高效半解析方法分析周期正交加筋板的振动-声辐射特性
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摘要
为了对水下无穷大双周期正交加筋板结构模型在简谐面力激励下的振动响应及声辐射特性进行更为合理的理论预测与分析,建立了加筋板结构的数学模型。结合傅里叶变换、泊松迭加公式及空间波数法,将周期加筋板的振动响应及辐射声压表达为关于结构位移谐波分量的函数方程,对加筋板模型提出了高效分析求解方法并进行了谐波分量截断求解。验证了方法的正确性,并分析了结构的振动特性以及加强筋周期间距和扭矩对辐射声压的影响。结果表明,加强筋的扭转作用影响加筋板结构的振动模态频率,对于较高精度要求的工程应用,加强筋的扭转作用不能忽略。通过调节加强筋周期间距及横截面尺寸,可以降低薄板在较低频域区间的远场辐射声压。
For performing a more reasonable theoretical forecasting and analysis of the vibration response and acoustic radiation characteristics of an infinite plate, which is stimulated by an harmonic plane pressure and stiffened by two periodical sets of orthogonal ribs, corresponding mathematical models are respectively established. Combined the technique of Fourier transforms, Poisson summation equations and space harmonic method, the vibration response and acoustic radiation pressure of the rib-stiffened plate are expressed as functions of infinite sets of displacement harmonic amplitudes, and then corresponding efficient solving methods are proposed and approximate solutions for finite terms of the harmonic amplitudes are also provided by employing the truncation technique. The validity of the proposed methods is verified and the effects of the vibration response, rib spacing and torsional moment of the ribs on the radiation pressure are also examined. Theoretical results indicate that the modal frequencies of the stiffened plate can be affected by the torsional moment of the ribs, which thus can not be neglected for engineering applications of high precision. By adjusting rib spacing and cross section area of the ribs, the far field radiation pressure of the plate can be reduced by the attachment of the ribs in the low frequency range.
For performing a more reasonable theoretical forecasting and analysis of the vibration response and acoustic radiation characteristics of an infinite plate, which is stimulated by an harmonic plane pressure and stiffened by two periodical sets of orthogonal ribs, corresponding mathematical models are respectively established. Combined the technique of Fourier transforms, Poisson summation equations and space harmonic method, the vibration response and acoustic radiation pressure of the rib-stiffened plate are expressed as functions of infinite sets of displacement harmonic amplitudes, and then corresponding efficient solving methods are proposed and approximate solutions for finite terms of the harmonic amplitudes are also provided by employing the truncation technique. The validity of the proposed methods is verified and the effects of the vibration response, rib spacing and torsional moment of the ribs on the radiation pressure are also examined. Theoretical results indicate that the modal frequencies of the stiffened plate can be affected by the torsional moment of the ribs, which thus can not be neglected for engineering applications of high precision. By adjusting rib spacing and cross section area of the ribs, the far field radiation pressure of the plate can be reduced by the attachment of the ribs in the low frequency range.
引文
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2 Mead D J,Pujara K K.Space-harmonic analysis of periodically supported beams:response to convected random loading.J.Sound Vib.,1971;14(4):525-541
3 Mace B R.Sound radiation from a plate reinforced by two sets of parallel stiffeners.J.Sound Vib.,1980;71(3):435-441
