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Article(id=1228634264162464324, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228634261138374834, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2024.07.013, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1664726400000, receivedDateStr=2022-10-03, revisedDate=1668355200000, revisedDateStr=2022-11-14, acceptedDate=null, acceptedDateStr=null, onlineDate=1770858835497, onlineDateStr=2026-02-12, pubDate=1722096000000, pubDateStr=2024-07-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770858835497, onlineIssueDateStr=2026-02-12, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770858835497, creator=13701087609, updateTime=1770858835497, updator=13701087609, issue=Issue{id=1228634261138374834, tenantId=1146029695717560320, journalId=1225147924628267009, year='2024', volume='37', issue='7', pageStart='1089', pageEnd='1268', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770858834775, creator=13701087609, updateTime=1770859016311, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228635022622654927, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228634261138374834, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228635022622654928, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228634261138374834, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1211, endPage=1220, ext={EN=ArticleExt(id=1228634265903100501, articleId=1228634264162464324, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Characteristics of pressure resistance and sound absorption on anechoic coating with metal perforated plate under hydrostatic pressure, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

An underwater acoustic structure with metal perforated plate inserted into the traditional anechoic coating is proposed to improve the pressure resistance and sound absorption performance of the structure. The deformation of the acoustic structure under different hydrostatic pressure is studied by the static method. By establishing the acoustic finite element equation under the action of hydrostatic pressure，the sound absorption effect of the acoustic structure under different hydrostatic pressure is analyzed. Compared with the traditional anechoic coating，under the hydrostatic pressure of 0 to 6 MPa，the acoustic structure achieves better broadband sound absorption in the mid-to-high frequency range. In addition，the effects of the thickness，material and porosity of the metal perforated plate on the sound absorption performance of the acoustic structure are discussed. The research shows that the underwater anechoic coating with metal perforated plate is an effective design to improve the pressure resistance and sound absorption performance of underwater acoustic structure.

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为改善静水压力作用下传统声学覆盖层的吸声性能，提出了将金属孔板插入传统声学覆盖层中的水下声学覆盖层结构。以静力学方法研究了该声学覆盖层结构在不同静水压力下的形变情况。通过建立静水压力作用下的声学有限元方程，分析了该声学结构在不同静水压力下的吸声效果。与传统声学覆盖层相比，在静水压力为0~6 MPa时，该声学结构在中、高频段获得了更好的宽频吸声效果。此外，还讨论孔板厚度、孔板材料及孔板孔隙率对该声学结构吸声性能的影响。研究表明设计含金属孔板声学覆盖层可有效改善静水压力条件下水下声学结构的吸声性能。

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靳国永（1980―），男，博士，教授。E-mail：。
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贾薪宇（1989—），男，博士研究生。E-mail：。

