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Article(id=1243896231253094576, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896229885751465, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2025.08.013, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1739894400000, receivedDateStr=2025-02-19, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774497572005, onlineDateStr=2026-03-26, pubDate=1755619200000, pubDateStr=2025-08-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774497572005, onlineIssueDateStr=2026-03-26, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774497572005, creator=13701087609, updateTime=1774497572005, updator=13701087609, issue=Issue{id=1243896229885751465, tenantId=1146029695717560320, journalId=1240685776644648972, year='2025', volume='29', issue='8', pageStart='1181', pageEnd='1342', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774497571678, creator=13701087609, updateTime=1774501555614, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243912939799949656, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896229885751465, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243912939799949657, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243896229885751465, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1309, endPage=1318, ext={EN=ArticleExt(id=1243896231504752817, articleId=1243896231253094576, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Analysis of vibration characteristics of rectangular plates excited by turbulent boundary layer under flexible boundary constraints, columnId=1241023038381158513, journalTitle=Journal of Ship Mechanics, columnName=Hydro/Structural Acoustics, runingTitle=null, highlight=null, articleAbstract=

The flexible boundary constraints have a significant effect on the vibration characteristics of rectangular stiffened plates excited by turbulent boundary layer. In this paper, springs were used to simulate flexible boundary constraints. The response function of an underwater rectangular plate was derived based on the energy principle, combined with the power spectra density expression caused by turbulent boundary layer, and the power spectral density of the plate velocity was obtained. It is shown that the boundary spring stiffness has an effect on the response of the plate. As the spring stiffness of the boundary displacement increases, the vibration response of the plate at low frequencies decreases. The effect of the boundary spring stiffness on the vibration response of plate excited by TBL converges when the boundary displacement spring stiffness kd is larger than 1010 N/m2. The effect of stiffened rib direction and the number of stiffened ribs on the vibration response of stiffened plate was also studied in this paper. Compared with an unreinforced plate, the vibration response of a stiffened plate at low frequency was effectively reduced. The results can serve as a theoretical reference for the analysis of the vibration characteristics of rectangular stiffened plates excited by turbulent boundary layer under flexible boundary constraints.

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本文采用半解析法开展弹性边界下矩形加筋板在湍流脉动压力激励下的振动研究。引入人工线分布弹簧模拟弹性边界，基于能量原理求解矩形薄板流激受迫振动响应，获得平板表面振动速度的自功率谱密度函数。研究表明：人工弹簧刚度对平板流激振动响应有影响；随着边界位移弹簧刚度增大，低频下平板均方振速响应值不断减小；当边界线分布位移弹簧刚度大于1010 N/m2时，边界对平板流激振动响应的影响较小。讨论了加筋方向和加筋数量对于平板流激振动响应的影响，与无筋平板相比，加筋平板能有效降低平板流激低频振动响应。研究结果可为分析不同边界约束下矩形加筋板流激振动性能提供理论参考。

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通讯作者，E-mail：
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张成（1996-），男，硕士

李天匀（1969-），男，教授，通讯作者，E-mail：。

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张成（1996-），男，硕士

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张成（1996-），男，硕士

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李天匀（1969-），男，教授，通讯作者，E-mail：。

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李天匀（1969-），男，教授，通讯作者，E-mail：。

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Parameters of plate and fluid

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参数名称符号/单位数值
平板长度a/m0.9144
平板宽度b/m0.6096
平板厚度h/m0.006 35
弹性模量E/Pa2.1×1011
泊松比µ0.27
平板密度ρp/（kg·m−3）7800
结构损耗因子r0.01
流体密度ρf/（kg·m−3）1000
流体声速cf/（m·s−1）1500
来流速度U0/（m·s−1）5.1816
边界层厚度δ/mm0.021
来流距离L/m1
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平板材料参数及流体参数

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参数名称符号/单位数值
平板长度a/m0.9144
平板宽度b/m0.6096
平板厚度h/m0.006 35
弹性模量E/Pa2.1×1011
泊松比µ0.27
平板密度ρp/（kg·m−3）7800
结构损耗因子r0.01
流体密度ρf/（kg·m−3）1000
流体声速cf/（m·s−1）1500
来流速度U0/（m·s−1）5.1816
边界层厚度δ/mm0.021
来流距离L/m1
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First 6 natural frequencies of plate in water

