表示立柱的模态位移，表示立柱的振型函数。将其代入拉格朗日方程得：
式中　 ，为风机塔筒模态质量；，为风机塔筒模态刚度；，为阻尼索影响系数，其中n为滑轮组位移放大系数，当模型为单索时，n=1。
根据悬臂梁振动理论，立柱振型函数为：
立柱的边界条件为：
式中　 为立柱的固有频率，。
则根据频率方程：
可得，其中，的物理含义为顶部集中质量与立柱质量之比，为线密度，A为立柱截面积。
令，引入状态向量，则式（2）可化为：
其中：
对于立柱自由振动，方程（6）右边=0，将代入式（6）中，得：
式中　 为待求特征值。
方程（7）的特征值矩阵为E，特征向量矩阵为V，将特征值代入Z中，得：
由式（8）得立柱固有频率为：
式中　 表示实部；表示虚部。
阻尼比理论值为：
2　模型试验验证
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2.1　试验模型
试验采用6 m高立柱模拟塔筒，如图3所示，该模型为矩形空心钢管，截面尺寸为（50×30×3） mm3，立柱顶部为（8×2.5） kg质量块，底部至顶部每隔0.5 m分布（2×2.5） kg小质量块，横梁安装位置高度为1.3 m，长度为0.5 m，一端锚固在立柱上，拉索采用直径为1.0 mm的钢丝绳，试验模型参数如表1所示。阻尼索包含拉索、复位弹簧和管式电涡流阻尼器，电涡流阻尼器由铜管与磁铁组成，如图3（b）所示。试验过程中为了加大电涡流阻尼器耗能效率，在横梁端部与地基边缘支座处安装滑轮组，将横梁端部与地基支座间的线位移放大，再驱动电涡流阻尼器运动耗能，试验现场如图4所示。
试验采用铁铷硼高强磁铁，每片磁铁外径为48 mm、内径为10 mm、厚度为20 mm，磁铁采用同极相斥方式逐级增加，磁铁间采用15 mm厚塑料螺母分隔；紫铜管内径为55 mm、外径为65 mm。阻尼器磁铁数量与电涡流阻尼器黏性阻尼系数的关系经试验测得如表2所示［21］。
2.2　第一阶模态附加阻尼比
对立柱施加人工共振激励，使其产生第一阶自由振动，当达到一定幅值后停止激励，立柱继续自由衰减振动，用激光位移计采集立柱某高度处的位移时程，采用最小二乘法拟合衰减包络线得到不同阻尼器黏性阻尼系数下的立柱阻尼比。
当未安装阻尼索时，裸立柱的振动位移时程如图5（a）所示，在立柱安装阻尼索后，通过改变铜管中磁铁的数量，从而获得不同黏性阻尼系数下立柱的位移时程。图5（b）为未装磁铁，即阻尼器黏性阻尼系数为0时的振动位移时程。图5（c）和图5（d）分别为阻尼索安装3级和5级磁铁电涡流阻尼器时立柱的振动位移时程。由图5可以看出，随着阻尼索阻尼器磁铁数量的增加，即黏性阻尼系数的增大，立柱自由振动衰减越来越快，表明阻尼索能够快速地消耗结构振动的能量。
为避免振幅对阻尼比分析结果的影响，除无阻尼索的裸立柱自由振动外，计算阻尼比时，选取测点振幅峰值从2 mm衰减至1 mm左右的区间进行拟合，如图5所示。由拟合结果获得：裸立柱结构（无阻尼索）本身第一阶阻尼比为0.21%；阻尼索阻尼器黏性阻尼系数为0时立柱阻尼比为0.56%。说明拉索预张力作用于滑轮上，各滑轮轴承内产生的摩擦力消耗了部分动能。
附加阻尼比试验值包括两部分：滑轮摩擦力产生的阻尼比与结构本身阻尼比之和、阻尼器产生的阻尼比：
式中　 为阻尼器黏性阻尼系数c=0时试验测得的阻尼比，实测阻尼器黏性阻尼比与解析式（10）得到的阻尼比的关系如图6和表3所示。
由图6及表3可知，随着电涡流阻尼器黏性阻尼系数的增大，塔筒模型的阻尼比也随之增大。黏性阻尼系数从0增加到145 N·s/m时，塔筒模型试验实测阻尼比由0.56%增加到2.36%，由阻尼器黏性阻尼力产生的附加阻尼比由0增大到1.80%。第一阶模态振动附加阻尼比的理论值与试验值对比关系如图6所示，两者基本吻合。在电涡流阻尼器黏性阻尼系数较小的情况下，立柱的附加阻尼比与黏性阻尼系数成正比。
2.3　第二阶模态附加阻尼比
对模型进行第二阶模态自由振动试验，采用同样的方法，立柱衰减振动位移时程如图7所示，计算阻尼比时，选取测点振幅峰值从2 mm衰减至1 mm左右的区间进行拟合，得到立柱附加阻尼比理论值和试验值如表4所示。
由图7及表4可知，立柱第二阶自由振动下，立柱自身阻尼比为0.05%，安装阻尼索后，电涡流阻尼器黏性阻尼系数为0时，结构阻尼比为0.22%。随着电涡流阻尼器黏性阻尼系数的增大，结构附加阻尼比也随之增加，立柱试验实测阻尼比由0.22%增大到4.93%，由阻尼器黏性阻尼力产生的附加阻尼比由0增大到4.71%。第二阶模态振动附加阻尼比的理论值与试验值对比关系如图8所示，两者基本吻合。在电涡流阻尼器黏性阻尼系数较小的情况下，立柱的附加阻尼比与黏性阻尼系数呈正比。