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贾薪宇（1989—），男，博士研究生。E-mail：。

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贾薪宇（1989—），男，博士研究生。E-mail：。

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Journal of Vibration and Shock， 2016， 35（6）： 59-63., articleTitle=Measurement of viscoelastic dynamic parameters of polymer materials under hydrostatic pressure, refAbstract=null), Reference(id=1228634287654760973, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228634264162464324, doi=null, pmid=null, pmcid=null, year=2004, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=［24］, rfOrder=38, authorNames=王曼, journalName=null, refType=null, unstructuredReference=王曼. 水声吸声覆盖层理论与实验研究［D］. 哈尔滨： 哈尔滨工程大学， 2004., articleTitle=水声吸声覆盖层理论与实验研究, refAbstract=null), Reference(id=1228634287793173013, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228634264162464324, doi=null, pmid=null, pmcid=null, year=2004, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=［24］, rfOrder=39, authorNames=Wang Man, journalName=null, refType=null, unstructuredReference=Wang Man. Theoretical and experimental study on underwater anechoic coating［D］. Harbin： Harbin Engineering University， 2004．, articleTitle=Theoretical and experimental study on underwater anechoic coating, refAbstract=null), Reference(id=1228634287893836314, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228634264162464324, doi=null, pmid=null, pmcid=null, year=2022, volume=533, issue=null, pageStart=116985, pageEnd=null, url=null, language=null, rfNumber=［25］, rfOrder=40, authorNames=Yang H B, Zhao H G, Wen J H, journalName=Journal of Sound and Vibration, refType=null, unstructuredReference=Yang H B， Zhao H G， Wen J H. Theory and numerical method for the effects of hydrostatic pressure on sound absorption of underwater acoustic coatings with air cavities［J］. 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Applied Acoustics， 2019， 143： 200-210., articleTitle=Sound absorption by rubber coatings with periodic voids and hard inclusions, refAbstract=null), Reference(id=1228634288065802792, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228634264162464324, doi=null, pmid=null, pmcid=null, year=2011, volume=45, issue=9, pageStart=1340, pageEnd=1350, url=null, language=null, rfNumber=［27］, rfOrder=42, authorNames=陶猛, 卓琳凯, journalName=上海交通大学学报, refType=null, unstructuredReference=陶猛， 卓琳凯. 静水压力下吸声覆盖层的声学性能分析［J］. 上海交通大学学报， 2011， 45（9）： 1340-1350., articleTitle=静水压力下吸声覆盖层的声学性能分析, refAbstract=null), Reference(id=1228634288158077482, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228634264162464324, doi=null, pmid=null, pmcid=null, year=2011, volume=45, issue=9, pageStart=1340, pageEnd=1350, url=null, language=null, rfNumber=［27］, rfOrder=43, authorNames=Tao Meng, Zhuo Linkai, journalName=Journal of Shanghai Jiao Tong University, refType=null, unstructuredReference=Tao Meng， Zhuo Linkai. Effect of hydrostatic pressure on acoustic performance of sound absorption coating［J］. 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label=Fig.5, caption=Schematic diagram of unit and section deformation of traditional anechoic coating under different hydrostatic pressures, figureFileSmall=ygfodF1Yajzeql454God2Q==, figureFileBig=ATnp7Jw3MMNm7Uh4CFY4og==, tableContent=null), ArticleFig(id=1228634280130179184, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228634264162464324, language=CN, label=图5, caption=传统声学覆盖层在不同静水压下单元结构及截面形变示意图, figureFileSmall=ygfodF1Yajzeql454God2Q==, figureFileBig=ATnp7Jw3MMNm7Uh4CFY4og==, tableContent=null), ArticleFig(id=1228634280276979829, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228634264162464324, language=EN, label=Fig.6, caption=Schematic diagram of unit and section deformation of anechoic coating with metal perforated plate under different hydrostatic pressures, figureFileSmall=V6Ss/oTBeUKjfulUpOelFA==, figureFileBig=7JOdiVMM85YiBYUBzCA7bA==, tableContent=null), ArticleFig(id=1228634280365060221, tenantId=1146029695717560320, 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absorption coefficients of anechoic coatings with different porosity of metal perforated plates under normal pressure, figureFileSmall=Ent9aNZtizMcPaZK9BOkpA==, figureFileBig=HEYjkgqUfRtKnf5rVZVzRw==, tableContent=null), ArticleFig(id=1228634282621595904, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228634264162464324, language=CN, label=图17, caption=常压下不同孔隙率金属孔板材料声学覆盖层吸声系数, figureFileSmall=Ent9aNZtizMcPaZK9BOkpA==, figureFileBig=HEYjkgqUfRtKnf5rVZVzRw==, tableContent=null), ArticleFig(id=1228634282718064903, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228634264162464324, language=EN, label=Tab.1, caption=

Static material parameters of anechoic coating

, figureFileSmall=null, figureFileBig=null, tableContent=
材料密度/(kg·m-3)杨氏模量/Pa泊松比损耗因子
橡胶9008.9×1060.4960.3
铝27307.0×10100.33-
钢78302.06×10110.28-
), ArticleFig(id=1228634282801950988, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228634264162464324, language=CN, label=表1, caption=

声学覆盖层组成结构的静态材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
材料密度/(kg·m-3)杨氏模量/Pa泊松比损耗因子
橡胶9008.9×1060.4960.3
铝27307.0×10100.33-
钢78302.06×10110.28-
), ArticleFig(id=1228634282885837074, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228634264162464324, language=EN, label=Tab.2, caption=

