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Article(id=1243253926213038838, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243253924128469739, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2025.07.014, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1737216000000, receivedDateStr=2025-01-19, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774344434549, onlineDateStr=2026-03-24, pubDate=1752940800000, pubDateStr=2025-07-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774344434549, onlineIssueDateStr=2026-03-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774344434549, creator=13701087609, updateTime=1774344434549, updator=13701087609, issue=Issue{id=1243253924128469739, tenantId=1146029695717560320, journalId=1240685776644648972, year='2025', volume='29', issue='7', pageStart='1013', pageEnd='1180', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774344434053, creator=13701087609, updateTime=1774501521460, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243912796535107926, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243253924128469739, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243912796535107927, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1243253924128469739, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1159, endPage=1166, ext={EN=ArticleExt(id=1243253926498251517, articleId=1243253926213038838, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Calculation method of coupling loss factor of underwater ribbed plate-acoustic cavity system, columnId=1241023038381158513, journalTitle=Journal of Ship Mechanics, columnName=Hydro/Structural Acoustics, runingTitle=null, highlight=null, articleAbstract=

Ribbed plate structures are widely used in ship structural design due to their high structural stiffness and strength. In this paper, based on the frequency band analysis model of ribbed plates and the statistical energy analysis (SEA) parameter calculation method of the acoustic cavity subsystem, a calculation model of the radiation efficiency between the ribbed plate structure and the acoustic cavity was established, and the influence of fluid load was taken into account, thus the method for calculating the coupling loss factor of an underwater ribbed plate with an acoustic cavity was obtained. Further, the calculation method was verified by using SEA commercial software. The effects of fluid load and structural reinforcement on the coupling characteristics were studied and analyzed. The results show that the fluid load and structural reinforcement mainly affect the radiation efficiency and coupling loss factor in the frequency band below the cut-off frequency of the coupling structure, and have little effect on that in the frequency band above the cut-off frequency. The research results of this paper can provide theoretical support for the prediction of ship cabin noise and acoustic design.

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加筋板结构因其具有较高的结构刚度和强度，被广泛应用于船舶结构设计。本文在加筋板分频段分析模型基础上结合声空腔子系统统计能量分析（SEA）参数计算方法，建立了加筋板结构与声空腔间的辐射效率计算模型，并考虑流体负载的影响，从而获得了水下加筋板-声空腔耦合损耗因子计算方法，进一步使用SEA商用软件对计算方法进行了验证。研究分析了流体负载和结构加筋对耦合特性的影响，结果表明：流体负载和结构加筋主要影响耦合结构截止频率以下频段的辐射效率和耦合损耗因子，对截止频率以上的频段影响较小。研究成果可为船舶舱室噪声预报与声学设计提供理论支撑。

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通讯作者，E-mail：
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陆斌（1994-），男，硕士，工程师

盛美萍（1970-），女，博士，教授，通讯作者，E-mail：。

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陆斌（1994-），男，硕士，工程师

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陆斌（1994-），男，硕士，工程师

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盛美萍（1970-），女，博士，教授，通讯作者，E-mail：。

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Geometric and material parameters of reinforced plate structure

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名称数值单位名称数值单位
长度Lx4.7124m筋高度h0.04m
宽度Ly2m筋杨氏模量Er2.1×1011Pa
厚度h0.008m筋密度ρr7800kg/m3
杨氏模量E2.1×1011Pa筋泊松比μr0.3125/
密度ρ7800kg/m3沿x方向筋间距Sx0.4712m
泊松比μ0.3125/沿y方向筋间距Sy0.1333m
筋宽度b0.016m
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加筋板结构几何及材料参数表

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名称数值单位名称数值单位
长度Lx4.7124m筋高度h0.04m
宽度Ly2m筋杨氏模量Er2.1×1011Pa
厚度h0.008m筋密度ρr7800kg/m3
杨氏模量E2.1×1011Pa筋泊松比μr0.3125/
密度ρ7800kg/m3沿x方向筋间距Sx0.4712m
泊松比μ0.3125/沿y方向筋间距Sy0.1333m
筋宽度b0.016m
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水下加筋板-声空腔耦合损耗因子计算方法研究
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陆斌 1 , 盛美萍 1, 2 , 郭志巍 1, 2 , 程一鹏 2 , 杨长江 1, 2
船舶力学 | 流体与结构声学 2025,29(7): 1159-1166
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船舶力学 | 流体与结构声学 2025, 29(7): 1159-1166
水下加筋板-声空腔耦合损耗因子计算方法研究
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陆斌1, 盛美萍1, 2 , 郭志巍1, 2, 程一鹏2, 杨长江1, 2
作者信息
  • 1.西北工业大学　宁波研究院，浙江　宁波　315048
  • 2.西北工业大学　航海学院，西安　710068