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固有频率/Hz1阶2阶3阶4阶5阶6阶
FEM16.54843.48376.60290.573108.728163.130
本文方法15.56643.58276.73190.701108.983163.645
相对误差（%）−0.109−0.228−0.168−0.141−0.235−0.316
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水下平板前6阶固有频率

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固有频率/Hz1阶2阶3阶4阶5阶6阶
FEM16.54843.48376.60290.573108.728163.130
本文方法15.56643.58276.73190.701108.983163.645
相对误差（%）−0.109−0.228−0.168−0.141−0.235−0.316
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Parameters and size of plate in Case a

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参数名称符号/单位数值
平板长度a/m0.65
平板宽度b/m0.6
平板厚度h/m0.005
弹性模量E/Pa2.1×1011
泊松比µ0.3
平板密度ρp/（kg·m−3）7800
结构损耗因子r0.01
流体密度ρf/（kg·m−3）1000
流体声速cf/（m·s−1）1500
来流速度U0/（m·s−1）3.0867
边界层厚度δ/mm0.0211
来流距离L/m1
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方案a平板尺寸及参数

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参数名称符号/单位数值
平板长度a/m0.65
平板宽度b/m0.6
平板厚度h/m0.005
弹性模量E/Pa2.1×1011
泊松比µ0.3
平板密度ρp/（kg·m−3）7800
结构损耗因子r0.01
流体密度ρf/（kg·m−3）1000
流体声速cf/（m·s−1）1500
来流速度U0/（m·s−1）3.0867
边界层厚度δ/mm0.0211
来流距离L/m1
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Section size and properties of rib

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参数名称符号/单位数值
加筋截面宽度ar/m0.004
加筋截面高度br/m0.02
弹性模量E/Pa2.1×1011
结构损耗因子r0.01
泊松比µ0.3
平板密度ρp/（kg·m−3）7800
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单根筋截面尺寸和属性

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参数名称符号/单位数值
加筋截面宽度ar/m0.004
加筋截面高度br/m0.02
弹性模量E/Pa2.1×1011
结构损耗因子r0.01
泊松比µ0.3
平板密度ρp/（kg·m−3）7800
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弹性边界条件下矩形薄板流激振动分析
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张成 1, 3 , 李天匀 1, 2, 3 , 朱翔 1, 2, 3 , 尚保佑 1, 3
船舶力学 | 流体与结构声学 2025,29(8): 1309-1318
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船舶力学 | 流体与结构声学 2025, 29(8): 1309-1318
弹性边界条件下矩形薄板流激振动分析
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张成1, 3, 李天匀1, 2, 3 , 朱翔1, 2, 3, 尚保佑1, 3
作者信息
  • 1.华中科技大学　船舶与海洋工程学院，武汉　430074
  • 2.高新船舶与深海开发装备协同创新中心，上海　200240
  • 3.船舶与海洋水动力湖北省重点实验室，武汉　430074

    • 张成（1996-），男，硕士

    李天匀（1969-），男，教授，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：
Analysis of vibration characteristics of rectangular plates excited by turbulent boundary layer under flexible boundary constraints
Cheng ZHANG1, 3, Tian-yun LI1, 2, 3 , Xiang ZHU1, 2, 3, Bao-you SHANG1, 3
Affiliations
  • 1.School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
  • 2.Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), Shanghai 200240, China
  • 3.Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics (HUST), Wuhan 430074, China
出版时间: 2025-08-20 doi: 10.3969/j.issn.1007-7294.2025.08.013
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摘要
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本文采用半解析法开展弹性边界下矩形加筋板在湍流脉动压力激励下的振动研究。引入人工线分布弹簧模拟弹性边界，基于能量原理求解矩形薄板流激受迫振动响应，获得平板表面振动速度的自功率谱密度函数。研究表明：人工弹簧刚度对平板流激振动响应有影响；随着边界位移弹簧刚度增大，低频下平板均方振速响应值不断减小；当边界线分布位移弹簧刚度大于1010 N/m2时，边界对平板流激振动响应的影响较小。讨论了加筋方向和加筋数量对于平板流激振动响应的影响，与无筋平板相比，加筋平板能有效降低平板流激低频振动响应。研究结果可为分析不同边界约束下矩形加筋板流激振动性能提供理论参考。