Material parameters of metal perforated plate

, figureFileSmall=null, figureFileBig=null, tableContent=
材料密度/(kg·m-3)杨氏模量/Pa泊松比损耗因子
铅116004.0×10100.35—
铝27307.0×10100.33—
钢78302.06×10110.28—
), ArticleFig(id=1228634283024249111, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228634264162464324, language=CN, label=表2, caption=

金属孔板材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
材料密度/(kg·m-3)杨氏模量/Pa泊松比损耗因子
铅116004.0×10100.35—
铝27307.0×10100.33—
钢78302.06×10110.28—
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静压下带金属孔板声学覆盖层的耐压与吸声特性
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贾薪宇 , 靳国永 , 叶天贵 , 闫燕
振动工程学报 | 2024,37(7): 1211-1220
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振动工程学报 | 2024, 37(7): 1211-1220
静压下带金属孔板声学覆盖层的耐压与吸声特性
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贾薪宇 , 靳国永 , 叶天贵, 闫燕
作者信息
  • 哈尔滨工程大学动力与能源工程学院，黑龙江　哈尔滨　150001

    • 贾薪宇（1989—），男，博士研究生。E-mail：。

通讯作者:

靳国永（1980―），男，博士，教授。E-mail：。
Characteristics of pressure resistance and sound absorption on anechoic coating with metal perforated plate under hydrostatic pressure
Xin-yu JIA , Guo-yong JIN , Tian-gui YE, Yan YAN
Affiliations
  • College of Power and Energy Engineering，Harbin Engineering University，Harbin 150001，China
出版时间: 2024-07-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.07.013
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摘要
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为改善静水压力作用下传统声学覆盖层的吸声性能，提出了将金属孔板插入传统声学覆盖层中的水下声学覆盖层结构。以静力学方法研究了该声学覆盖层结构在不同静水压力下的形变情况。通过建立静水压力作用下的声学有限元方程，分析了该声学结构在不同静水压力下的吸声效果。与传统声学覆盖层相比，在静水压力为0~6 MPa时，该声学结构在中、高频段获得了更好的宽频吸声效果。此外，还讨论孔板厚度、孔板材料及孔板孔隙率对该声学结构吸声性能的影响。研究表明设计含金属孔板声学覆盖层可有效改善静水压力条件下水下声学结构的吸声性能。

声学覆盖层  /  金属孔板  /  静水压力  /  形变  /  吸声性能

An underwater acoustic structure with metal perforated plate inserted into the traditional anechoic coating is proposed to improve the pressure resistance and sound absorption performance of the structure. The deformation of the acoustic structure under different hydrostatic pressure is studied by the static method. By establishing the acoustic finite element equation under the action of hydrostatic pressure，the sound absorption effect of the acoustic structure under different hydrostatic pressure is analyzed. Compared with the traditional anechoic coating，under the hydrostatic pressure of 0 to 6 MPa，the acoustic structure achieves better broadband sound absorption in the mid-to-high frequency range. In addition，the effects of the thickness，material and porosity of the metal perforated plate on the sound absorption performance of the acoustic structure are discussed. The research shows that the underwater anechoic coating with metal perforated plate is an effective design to improve the pressure resistance and sound absorption performance of underwater acoustic structure.