    • 陆斌（1994-），男，硕士，工程师

    盛美萍（1970-），女，博士，教授，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：
Calculation method of coupling loss factor of underwater ribbed plate-acoustic cavity system
Bin LU1, Mei-ping SHENG1, 2 , Zhi-wei GUO1, 2, Yi-peng CHENG2, Chang-jiang YANG1, 2
Affiliations
  • 1.Ningbo Research Institute of Northwestern Polytechnical University, Ningbo 315048, China
  • 2.School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710068, China
出版时间: 2025-07-20 doi: 10.3969/j.issn.1007-7294.2025.07.014
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摘要
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加筋板结构因其具有较高的结构刚度和强度，被广泛应用于船舶结构设计。本文在加筋板分频段分析模型基础上结合声空腔子系统统计能量分析（SEA）参数计算方法，建立了加筋板结构与声空腔间的辐射效率计算模型，并考虑流体负载的影响，从而获得了水下加筋板-声空腔耦合损耗因子计算方法，进一步使用SEA商用软件对计算方法进行了验证。研究分析了流体负载和结构加筋对耦合特性的影响，结果表明：流体负载和结构加筋主要影响耦合结构截止频率以下频段的辐射效率和耦合损耗因子，对截止频率以上的频段影响较小。研究成果可为船舶舱室噪声预报与声学设计提供理论支撑。

加筋板  /  板-声腔耦合系统  /  统计能量分析  /  耦合损耗因子  /  辐射效率

Ribbed plate structures are widely used in ship structural design due to their high structural stiffness and strength. In this paper, based on the frequency band analysis model of ribbed plates and the statistical energy analysis (SEA) parameter calculation method of the acoustic cavity subsystem, a calculation model of the radiation efficiency between the ribbed plate structure and the acoustic cavity was established, and the influence of fluid load was taken into account, thus the method for calculating the coupling loss factor of an underwater ribbed plate with an acoustic cavity was obtained. Further, the calculation method was verified by using SEA commercial software. The effects of fluid load and structural reinforcement on the coupling characteristics were studied and analyzed. The results show that the fluid load and structural reinforcement mainly affect the radiation efficiency and coupling loss factor in the frequency band below the cut-off frequency of the coupling structure, and have little effect on that in the frequency band above the cut-off frequency. The research results of this paper can provide theoretical support for the prediction of ship cabin noise and acoustic design.