湍流脉动压力  /  平板振动  /  弹性边界  /  声振耦合

The flexible boundary constraints have a significant effect on the vibration characteristics of rectangular stiffened plates excited by turbulent boundary layer. In this paper, springs were used to simulate flexible boundary constraints. The response function of an underwater rectangular plate was derived based on the energy principle, combined with the power spectra density expression caused by turbulent boundary layer, and the power spectral density of the plate velocity was obtained. It is shown that the boundary spring stiffness has an effect on the response of the plate. As the spring stiffness of the boundary displacement increases, the vibration response of the plate at low frequencies decreases. The effect of the boundary spring stiffness on the vibration response of plate excited by TBL converges when the boundary displacement spring stiffness kd is larger than 1010 N/m2. The effect of stiffened rib direction and the number of stiffened ribs on the vibration response of stiffened plate was also studied in this paper. Compared with an unreinforced plate, the vibration response of a stiffened plate at low frequency was effectively reduced. The results can serve as a theoretical reference for the analysis of the vibration characteristics of rectangular stiffened plates excited by turbulent boundary layer under flexible boundary constraints.

turbulent boundary layer  /  vibration of plate  /  flexible boundary constraint  /  acoustics-vibration coupling
张成, 李天匀, 朱翔, 尚保佑. 弹性边界条件下矩形薄板流激振动分析. 船舶力学, 2025 , 29 (8) : 1309 -1318 . DOI: 10.3969/j.issn.1007-7294.2025.08.013
Cheng ZHANG, Tian-yun LI, Xiang ZHU, Bao-you SHANG. Analysis of vibration characteristics of rectangular plates excited by turbulent boundary layer under flexible boundary constraints[J]. Journal of Ship Mechanics, 2025 , 29 (8) : 1309 -1318 . DOI: 10.3969/j.issn.1007-7294.2025.08.013
正文
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0　引言