anechoic coating  /  metal perforated plate  /  hydrostatic pressure  /  deformation  /  sound absorption performance
贾薪宇, 靳国永, 叶天贵, 闫燕. 静压下带金属孔板声学覆盖层的耐压与吸声特性. 振动工程学报, 2024 , 37 (7) : 1211 -1220 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.07.013
Xin-yu JIA, Guo-yong JIN, Tian-gui YE, Yan YAN. Characteristics of pressure resistance and sound absorption on anechoic coating with metal perforated plate under hydrostatic pressure[J]. Journal of Vibration Engineering, 2024 , 37 (7) : 1211 -1220 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.07.013
正文
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引言
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声学覆盖层是敷设在水下航行器外表面用以实现声隐身性能的关键部件。随着反潜探测技术的不断发展［1］，为进一步提高水下航行器的生存能力，提高和改善声学覆盖层吸声性能的研究工作得到了蓬勃发展，涌现了许多新型的结构设计［2⁃6］与研究方法［7⁃10］，在较宽的频率范围能够获得良好的吸声效果［11⁃13］。
目前，对声学覆盖层的研究工作多数是在常压下进行的，但水下航行器是在深水中工作，必然受高静水压力的作用。因此，在静水压力下声学覆盖层的设计与研究得到了许多学者的关注。姜闻文等［14］利用有限元方法研究了在不同静水压力下，声学覆盖层内不同腔体的变形情况及声学性能的变化规律，其研究表明，吸声频带随静水压力增加而向高频方向移动，其研究工作指明了空腔有效容积与吸声曲线频带的对应关系。姚熊亮等［15］基于非均匀波导理论推导出多层结构的吸声系数，研究了静水压力与腔型对声学覆盖层吸声系数的影响，其研究成果进一步指出了静水压力对声学覆盖层吸声性能具有重要影响，在实际应用中不可忽略。Humphrey等［16］利用耐压水箱实验方法，模拟了深度达700 m的深海环境，同时测试了声学覆盖层在静水压力为2.8 MPa时的声反射和声透射性能，为实验模拟研究高静水压力下声学覆盖层的声学性能提供了思路。张冲等［17］利用移动网格建模方法，在结构受压变形的基础上直接计算分析了带有球腔的声学覆盖层的吸声效果，并对比了腔压对腔体形变和吸声性能的影响，该研究成果改进了以往先求结构变形再对结构重新建模的计算方法，简化了建模过程，为后续工作提供了简便方法。Thieury等［18］通过数值模型研究了静水压力对橡胶声学覆盖层声反射的影响，并考虑了静水压力引起的空腔体积变化，其研究工作指明了在静水压力作用下，空腔大小、空腔距离以及弹性基体的流变性对结构声学性能的影响。Gu等［19］采用实验的方法，对带有局域共振单元的声学覆盖层的性能进行了分析，证明了带有局域共振单元的吸声结构在静水压力下可以获得更好的低频吸声效果，为耐压型声学覆盖层的设计提供了借鉴思路。董文凯等［20］在研究静压力下水下声学覆盖层吸声性能的同时考虑了腔压对形变的影响，仿真结果显示静水压力越大，腔压对吸声体声学性能的作用越明显。Zhang等［21］基于唯象理论研究了静水压力下含有亚波长压电阵列的半主动声学覆盖层的几何变形和声学性能，并探讨了相应吸声效果的变化规律，其研究工作既以提高声学覆盖层吸声性能为研究目的，又同时考虑静水压力对吸声效果的影响。对于静水压力下材料参数的变化，尚未有成熟的理论与经验公式，仍主要以实验研究为主［22⁃23］。因此，目前对不同静水压力下声学覆盖层的研究，主要以结构的形变对其声学性能的影响为主。