ribbed plate  /  plate-cavity coupling system  /  statistical energy analysis  /  coupling loss factor  /  radiation efficiency
陆斌, 盛美萍, 郭志巍, 程一鹏, 杨长江. 水下加筋板-声空腔耦合损耗因子计算方法研究. 船舶力学, 2025 , 29 (7) : 1159 -1166 . DOI: 10.3969/j.issn.1007-7294.2025.07.014
Bin LU, Mei-ping SHENG, Zhi-wei GUO, Yi-peng CHENG, Chang-jiang YANG. Calculation method of coupling loss factor of underwater ribbed plate-acoustic cavity system[J]. Journal of Ship Mechanics, 2025 , 29 (7) : 1159 -1166 . DOI: 10.3969/j.issn.1007-7294.2025.07.014
正文
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0　引言
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加筋板类结构与内部声腔的耦合声振问题一直是振动声学相关领域的重要研究方向。加筋板结构被广泛应用于各工程领域，如舰船、潜艇、飞机、火箭、车辆等重要运载装备的各类舱室结构中[1-2]。长久以来，国内外学者对板结构-声耦合问题的研究一直在持续进行中。早期，Dowel等[3]研究分析了声腔与飞机壁板结构之间的作用关系，以此为契机开展了结构-声耦合问题研究。随后，Dowell等[4]在前期研究基础上建立了板-声腔系统的结构-声耦合数学理论模型，利用该模型分析了板-声腔耦合系统的声振固有特性，并开展了实验验证。Pan等[5]研究了板结构-声腔耦合系统声振特性，结果表明耦合系统的每阶模态都包含了板结构振动模态和声场模态两部分。David等[6]使用“Onera-MF方法”计算弹性板与空腔耦合结构系统的频率响应，经验证该方法适用于中频域。
对于弹性板-声腔耦合结构的声振问题，国内学者也进行了大量的研究。黎胜等[7]建立加筋板结构声传输模型，研究了板厚、肋间距、肋惯性矩和边界条件等因素对声传输特性的影响。靳国永等[8]研究了弹性板结构封闭声腔的耦合机制和耦合特性，以及耦合特性对系统模态和固有频率的影响及影响程度，发现了规则结构-声腔模态簇耦合特性。俞孟萨等[9]利用集成模态法和虚拟膜技术建立了非规则声腔自噪声计算声学模型，该模型可预报声腔内部噪声的低中频分量，为研究结构与复杂声腔耦合模型提供了新的思路。刘进等[10]将加肪声呐透声窗结构简化为矩形板和矩形声腔组成的规则模型，研究了垂向肋骨间距对声呐自噪声的影响。王园[11]和程传峰等[12]利用声振耦合理论和模态叠加法研究了加筋板与封闭梯形声腔（矩形声腔）耦合结构的声振响应情况。孔德瑜等[13]对比分析了声腔-弹性板声振耦合模型分别在点力激励和点声源激励下，声腔厚度、激励位置以及边界条件等对弹性板声辐射特性的影响和区别。
目前，国内外大部分工作主要针对弹性板-声腔耦合结构开展研究，耦合结构形式相对简单，而实际工程中的板-声腔耦合结构更为复杂。以舰船舱室结构为例，其板结构以加筋板为主体，加筋板的一面常处于含流体负载（海水）状态。因此，本文主要研究这类水下加筋板与声空腔的耦合结构的耦合损耗因子及辐射效率理论计算方法，具有重要的工程应用价值。
本文先从结构振动方程入手，在对结构频散特性进行分析的基础上，采用统计能量分析方法（SEA）针对含流体负载的加筋板结构和声空腔的辐射效率和耦合损耗因子这两个主要声振特性参数进行计算，基于此可对耦合系统进行声振特性预报，为复杂船舶结构声学设计提供理论指导。
1　理论计算模型
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1.1　水下加筋板结构统计能量分析参数计算模型
加筋板结构示意图如图1所示，其基底板长为Lx，宽为Ly，厚为h，基底板的杨氏模量为E，密度为ρ，泊松比为μ；板面上正交布置有Nx条沿y方向的筋和Ny条沿x方向的筋，二者间距分别为Sx和Sy，截面积分别为Ax和Ay，密度分别为ρx和ρy，应用最小势能原理对其振动特性进行分析。
在加筋板结构统计能量分析参数计算时，根据弯曲波波长λB与两方向上筋间距Sx和Sy的大小关系，可将筋对结构等效面密度M、x方向等效刚度Dx与y方向等效刚度Dy的影响分为以下四种情况进行讨论。其中，D为均匀板弯曲刚度，GxJx与GyJy为筋的扭转系数。
（1）当弯曲波波长大于二个方向上筋间距最大值时，即λB > max（Sx,Sy），有
（2）当弯曲波波长大于x方向的筋间距而小于y方向的筋间距时，即Sx < λB < Sy，有
（3）当弯曲波波长大于y方向的筋间距但小于x方向的筋间距时，即Sy < λB < Sx，有
（4）当弯曲波波长小于二个方向上的筋间距最小值时，即λB < min（Sx,Sy），该种情况可忽略筋对均匀板结构的影响，此时M=ρh，Dx=D，Dy=D。
利用最小势能原理可计算得到含流体负载的加筋板结构的弯曲波波数：
式中，M′为考虑流体负载后的等效面密度，具体计算公式为
式中，为均匀板弯曲波波数，ρ0为流体密度，k0=ω/c0为流体中的声波数。
根据不含流体负载的均匀板纵波波速和剪切波波速传统计算理论[14]，推导出含流体负载加筋板的纵波波速CL和剪切波波速CS的计算公式，具体分别为
式中，ρr、hr和Sr分别为筋的密度、高度和筋与板之间的接触面积，S为基底板的表面积。
含流体负载的加筋板纵波波数KL与剪切波波数KS可通过公式[14]计算得到，即
加筋板纵波模态密度nL（ω）和剪切波模态密度nS（ω）可通过公式[14]计算得到，即
通过上述的理论计算模型即可得到水下加筋板结构的波数、波速和模态密度。