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潜艇在水下航行时，板壳结构在湍流脉动压力激励下会产生结构自噪声，不利于声呐正常工作。因此，降低导流罩在湍流脉动激励下的自噪声具有重要的工程意义。湍流脉动压力作为时空随机激励，需要借助统计学分析原理，获取其功率谱密度函数以定量地分析它与结构相互作用的耦合程度。
Corcos[1]在壁压试验结果的基础上总结提出了湍流边界层脉动压力的频率-波数谱模型；Strawderman[2]考虑在简支平板振动的基础上，将平板两侧的流体视为半无限域声场，通过平板表面的振速连续条件将平板振动方程与声场波动方程建立联系，分析了考虑流体与结构振动之间的耦合效应时，无限大平板和有限简支平板的流激振动响应；陈美霞等[3]采用半数值半解析的方法开展了湍流激励下平板、单双层圆柱壳的声振特性研究，并且量化分析了来流速度对平板流激振动特性的影响；吕世金等[4]将湍流脉动压力功率谱视为输入力源，分析了无限大加肋平板的声辐射特性，并探讨了肋骨参数变化对结构流激声辐射的影响；徐嘉启等[5]在此基础上采用固体三维弹性波理论研究了贴敷柔性层对加肋平板流激噪声的影响机理，但其研究对象依然为周期加筋的无限大薄板，而实际结构往往是复杂边界约束下的有限大结构；Li等[6]通过引入边界虚拟弹簧以模拟弹性边界，并在平板位移函数处添加补充项以保证位移函数在边界处满足弹性边界的条件。目前针对弹性边界条件下的薄板在流体激励下的振动分析较为匮乏。
本文在此基础上，采用改进的傅里叶级数作为加筋平板的位移函数，分别计算加筋板的弯曲应变能和动能，同时考虑水下结构振动与声场之间的耦合作用，得出水下加筋平板的响应函数；结合湍流脉动压力谱模型，求解加筋平板的振动响应，并分析加筋方向、数量以及不同边界条件约束对平板流激振动响应的影响。
1　基本理论
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1.1　湍流脉动压力模型
常见的舰船艏部声呐导流罩为加筋曲壳结构，复杂的壳体曲率使得导流罩在湍流脉动压力激励下的振动特性研究难度较大。考虑到湍流度较高处对应的导流罩壳体曲率较小，将复杂的空间曲壳局部视为有限大的矩形加筋平板，将这一离散的子单元作为理论模型的对象。假设充分发展的湍流激励作用于嵌在无限大刚性障板的平板一侧，平板的另一侧接触的流体为静止状态。忽略平板振动和声辐射对于湍流边界层的影响，即湍流脉动压力谱模型中的流体密度、声速、边界层厚度均为常数，将湍流脉动压力视为独立的外力激励，它与平板振动和声场之间没有耦合。
Corcos提出了经典的湍流脉动压力谱模型[1]，脉动压力在空间域上的互功率谱密度函数表达式为
式中，Φp（ω）为平板表面上某点的湍流脉动压力自功率谱密度；ξ、η分别为平板表面两点沿来流方向和垂直来流方向的相对坐标，平板坐标系及来流方向如图1所示；Uc为湍流边界层沿来流方向的迁移速度，一般取来流速度U0的0.6~0.8倍。
针对不同频段ω与自功率谱之间的关系，平板表面脉动压力自功率谱Φp（ω）表达形式多样，本文采用Skudrzyk等[7]提出的自功率谱密度函数，其形式如下：
式中，，当流体为水时，ε取值为1，当流体为空气时，ε取值为3；ρf为流体密度；U0为来流速度；δ为边界层厚度。对于平板而言，湍流边界层厚度，雷诺数，其中L为来流距离，v为流体运动粘性系数。
1.2　薄板振动响应函数
根据Kirchhoff薄板理论，矩形薄板小变形振动微分方程为
式中，ρ为平板材料密度，h为平板厚度，q（x，y，t）为单位面积平板承受的横向载荷。对于四边简支约束的平板而言，方程（3）的解可以写为
式中，a、b分别为矩形平板的长、宽，m、n分别为沿矩形薄板长、宽方向的模态半波数，Amn为待定系数，eiωt为简谐时间因子。
考虑到本文研究对象——矩形平板为声呐导流罩曲壳结构上的子单元，平板的边界条件更接近于弹性边界，而非简支边界。本文参考文献[8]中的处理方式，将边界条件对平板的约束转化为均布于边界处的人工位移弹簧和人工转角弹簧约束，通过调整弹簧的刚度以模拟薄板的弹性边界条件或经典边界条件，采用改进的傅里叶级数[9]构造矩形薄板的位移函数，改进的傅里叶级数由傅里叶级数和额外的补充项组成，具体表达为
式中，m=1，2，3...；n=1，2，3...；a、b分别为矩形平板的长、宽。
矩形平板横向位移函数可写为
式中，M、N分别为位移函数fm(x)、gn(y)的截断项数，本文选取的截断项数M=N=13，文献[10]中验证了截断数的收敛性；A为待定系数Amn依次组成的列向量；ζ为fm(x)、gn(y)各项的乘积组成的列向量。