基于以上讨论，本文以静水压力条件下改善声学覆盖层吸声特性为研究目标，设计了一种带有金属孔板的水下声学覆盖层结构。讨论在不同静水压力下声学覆盖层的形变量，研究该声学结构的耐压性能。基于有限元方法建立静水压力作用下结构的声学有限元方程，并通过已有文献验证所建立模型的有效性和正确性。基于所建立的声学模型，开展在不同静水压力下所设计的声学覆盖层吸声特性的研究。此外，通过计算对比分析了孔板材料、孔板厚度以及孔板孔隙率等因素对所设计声学结构吸声性能的影响规律。
1　模型建立与计算方法
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1.1　模型建立
本文提出的声学复合结构主要由黏弹性基体层、金属孔板以及钢板背衬组成。其中，基体层中分布着沿x和y方向呈周期性排列的球型空腔结构，在此结构的基础上，按一定规律插入沿x方向呈周期分布、y方向无限大的金属孔板，具体形式如图1所示。根据结构的设计特点，周期结构的晶格常数a为30 mm，在黏弹性基体层后连接钢背衬以模拟水下航行器实际的应用条件，背衬后为空气。图2为声学覆盖层单一周期单元结构及其截面示意图，其中基体层厚度t1 = 50 mm，圆形空腔直径d =24 mm。钢板背衬厚度ts = 5 mm。胞元内插入的金属孔板尺寸b × c=18 mm × 30 mm，厚度tb为1 mm，在金属板上呈均匀分布的圆柱孔孔径为1 mm，孔隙率σ为16%。基体层前端为半无限大流体域，流体介质假设为海水。入射平面波垂直于x⁃y平面，沿z正方向从半无限流体域入射。
1.2　计算理论
1.2.1　声学有限元方程
本文利用有限元法对声学结构的吸声性能进行分析，假设流体域为理想流体，满足均匀、无黏滞吸收、静态流速为零、声波小振幅等理想条件，声波的波动方程可以写成如下形式：
式中　 p为声压；c为流体介质中的声速。
由于复合声学结构内部呈现周期性分布，在建立有限元模型时只需对其中一个周期单元进行分析，即可满足计算要求。通过一系列数学推导，基于有限元方法，获得有限元单元的质量矩阵、刚度矩阵、流⁃固耦合矩阵，通过求和运算，集总成所研究周期单元的流体域和结构域整体刚度矩阵、质量矩阵以及流⁃固耦合矩阵，进而得到流体域离散方程和结构中的控制方程分别为［24］：
式中　 Mf和Kf分别为选取周期单元流体域的质量矩阵和刚度矩阵；Ms和Ks分别为选取周期单元结构域中的质量矩阵和刚度矩阵；R为选取周期单元的流⁃固耦合矩阵；u为结构域中节点位移的向量矩阵；p为流体域中节点的声压向量矩阵；Ψf为作用在流体域界面的声压梯度；Fs为施加在结构域的激励；为流体密度。
根据公式（2）和（3），周期单元的流⁃固耦合方程可以表示为：
式中　 表示流体域边界法向上的节点压力载荷向量矩阵。Ff表示的是施加在流体边界的等效载荷矩阵；为角频率。
由于声学覆盖层中的圆形空腔与金属孔板结构呈周期性分布，流体域也沿着结构周期方向无限延伸，且流体介质为均匀的理想流体，因此周期单元中结构域中节点的位移与流体域中节点的声压均满足Bloch方程，即：
式中　 代表分布函数，可表示为某节点的位移或声压；dx和dy分别表示x和y方向上的晶格单元距离。
反射和透射声压可以用级数之和的形式表示为：
式中　 kx，ky，kz分别为x，y，z方向的波数；Rnm和Tnm分别为反射声波和透射声波的m，n阶系数。
通过流⁃固耦合方程（4）以及周期边界条件（5），可以求出入射面上的反射声压与透射面上的透射声压，进而求解出通过该吸声结构的平面波反射系数R及透射系数T，表达式如下：
式中　 N为反射边界或透射边界的有限元节点数量，因此结构的吸声系数。实际上，钢的特性阻抗与空气相差极大，导致二者阻抗失配，透射系数几乎为零，所以最终计算出通过该结构的吸声系数。
1.2.2　静水压下的有限元方程
目前，普遍采用二次建模法来研究水下声学覆盖层受静水压力作用下的声学性能。即先求解结构受静水压作用后的变形量，再根据变形量重新建立规则的几何模型及网格划分，此方法过程繁琐且后续的计算误差较大。因此，本文利用线性化理论，将结构受静水压力作用产生的势能直接加载到声学有限元方程中，形成考虑静水压力作用的流⁃固耦合有限元方程。
考虑静水压力作用后，结构的振动控制方程可以写成：
式中　 K0为与作用于声波入射面A0上的静水压力P0相关的刚度矩阵；Kr0为与静水压力作用下结构域Vs的静态预应力Pr0相关的刚度矩阵，其结构形式如下［25］：
式中　 Np为面单元的形函数；Nδ为有限单元的位移插值形函数。结合流体域的有限元方程式（2），静水压力作用下的周期单元的流⁃固耦合方程可以表示为：