1.2　水下加筋板-声空腔耦合损耗因子和辐射效率计算模型
含流体负载的加筋板-声空腔耦合损耗因子计算模型的耦合结构示意图如图2所示，其中灰色长方体为声空腔，上面绿色面为加筋板结构，两者耦合类型为面耦合。
加筋板与声空腔之间的相互耦合作用可以用结构-声空腔间的辐射效率进行表征。在计算辐射效率时，需要考虑两个重要的频率。第一个是加筋板的x和y方向上的第一模态频率f11，其表达式为
第二个是满足加筋板声辐射条件的临界频率，也称截止频率，只有当弯曲振动的频率大于截止频率时，加筋板才能辐射声波，其表达式为
式中，c0为波在周围介质中的传播速度，l1，l2和t分别为板的长度、宽度和厚度，CL为纵波在加筋板中传播的速度。
根据所获得的两个频率f11和fc，加筋板-声空腔耦合结构的损耗因子可通过标准EN 12354-1:2000[15]中的相关公式计算得到，即
式中，σf和ηtot的具体计算公式为
式中，ηint为加筋板结构内损耗因子，辐射效率σ和Λ可参考标准EN 12354-1:2000[15]中的计算方法进行计算。
2　算例分析
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本章主要通过算例验证本文理论计算模型的准确性和有效性，分析流体负载和加筋结构对辐射效率和耦合损耗因子的影响。本章算例中声空腔的长度为4.7124 m，宽度为2 m，高度为2 m，声空腔介质密度为1.21 kg/m3，介质声速为343 m/s。加筋板流体负载密度为1026 kg/m3，流体声速为1500 m/s。加筋板和均匀板的结构参数如表1所示。
2.1　理论计算模型正确性和有效性验证
通过采用理论模型得到的计算结果与现有商用软件VA ONE计算结果进行对比，如图3所示。
由图3可知，理论模型计算得到的含流体负载的加筋板-声空腔耦合损耗因子及辐射效率与VA ONE的计算结果在300 Hz之后的中高频段吻合较好，可以证明本文中的理论计算模型在中高频声振预报中具有较好的准确性和有效性。
2.2　流体负载对辐射效率和耦合损耗因子的影响
以加筋板-声空腔耦合系统为例，通过算例分析流体负载（海水）对耦合损耗因子和辐射效率的影响，对比了含流体负载和不含流体负载情况下的辐射效率和耦合损耗因子，结果如图4所示。
由图4可知，含流体负载的耦合系统中板的辐射效率在截止频率以下频段内要明显小于不含流体负载的辐射效率，从而导致含流体负载的耦合系统的耦合损耗因子在截止频率以下频段内要小于不含流体负载的耦合损耗因子，而截止频率以上频段的辐射效率和耦合损耗因子基本保持不变。因此流体负载主要影响耦合结构截止频率以下频段的辐射效率和耦合损耗因子，对截止频率以上频段的影响较小。
2.3　加筋结构对辐射效率和耦合损耗因子的影响
通过算例分析加筋结构对耦合损耗因子和辐射效率的影响，其中加筋板和均匀板（不加筋）的一面均在流体负载状态下，流体介质为海水，算例对比结果如图5所示。
由图5可知，加筋结构的辐射效率在截止频率以下频段内要明显大于不加筋结构的辐射效率，由其组成的耦合系统的耦合损耗因子，在截止频率以下频段内要大于不加筋结构的耦合损耗因子，而截止频率以上频段的辐射效率和耦合损耗因子基本保持不变。因此，加筋主要影响了耦合结构截止频率以下频段的辐射效率和耦合损耗因子，加筋会增大辐射效率和耦合损耗因子，而对截止频率以上频段的影响较小。
3　结论
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本文基于统计能量分析方法构建了含流体负载的加筋板-声空腔耦合结构的声振预报模型，辐射效率和耦合损耗因子的理论计算结果与商用软件VA ONE结果吻合较好，通过数值算例验证了文中分析模型的正确性和有效性。利用理论计算模型研究分析了流体负载和加筋结构对辐射效率和耦合损耗因子的影响，结果表明：
（1）流体负载主要影响耦合结构截止频率以下频段的辐射效率和耦合损耗因子，对截止频率以上频段的影响较小，附加流体负载后截止频率以下频段的辐射效率和耦合损耗因子均变小。
（2）加筋主要影响耦合结构截止频率以下频段的辐射效率和耦合损耗因子，会增大辐射效率和耦合损耗因子，而对截止频率以上频段的影响较小。
基金
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  • 宁波市自然科学基金资助项目(2021J057)
  • 国家自然科学基金资助项目(52301388)
  • 船舶总体性能创新研究开放基金资助项目(33122232)
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2025年第29卷第7期
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doi: 10.3969/j.issn.1007-7294.2025.07.014
  • 接收时间：2025-01-19
  • 首发时间：2026-03-24
  • 出版时间：2025-07-20
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  • 收稿日期：2025-01-19
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宁波市自然科学基金资助项目(2021J057)
国家自然科学基金资助项目(52301388)
船舶总体性能创新研究开放基金资助项目(33122232)
作者信息
    1.西北工业大学　宁波研究院，浙江　宁波　315048
    2.西北工业大学　航海学院，西安　710068

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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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