4 Mace B R.The response of a fluid-loaded,beam-stiffened plate.J.Sound Vib.,1981;79(3):439-542
5 XIN Fengxian,LU Tianjian,CHEN Changqing.Sound transmission across lightweight all-metallic sandwich panels with corrugated cores.Chinese Journal of Acoustics,2009;28(3):231-243
6 Lee J H,Kim J.Analysis of sound transmission through periodically stiffened panels by space-harmonic expansion method.J.Sound Vib.,2002;251(3):349-366
7 Lin T R,Pan J.A closed form solution for the dynamic response of finite ribbed plates.J.Acoust.Soc.Am.,2006;119(2):917-925
8 Maxit L.Wavenumber space and physical space responses of a periodically ribbed plate to a point drive:A discrete approach.Appl.Acoust.,2009;70(4):563-578
9 GONG Jiayuan,AN Junying,MA Li,XU Haiting.Acoustic reflection of rib-stiffened double plates coated with a viscoelastic layer.Chinese Journal of Acoustics,2014;33(3):193-211
10 Liu B L.Noise radiation of aircraft panels subject to turbulent boundary layer excitations.J.Sound Vib.,2008;314(3-5):693-711
11 Mejdi A,Atalla N.Dynamic and acoustic response of bidirectionally stiffened plates with eccentric stiffeners subject to airborne and structure-borne excitations.J.Sound Vib.,2010;329(21):4422-4439
12 Legault J,Mejdi A,Atalla N.Vibro-acoustic response of orthogonally stiffened panels:The effects of finite dimensions.J.Sound Vib.,2011;330(24):5928-5948
13 Xin F X,Lu T J.Transmission loss of orthogonally ribstiffened double-panel structures with cavity absorption.J.Acoust.Soc.Am.,2011;129(4):1919-1934
14桂洪斌,赵德友,郑云龙.加肋板稳态简谐响应的粘弹性阻尼控制研究.声学学报,2002;27(2):117-120
15马玺越,陈克安,丁少虎,张冰瑞.双层加筋板低频声的隔离与有源控制.声学学报,2014;39(4):479-488
16黎胜,杨婧媛.水下加筋板振动声辐射的代理模型研究.声学学报,2010;35(6):659-664
17 GONG Jiayuan,AN Junying,MA Li,XU Haiting.Numerical quadrature for singular and near-singular integrals of boundary element method and its applications in largescale acoustic problems.Chinese Journal of Acoustics,2017;36(3):289-301
18庞福振,陈林,缪旭弘,姚熊亮.无限大正交加筋层合板的隔声性能分析·上海交通大学学报,2014;48(8):1090-1096
19金叶青,庞福振,姚熊亮,张阿曼.均匀流中剪切变形加筋层合板声与振动特性研究.物理学报,2013;62(13):134306
20金叶青,庞福振,姚熊亮,孙龙泉.基于波数域直接求解法的正交加筋板声辐射研究.声学学报,2014;39(2):205-214
21 Shen C,Xin F X,Cheng L,Lu T J.Sound radiation of orthogonally stiffened laminated composite plates under airborne and structure borne excitations.Composites Science and Technology,2013;84(4):51-57
22金叶青,庞福振,姚熊亮,叶曦.一种分析周期加筋板声辐射的高效方法.声学学报,2013;38(3):338-345
23尹剑飞,温激鸿,肖勇,温熙森.基于高级统计能量分析的周期加筋板振动特性研究.物理学报,2015;64(13):134301
24 Yin X W,Gu X J,Cui H F,Shen R Y.Acoustic radiation from a laminated composite plate reinforced by doubly periodic parallel stiffeners.J.Sound Vib.,2007;306(3-5):877-889
25 Cao X T,Hua H X,Zhang Z Y.Sound radiation from shear deformable stiffened laminated plates.J.Sound Vib.,2011;330(16):4047-4063
26吴文伟,冷文浩,沈顺根.具有等间距相同加强筋板的声辐射.中国造船,1999;146(3):72-81
27 Wang J,Lu T J,Woodhouse J,Langley R S,Evans J.Sound transmission through lightweight double-leaf partitions:theoretical modeling.J.Sound Vib.,2005;286(4-5):817-847
28陈海龙,金叶青,庞福振.一种分析单向加筋板隔声性能的解析-数值耦合法.船舶力学,2013;17(8):952-959
29金叶青,庞福振,姚熊亮,王献忠.基于板梁组合理论的正交加筋板声振特性分析.振动工程学报,2012;25(5):579-588
30陈林,庞福振,陈海龙,金叶青,姚熊亮.无限大单向加筋层合板隔声性能研究.振动与冲击,2013;32(22):88-94
31他得安,刘振清,贺鹏飞.管材超声检测中导波模式及频厚积的选择.同济大学学报,2004;32(5):696-700
32他得安,刘振清.充粘液管材中超声纵向轴对称导波的频散特性分析.声学学报,2005;30(3):193-200
33邹春平,陈端石,华宏星.船舶水下辐射噪声特性研究.船舶力学,2004;8(1):112-124
2 Mead D J,Pujara K K.Space-harmonic analysis of periodically supported beams:response to convected random loading.J.Sound Vib.,1971;14(4):525-541