通过求解方程（12），可以得到流体域的节点声压，进而根据前文分析的方法，求解出声学结构在静水压力条件下的吸声系数。
1.3　数值计算模型准确性验证
为了验证本文有限元计算模型的正确性与适用性，利用文本计算方法建立文献［26］中的水下声学覆盖层模型，并与文献中对声学覆盖层吸声系数的计算结果进行比对。从图3的对比结果中可以看出，利用本文计算方法得到的声学覆盖层吸声系数计算结果与文献［26］中的数值仿真结果基本一致。而改变声学覆盖层内部的周期结构形式，相当于只改变了结构内部不同材料之间的耦合边界条件，并没有改变声⁃固耦合边界。在利用有限元计算时，只是代入方程的条件参数不同，而未改变方程形式。文献［26］中的声学覆盖层的结构同样是在黏弹性基体层具有空腔与金属类填充物，与文本结构的边界条件一致。因此，可以验证本文所用的声学计算方法是正确的，并可适用于内部结构更为复杂的声学覆盖层计算中。此外，在有限元单元网格划分过程中，网格单元的最小尺寸遵循小于材料中剪切波波长1/4的设计原则［24］，以满足计算精度的要求。
为了进一步说明本文建立的在静水压力作用下的声学有限元方程的准确性，利用本文计算方法与文献［20］中声学覆盖层在1.5 MPa静水压力下的吸声系数作了对比，如图4所示。从对比结果中可以得出，利用本文计算方法得到声学覆盖层在1.5 MPa静水压力下的吸声系数计算结果与文献［20］中解析法求得结果较吻合，进一步说明了本文所建立的数值求解方法的正确性。
2　不同静压下声学覆盖层的形变与吸声性能
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2.1　不同静压下声学覆盖层的形变分析
目前，水下航行器声学覆盖层主要以含有空腔结构的橡胶材料为主，在大潜深条件下，水下航行器在几百米的水下通常要承受几兆帕的静水压力，这将使声学覆盖层产生较大变形，特别是内部空腔结构。为了更好地分析静水压力对声学覆盖层的影响，本文通过静力学分析方法在一个周期单元的声压入射面施加均布载荷来模拟声学覆盖层在不同静压下的形变情况。因x，y方向为假设的无限大平面，周期边界处指定x和y方向位移为零。背衬处边界为固定约束以模拟实际水下航行器应用条件。表1给出了本文所分析声学结构的静态材料参数。图5给出了不同静水压作用下无金属孔板的传统声学覆盖层的形变情况。从图5中可以看出，带有球腔的传统声学覆盖层在静水压力载荷的作用下，会产生较大形变。随着静水压的增加，结构的变形越大，空腔占有率（穿孔率）越低。图6给出了不同静水压作用下带有金属孔板的声学覆盖层的形变情况。从图6中可以看出，插入金属孔板后，声学覆盖层的受压形变量有所减小，并随着压力的增大，形变量减小得更明显。图7所示为传统声学覆盖层和带有金属孔板声学覆盖层在6 MPa静水压力下的内部球腔形变对比。可以看出，相对于传统声学覆盖层，在6 MPa的高静水压力下，插入金属孔板的声学覆盖层中的空腔形变量减少了5%以上。因此可以得出，因金属的杨氏模量较大，通过在传统声学覆盖层中插入金属孔板，相当于提高了声学覆盖层整体的等效模量，在一定程度上提高声学结构在大潜深、高静水压力下的耐压性能。
2.2　不同静压下声学覆盖层的吸声性能分析
为了研究静水压力对声学覆盖层吸声性能的影响规律，本文分别计算了在不同静水压力下无金属孔板与带金属孔板两种声学结构的吸声系数。在进行声学计算时，黏弹性材料参数选用由实验拟合数据得到的动态力学参数［27］，此时作为基体材料橡胶的杨氏模量E与损耗因子η随频率f变化为E=8.9×106+2.3×103-10‒2和η=0.2+1.2×10‒4f-8.2×10‒9。此外，计算过程中选用海水作为流体域，其密度和声速分别为1070 kg/m3和1540 m/s。
图8为不受静水压力下带有金属孔板的声学覆盖层与无金属孔板的传统声学覆盖层的吸声性能对比。如图8所示，与传统声学覆盖层相比，本文提出的带有金属孔板的声学覆盖层的吸声系数在中、高频段增大。