根据平板振动理论，平板的弯曲应变能Up和动能Tp分别为
式中，D=Eh3/(12(1-µ2))是薄板单位宽度的弯曲刚度，h为平板厚度，E为平板材料弹性模量，µ为泊松比，ρp为平板材料密度。
边界人工弹簧的弹性势能为
式中，kd1、kd2、kd3、kd4分别表示矩形平板四边平动弹簧刚度，kr1、kr2、kr3、kr4表示矩形平板四边转角弹簧刚度。
对于嵌在无限大声障板的平板而言，单侧辐射声场对平板所做的功为
式中，prad为平板表面辐射声压。由Rayleigh积分可知，平板任意一点（x，y）处的声压可表示为
式中，，为辐射声场的波数，cf为流体声速。
作用于平板（x0，y0）处的点激励对平板做的功为
式中，F为点激励幅值，δ（）为二维狄拉克函数。
由于无限大声障板的存在，双面覆水平板两侧声压大小相等，声压相位相反，故平板两侧声场对平板做功为
若平板单侧加筋，则需根据加筋方向和加筋位置计算双向加筋的应变能和动能。本文将筋等效为欧拉梁，横纵筋的应变能表达为
式中，Dx、Dy分别为横向筋和纵向筋在与平板耦合振动下的抗弯刚度，nx、ny分别为横、纵加筋数目，y=bi，x=aj分别指横、纵筋的位置，其中，，ni=1，2，...，nx；nj=1，2，...，ny。
横纵筋的动能为
式中，ρrx、ρry分别为横、纵筋的材料密度，Srx、Sry分别为横纵筋各自截面面积。
综合式（7）~（15），水下加筋平板的能量泛函可以表达为
根据Hamilton变分原理，薄板的能量泛函应满足：
将平板的应变能Up和动能Tp、双向加筋的应变能Uribs和动能Tribs、边界人工弹簧应变能Us、双面声场做功WR以及点激励做功WF代入式（17），可以得出平板动力学方程：
式中，Kp为平板自身刚度矩阵，Kribs为横纵向加筋的刚度矩阵，Ks为边界弹簧刚度矩阵，Mp为平板质量矩阵，Mribs为横纵向加筋的质量矩阵，MR为声振耦合效应矩阵，F为点激励矩阵。
求解方程（18）得到平板位移函数中的待定系数A0，代入式（6）中得出平板在点激励作用下的位移。定义平板在点激励作用下的位移响应函数为
1.3　平板振动响应功率谱密度
根据随机激励理论，湍流激励下平板振动位移互功率谱密度函数为
式中，ξ、η分别表示沿x轴、y轴方向两点之间的相对距离。
若令式（20）中ξ=0，η=0，则平板位移互功率谱密度函数退化为平板上点（x，y）处的位移自功率谱密度Sww（x，y，ω）。
根据平板表面振动位移与速度、加速度之间的关系，可以得出平板流激振动速度自功率谱密度函数、平板流激振动加速度自功率谱密度函数分别为
平板振速均方谱密度为
2　算法验证
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为验证本文方法的正确性，以文献[2]中的四边简支平板为例，换算成国际单位制下的平板及流场参数，如表1所示。
选取平板表面A、B两点作为振动响应点，A点坐标为，B点坐标为；在频段为1~273 Hz内，频率间隔为2 Hz；在278~998 Hz频段范围内，间隔为5 Hz。
将本文方法得到A、B两点的振速自功率谱密度计算结果与文献[2]中结果进行对比，如图2所示。
水下结构的流激振速自功率谱密度本质上是结构表面某点在湍流脉动压力作用下振动响应的平方，水下平板流激振速频谱曲线的峰值频率对应于水下平板的固有频率[3]。本文方法以及有限元仿真软件计算出的水下平板前6阶固有频率如表2所示，水下平板前6阶振型如图3所示。
本文方法计算得到的水下平板前6阶固有频率与有限元软件求解结果相对误差小于0.5%，水下平板前6阶振型基本一致，确保了本文通过能量法建立的水下平板振动动力学模型的正确性。本文结果曲线与文献中提取的曲线趋势基本一致，响应峰值对应的频率与文献基本吻合，验证了本文方法的正确性。
本文误差主要源于平板位移函数的截断和数值积分的精度；文献结果的误差主要源于模态叠加的模态数截断，此外文献作者忽视了声振耦合项中的互辐射模态的影响，这也是本文结果高频响应峰值对应的频率与文献结果稍有偏差的主要原因。
3　弹性边界及加筋对平板流激振动特性的影响研究
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3.1　弹性边界对流激振动特性的影响分析
本节旨在研究弹性边界条件对平板流激振动响应的影响，方案a中平板及流体计算参数如表3所示。计算频率在1~273 Hz内，间隔为2 Hz；在278~998 Hz频率范围内，间隔为5 Hz。
令边界转角弹簧刚度kr=0 N/m3，调整边界位移弹簧刚度kd的取值，实现不同边界对于平板的弹性平动约束；令kdi=10i，i=2，3，...，12 N/m2，平板板面均方振速功率谱密度结果如图4（a）所示。随着边界平动弹簧刚度逐渐增大，平板均方振速谱密度逐步减小；当kd ⩾ 1010 N/m2时，低频下（1~200 Hz）平板均方振速响应值不再显著变化，如图4（b）所示。