由以上结果可知：（1）塔筒阻尼索减振附加阻尼比解析解（式（10））与试验值结果吻合。（2）由试验可知，阻尼索不仅能增大第一阶模态阻尼比，同一套阻尼索同时也能增大第二阶模态阻尼比，并且增加的模态阻尼比较大。
3　阻尼索参数分析
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由模型试验可知，阻尼索能为塔筒提供较大的附加阻尼比，同时附加阻尼比解析解与试验值结果吻合。采用解析解对阻尼索进行参数分析，影响阻尼索附加阻尼比的主要参数包括：阻尼器黏性阻尼系数c、横梁安装高度与长度l。为探究各参数对阻尼索附加阻尼比的影响，以上述试验模型为研究对象，分析阻尼索附加阻尼比与各参数的关系。
3.1　阻尼器黏性阻尼系数对附加阻尼比的影响
当横梁长度l=0.5 m，横梁安装高度=1.3 m，拉索刚度=9000 N/m，复位弹簧刚度=110 N/m时，取滑轮组阻尼索试验模型进行参数分析，不同黏性阻尼系数与阻尼索附加阻尼比的关系如图9所示。
由图9可知：（1）同一套阻尼索可同时为塔筒前两阶模态提供10%以上的附加阻尼比，对塔筒结构具有很好的减振效果；（2）当其他阻尼索参数一定时，对于塔筒第一阶模态振动，结构的附加阻尼比会随着阻尼器黏性阻尼系数的增大而增大；（3）对于塔筒第二阶模态振动，黏性阻尼系数增大到某一值后，附加阻尼比会随黏性阻尼系数的增大而减小，即存在某一最优黏性阻尼系数，可使第二阶模态振动的减振效果达到最优。
3.2　横梁长度与安装高度对附加阻尼比的影响
当阻尼器黏性阻尼系数c=145 N·s/m时，改变横梁安装高度与横梁长度l，阻尼索为塔筒提供的附加阻尼比如图10所示。
由图10可知：（1）当阻尼索其他参数一定时，对于塔筒第一阶模态振动，结构的附加阻尼比会随着横梁安装高度的增加而增大，也会随着横梁长度的增加而增大；（2）对于塔筒第二阶模态振动，结构附加阻尼比会随着安装高度先增大后减小。当横梁安装高度一定时，塔筒的附加阻尼比随着横梁长度的增加而增大。
4　结论
收起
本文采用自锚式阻尼索对风机塔筒的前两阶模态振动进行了减振理论分析与模型试验研究，主要结论如下：
（1）自锚式阻尼索可以同时大幅增加风机塔筒的前两阶模态阻尼比。
（2）阻尼器黏性阻尼系数存在最优值可使塔筒获得最大的附加阻尼比。
（3）阻尼索横梁越长，塔筒获得的最大附加阻尼比越大。
（4）阻尼索横梁存在最佳的安装高度，对于第一阶模态振动，安装高度越高，可使塔筒获得的附加阻尼比越大；对于第二阶模态振动，随着安装高度的增加，附加阻尼比呈先增大后减小的趋势。
基金
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  • 国家自然科学基金资助项目(52278307)
  • 国家自然科学基金资助项目(W2411050)
  • 湖南省自然科学基金资助项目(2022JJ30261)
文献
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2024年第37卷第11期
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doi: 10.16385/j.cnki.issn.1004-4523.2024.11.002
  • 接收时间：2022-11-06
  • 首发时间：2026-02-12
  • 出版时间：2024-11-28
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  • 收稿日期：2022-11-06
  • 修回日期：2023-03-03
基金
国家自然科学基金资助项目(52278307)
国家自然科学基金资助项目(W2411050)
湖南省自然科学基金资助项目(2022JJ30261)
作者信息
    1湖南科技大学土木工程学院，湖南　湘潭　411201
    2湖南科技大学结构抗风与振动控制湖南省重点实验室，湖南　湘潭　411201
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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