图9给出了常压下无金属孔板声学覆盖层与带金属孔板声学覆盖层在低频吸声峰（601 Hz）和中、高频处（1851 Hz，6000 Hz）的振动能量模态图。从图9可以得出，在低频吸声峰频率处，由于空腔的谐振作用，空腔上方的基体层沿垂直于覆盖层方向产生结构弯曲振动；此外，基体层作为弹性层和刚性背衬组成另一个共振系统，其共同作用使结构在较低频率处产生了较强的吸声效果，此时振动能量主要集中在背衬与基体。当在传统声学覆盖层中插入金属孔板后，并没有改变背衬与基体的组成结构，两种声学覆盖层的空腔结构的穿孔率一致，所以二者在低频处的吸声效果基本一致。而在中、高频段，由于基体内传递的声波在空腔边界处产生散射，散射波之间相长干涉，导致声波的波形转换，纵波转换为损耗更大的剪切波，增加了声能耗散。而相比于传统声学覆盖层，当在声学覆盖层插入金属孔板后，金属孔板本身及孔板的空腔结构，都增强了对声波的散射作用，加大了波形转换强度，进而加强了对能量的耗散。如图8所示，在中、高频段，当插入金属孔板后加强了声学覆盖层的吸声效果。
图10和11分别为无金属孔板声学覆盖层与带金属孔板的声学覆盖层在不同静水压力下的吸声系数对比图。从图中可以得出，当静水压力增大时，两种声学覆盖层吸声曲线的变化趋势与常压时保持一致。但随着静水压力的增大，两种声学结构的空腔变小，使得声学覆盖层穿孔率变小，故两者的吸声曲线总体上均向高频方向变化，且在中、高频段，两种结构的吸声效果有所增强。另外，两种声学覆盖层的低频吸声峰向高频移动的同时，吸声系数有所增大。
图12对比了在不同静水压力下无金属孔板的传统声学覆盖层与带金属孔板的声学覆盖层吸声系数随频率的变化规律。从图10~12中可以看出，两种声学覆盖层在静水压力下的吸声系数的变化规律与常压下的变化趋势一致，在中、高频段带有金属孔板的声学覆盖层的吸声系数大于无金属孔板的声学覆盖层。而静水压力相同的条件下，两种声学覆盖层在低频吸声峰的吸声效果基本一致。
为了更好地揭示在静水压力下，带金属孔板和无金属孔板声学覆盖层在变形后的吸声机理，本文分析了6 MPa静水压力下两种声学覆盖层的振动能量聚集形式。图13给出了6 MPa静水压力下两种声学覆盖层在低频吸声峰（1200 Hz）和中、高频处（1851 Hz，6000 Hz）的振动能量模态图。从图13中可以看出，由于在静水压力下，两种声学覆盖层的穿孔率变小，所以二者的低频吸声峰向高频移动并略有升高，此时的振动能量主要是由空腔谐振以及背衬与基体产生的结构共振引起的。在声学覆盖层中插入金属孔板后，对此影响不大，故两者在低频的吸声效果基本一致。在中、高频段，空腔结构受压变形后，增强了对入射声波的散射，改变了声波的传播方向，加大了声波的传播距离，并伴随着纵⁃横波的转换，加剧了结构的弯曲振动，使空腔谐振作用加强，增加了声波的能量损失。因此，如图10~12所示，相比常压条件，当声学覆盖层受到静水压力作用后，两种声学覆盖层在中、高频段的吸声效果得到提高，且随着静水压力的提高，中、高频段的吸声效果提高得更加明显。此外，通过对结构的吸声机理分析可知，金属孔板的小空腔结构是所设计结构提高声学性能的关键。金属材质作为空腔的支撑结构，能够使其在静水压力条件下保持空腔结构形式，以提高静水压力条件下结构声学性能的稳定性。
3　金属孔板影响覆盖层吸声性能的规律分析
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为了进一步改善声学覆盖层的吸声性能，本文研究了金属孔板材料、厚度、孔隙率对所设计声学覆盖层的声学性能的影响规律。
3.1　金属孔板材料对覆盖层吸声性能的影响
在保证其他材料参数不变的情况下，本文研究了不同金属孔板材料对所设计声学结构的吸声性能的影响规律。金属孔板材料参数如表2所示。为探究静水压力对覆盖层内金属孔板的影响，本文给出了在6 MPa静水压力作用下，声学覆盖层内3种不同材质的金属孔板的形变情况，如图14所示。从图中可以看出，在6 MPa静水压力下，覆盖层内以铅、铝、钢作为金属孔板材料时，金属孔板在静水压力作用方向分别产生了4.6°，3.1°和1°左右的弧度变形。因金属材料的杨氏模量较大，具有一定的耐压、抗变形能力，在静水压力的作用下，覆盖层内的金属孔板的形状参数变化较小，且6 MPa是本文研究的最大静水压力，在1~4.5 MPa的外压下，覆盖层内金属孔板形状参数的变化几乎可以忽略。因此，本节以及后续章节金属孔板材料参数对覆盖层吸声性能的影响规律的研究主要是在常压下进行的。
图15给出了常压下不同金属孔板材料的声学覆盖层吸声系数对比。结果表明，当金属孔板材料为铅时，声学覆盖层的吸声性能在中、高频段优于其他两种材料。根据图9所示的振动能量分布，低频吸声峰主要取决于空腔谐振以及背衬与基体产生的结构共振，所以金属孔板材料的改变对低频吸声峰几乎没有影响。而铅的质量密度较大，使基体层的等效阻抗增大，阻抗越大，在中、高频段对声波能量的衰减耗散更为充分。