3 Mace B R.Sound radiation from a plate reinforced by two sets of parallel stiffeners.J.Sound Vib.,1980;71(3):435-441
4 Mace B R.The response of a fluid-loaded,beam-stiffened plate.J.Sound Vib.,1981;79(3):439-542
5 XIN Fengxian,LU Tianjian,CHEN Changqing.Sound transmission across lightweight all-metallic sandwich panels with corrugated cores.Chinese Journal of Acoustics,2009;28(3):231-243
6 Lee J H,Kim J.Analysis of sound transmission through periodically stiffened panels by space-harmonic expansion method.J.Sound Vib.,2002;251(3):349-366
7 Lin T R,Pan J.A closed form solution for the dynamic response of finite ribbed plates.J.Acoust.Soc.Am.,2006;119(2):917-925
8 Maxit L.Wavenumber space and physical space responses of a periodically ribbed plate to a point drive:A discrete approach.Appl.Acoust.,2009;70(4):563-578
9 GONG Jiayuan,AN Junying,MA Li,XU Haiting.Acoustic reflection of rib-stiffened double plates coated with a viscoelastic layer.Chinese Journal of Acoustics,2014;33(3):193-211
10 Liu B L.Noise radiation of aircraft panels subject to turbulent boundary layer excitations.J.Sound Vib.,2008;314(3-5):693-711
11 Mejdi A,Atalla N.Dynamic and acoustic response of bidirectionally stiffened plates with eccentric stiffeners subject to airborne and structure-borne excitations.J.Sound Vib.,2010;329(21):4422-4439
12 Legault J,Mejdi A,Atalla N.Vibro-acoustic response of orthogonally stiffened panels:The effects of finite dimensions.J.Sound Vib.,2011;330(24):5928-5948
13 Xin F X,Lu T J.Transmission loss of orthogonally ribstiffened double-panel structures with cavity absorption.J.Acoust.Soc.Am.,2011;129(4):1919-1934
14桂洪斌,赵德友,郑云龙.加肋板稳态简谐响应的粘弹性阻尼控制研究.声学学报,2002;27(2):117-120
15马玺越,陈克安,丁少虎,张冰瑞.双层加筋板低频声的隔离与有源控制.声学学报,2014;39(4):479-488
16黎胜,杨婧媛.水下加筋板振动声辐射的代理模型研究.声学学报,2010;35(6):659-664
17 GONG Jiayuan,AN Junying,MA Li,XU Haiting.Numerical quadrature for singular and near-singular integrals of boundary element method and its applications in largescale acoustic problems.Chinese Journal of Acoustics,2017;36(3):289-301
18庞福振,陈林,缪旭弘,姚熊亮.无限大正交加筋层合板的隔声性能分析·上海交通大学学报,2014;48(8):1090-1096
19金叶青,庞福振,姚熊亮,张阿曼.均匀流中剪切变形加筋层合板声与振动特性研究.物理学报,2013;62(13):134306
20金叶青,庞福振,姚熊亮,孙龙泉.基于波数域直接求解法的正交加筋板声辐射研究.声学学报,2014;39(2):205-214
21 Shen C,Xin F X,Cheng L,Lu T J.Sound radiation of orthogonally stiffened laminated composite plates under airborne and structure borne excitations.Composites Science and Technology,2013;84(4):51-57
22金叶青,庞福振,姚熊亮,叶曦.一种分析周期加筋板声辐射的高效方法.声学学报,2013;38(3):338-345
23尹剑飞,温激鸿,肖勇,温熙森.基于高级统计能量分析的周期加筋板振动特性研究.物理学报,2015;64(13):134301
24 Yin X W,Gu X J,Cui H F,Shen R Y.Acoustic radiation from a laminated composite plate reinforced by doubly periodic parallel stiffeners.J.Sound Vib.,2007;306(3-5):877-889
25 Cao X T,Hua H X,Zhang Z Y.Sound radiation from shear deformable stiffened laminated plates.J.Sound Vib.,2011;330(16):4047-4063
26吴文伟,冷文浩,沈顺根.具有等间距相同加强筋板的声辐射.中国造船,1999;146(3):72-81
27 Wang J,Lu T J,Woodhouse J,Langley R S,Evans J.Sound transmission through lightweight double-leaf partitions:theoretical modeling.J.Sound Vib.,2005;286(4-5):817-847
28陈海龙,金叶青,庞福振.一种分析单向加筋板隔声性能的解析-数值耦合法.船舶力学,2013;17(8):952-959
29金叶青,庞福振,姚熊亮,王献忠.基于板梁组合理论的正交加筋板声振特性分析.振动工程学报,2012;25(5):579-588
30陈林,庞福振,陈海龙,金叶青,姚熊亮.无限大单向加筋层合板隔声性能研究.振动与冲击,2013;32(22):88-94
31他得安,刘振清,贺鹏飞.管材超声检测中导波模式及频厚积的选择.同济大学学报,2004;32(5):696-700
32他得安,刘振清.充粘液管材中超声纵向轴对称导波的频散特性分析.声学学报,2005;30(3):193-200
33邹春平,陈端石,华宏星.船舶水下辐射噪声特性研究.船舶力学,2004;8(1):112-124