在人工弹簧刚度kd=1012 N/m2，kr=0 N/m3时，保证了弹性边界模拟简支约束的收敛性，在此基础上令kd=1012 N/m2，kr=1012 N/m3以模拟固支约束，两种约束下1~200 Hz平板均方振速如图5所示。与简支约束相比，固支约束下平板均方振速响应整体更小，振速响应峰值对应的频率更大，与平板结构受迫振动响应规律一致。
3.2　加筋对平板流激振动响应的影响分析
在方案a的基础上，以加筋板代替平板作为研究对象，加筋板中的平板尺寸、材料属性和流体属性均与方案a一致，单根筋的截面尺寸及材料属性如表4所示。
本文将筋视为等效的欧拉梁，而梁的存在则使整个结构的中性轴下移，即梁结构在计算其弯曲截面惯性矩时需要进行偏心处理。文献[11]中给出修正后的偏心距为
式中，A1、A2分别为板、梁的横截面面积；e、e0分别为修正前后梁中性轴到板中面的距离，示意图如图6所示。图中C0、C1分别为板、梁横截面的形心。
为探究加筋数量对加筋板流激响应的影响，分别计算仅横向加筋（沿平板长边方向）、仅纵向加筋以及双向正交加筋时，不同加筋数量（n=1，2，3，4）下的平板均方振速。不同加筋数量下板面均方振速曲线如图7所示。
随着加筋数量的增加，加筋板结构整体刚度逐步增大，板面振速响应峰值对应的频率朝着高频移动，板面均方振速整体稍有减少。对比图7（a）与图7（b），相同加筋数量下，横向加筋平板低频下的振动响应稍小于纵向加筋板；与无筋的平板相比，加筋板低频下的均方振速稍小，但不同加筋数量的加筋板响应结果比较接近；如图7（c）中所示，双向加筋数量n ⩾ 2时，低频下平板振动响应无明显减少。
4　结论
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本文以弹性边界约束下的水下平板为对象，考虑平板两侧声场与结构振动之间的耦合效应，得出了水下平板的响应函数；结合湍流脉动压力的Corcos模型，求解出平板振动响应的功率谱密度。本文方法计算结果与现有文献吻合良好，证明了方法的正确性。
针对弹性边界约束、加筋数量和加筋方向对平板流激振动响应影响进行了对比分析，得出以下结论：
（1）随着边界位移弹簧刚度kd的增大，低频下平板均方振速响应值不断减小；当边界位移弹簧kd ⩾ 1010 N/m2时，边界弹簧约束近似于简支约束；在简支约束的基础上，添加边界转角约束，能有效降低平板均方振速响应。
（2）平板加筋能有效降低平板流激低频振动响应，就本文采用的平板尺寸和筋条截面尺寸而言，双向正交加筋数量n=2为最优的加筋方案；相同加筋数目情况下，沿长边加筋优于沿短边加筋。
基金
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  • 国家自然科学基金面上项目(52371318)
文献
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2025年第29卷第8期
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doi: 10.3969/j.issn.1007-7294.2025.08.013
  • 接收时间：2025-02-19
  • 首发时间：2026-03-26
  • 出版时间：2025-08-20
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  • 收稿日期：2025-02-19
基金
国家自然科学基金面上项目(52371318)
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    1.华中科技大学　船舶与海洋工程学院，武汉　430074
    2.高新船舶与深海开发装备协同创新中心，上海　200240
    3.船舶与海洋水动力湖北省重点实验室，武汉　430074

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2种不同金属材料的力学参数
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Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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