3.2　金属孔板厚度对覆盖层吸声性能的影响
保证其他材料参数不变，研究金属板厚度变化对所设计声学结构吸声性能的影响规律。图16为常压下，1 mm，2 mm，3 mm厚金属孔板的声学覆盖层吸声系数对比。从图16中可以看出，声学覆盖层中的金属孔板厚度越薄，在中、高频的吸声效果越好。这是因为，金属孔板较薄时，在中、高频段，受声波激励产生的振幅更大，振动更为剧烈，而产生的弯曲振动能量越大，声能损失越多。所以，薄金属孔板的声学覆盖层在中、高频段获得的吸声效果较好。
3.3　金属孔板孔隙率对覆盖层吸声性能的影响
保证其他研究参数不变，研究金属孔板孔隙率变化对声学覆盖层吸声性能的影响规律。图17所示为常压下，金属孔板孔隙率分别为16.3%和31.4%以及无孔金属板的声学覆盖层的吸声性能对比图。从图17中可以看出，随着孔隙率的增大，能够有效改善该声学结构在中、高频段的吸声效果，但较高的孔隙率也加大了工艺加工的难度，阻碍了实际应用。
4　结论
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本文设计了一种含有金属孔板的声学覆盖层结构，以静力学方法研究了该声学结构在不同静水压力下的形变情况。通过建立静水压力下的声学有限元方程，研究了该结构在静水压0~6 MPa范围内的吸声特性。在传统空腔型声学覆盖层内插入金属孔板后，在保持结构低频段的吸声效果的基础上，进一步丰富了声学结构内的吸声机制，改善了该结构在2~10 kHz频带范围的吸声效果，且在受到静水压力产生形变下，该声学结构在中、高频段的吸声效果依然优于传统声学覆盖层，提高了静水压力下结构声学性能的稳定性。此外，研究表明，调整孔板厚度、孔板材料及孔板孔隙率可以进一步提高该声学覆盖层的吸声性能。因此，带金属孔板声学覆盖层的结构设计能够在静水压力条件下改善结构的吸声性能，兼顾了结构耐压性与吸声性能。
基金
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  • 国家自然科学基金资助项目(52225109)
  • 国家自然科学基金资助项目(52241101)
  • 国家自然科学基金资助项目(52271309)
  • 黑龙江省自然科学基金资助项目(YQ2022E104)
  • 哈尔滨工程大学博士科创基金资助项目(3072023GIP0302)
文献
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参考文献 引证文献
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2024年第37卷第7期
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doi: 10.16385/j.cnki.issn.1004-4523.2024.07.013
  • 接收时间：2022-10-03
  • 首发时间：2026-02-12
  • 出版时间：2024-07-28
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  • 收稿日期：2022-10-03
  • 修回日期：2022-11-14
基金
国家自然科学基金资助项目(52225109)
国家自然科学基金资助项目(52241101)
国家自然科学基金资助项目(52271309)
黑龙江省自然科学基金资助项目(YQ2022E104)
哈尔滨工程大学博士科创基金资助项目(3072023GIP0302)
作者信息
    哈尔滨工程大学动力与能源工程学院，黑龙江　哈尔滨　150001

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靳国永（1980―），男，博士，教授。E-mail：。
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2种不同金属材料的力学参数
科
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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