饱和多孔介质板的吻合频率和临界频率分析
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摘要
板结构在隔声设计中应用广泛,而临界频率和吻合频率与板结构的声辐射和隔声性能有着密切的联系。从吻合效应产生的机理,形成吻合效应的条件出发,基于含液饱和多孔弹性薄板的振动控制方程,通过理论分析得到了饱和多孔薄板吻合频率和临界频率的计算公式。作为数值算例,对含液饱和多孔板的吻合频率和临界频率进行了参数分析。讨论了饱和多孔板的吻合频率随板厚、孔隙率、入射角和渗透系数的变化规律,并比较了不同孔隙率下饱和多孔板和弹性板的吻合频率随厚度和入射角的变化。结果表明,弹性板的吻合频率远远大于饱和多孔板的吻合频率,它们的吻合频率随厚度、入射角的增大而减小,随孔隙率的增大而增大,而渗透系数对吻合频率几乎没有影响。
Plate structures are widely used in acoustical insulation design,their critical frequency and coincidence frequencies are closely related to sound radiation and sound insulation performance of plate structures. From the mechanism of coincidence effect and conditions to cause coincidence effect,based on the vibration control equation of thin plates made of saturated porous materials,the calculation formulas for critical frequency and coincidence frequency of thin plates made of saturated porous materials were deduced through theoretical analysis. Using numerical examples,the parametric analysis for coincidence frequency and critical frequency of thin plates made of saturated porous materials were performed. The variation laws of coincidence frequency with changes of plate thickness,porosity,incident angle,and permeability coefficient were analyzed. The coincidence frequencies of thin plates made of saturated porous materials under different porosities were compared with those of elastic solid plate with changes of plate thickness and incident angle. Results showed that coincidence frequencies of single-phase elastic solid plates are much larger than those of thin plates made of saturated porous materials,their coincidence frequencies decrease with increase in plate thickness and incident angle,and increase with increase in porosity,while permeability coefficients almost have no effect on their coincidence frequencies.
Plate structures are widely used in acoustical insulation design,their critical frequency and coincidence frequencies are closely related to sound radiation and sound insulation performance of plate structures. From the mechanism of coincidence effect and conditions to cause coincidence effect,based on the vibration control equation of thin plates made of saturated porous materials,the calculation formulas for critical frequency and coincidence frequency of thin plates made of saturated porous materials were deduced through theoretical analysis. Using numerical examples,the parametric analysis for coincidence frequency and critical frequency of thin plates made of saturated porous materials were performed. The variation laws of coincidence frequency with changes of plate thickness,porosity,incident angle,and permeability coefficient were analyzed. The coincidence frequencies of thin plates made of saturated porous materials under different porosities were compared with those of elastic solid plate with changes of plate thickness and incident angle. Results showed that coincidence frequencies of single-phase elastic solid plates are much larger than those of thin plates made of saturated porous materials,their coincidence frequencies decrease with increase in plate thickness and incident angle,and increase with increase in porosity,while permeability coefficients almost have no effect on their coincidence frequencies.
引文
[1]王海军,郭杏林.板结构的吻合频率和临界频率特性研究[C]//第17届全国结构工程学术会议论文集(第Ⅲ册).北京:《工程力学》杂志社,2008:562-568.
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[14]BIOT M A.Theory of propagation of elastic waves in a fluidsaturated porous solid,I.Low-frequency range[J].The Journal of the Acoustical Society of America,1956,28(2):168-178.
[15]BIOT M A.Theory of propagation of elastic waves in a fluidsaturated porous solid,Ⅱ.Higher frequency range[J].The Journal of the Acoustical Society of America,1956,28(2):179-191.
[16]周凤玺,张家齐,曹小林.梯度饱和多孔材料中弹性波的截止频率[J].浙江大学学报(工学版),2016,50(4):744-749.ZHOU Fengxi,ZHANG Jiaqi,CAO Xiaolin.Analysis of cutoff frequencies for functionally graded fluid-saturated materials[J].Journal of Zhejiang University(Engineering Science),2016,50(4):744-749.
[17]ZHOU Fengxi,CAO Xiaolin.A transverse dynamic deflection model for thin plate made of saturated porous materials[J].Zeitschrift Für Naturforschung A,2016,71(10):943-948.
[18]阿肯巴赫.弹性固体中波的传播[M].徐值信,洪锦如,译.上海:同济大学出版社,1992.
[2]陆红艳.板结构的振动声辐射及其隔声性能研究[D].武汉:武汉理工大学交通学院结构部工程系,2003.
[3]YAIRI M,SAKAGAMI K,SAKAGAMI E,et al.Sound radiation from a double-leaf elastic plate with a point force excitation:effect of an interior panel on the structure-borne sound radiation[J].Applied Acoustics,2002,63(7):737-757.
[4]BHATTACHARYA M C,GUY R W,CROCKER M J.Coincidence effect with sound waves in a finite plate[J].Sound and Vibration,1971,18(2):157-169.
[5]TSUGIHASHI K,TANAKA T.A study on simulation technique of coincidence effect of rectangular plate[C]//Symposium on Environmental Engineering.Japan:The Japan Society of Mechanical Engineers,2004:153-156.
[6]TSUGIHASHI K,TANAKA T.A study on coincidence effect of rectangular plate by acoust-structural coupled analysis[C]//Symposium on Environmental Engineering.Japan:The Japan Society of Mechanical Engineers,2003:46-48.
[7]DUPONT T,PAVIC G,LAULAGNET B.Acoustic properties of lightweight micro-perforated plate systems[J].Acta Acustica United with Acustica,2003,89(2):201-212.
[8]REYNOLDS D D.Engineering principles of acoustics noise and vibration[M].Boston:Allyn&Baeon,1981.
[9]CREMER L,HEEKL M,UNGAR E E.Structure-borne sound[M].Berlin:Springer Verlag,1973.
[10]HEEKL M.The 10th fairey,richard memorial lecture-sound tansmission in buildings[J].Journal of Sound and Vibration,1981,77(2):165-189.
[11]NARYANAN S,SHANBHAG R.L.Sound transmission through a damped sandwich panel[J].Journal of Sound and Vibration,1982,80(3):315-327.
[12]BEARNEK L L.Noise and vibration contorl[M].New York:Mc Graw Hill,1971.
[13]RENJI K,NAIR P S,NARAYANAN S.Critical and coincidence frequencies of flat panels[J].Journal of Sound and Vibration,1997,205(1):19-32.
[14]BIOT M A.Theory of propagation of elastic waves in a fluidsaturated porous solid,I.Low-frequency range[J].The Journal of the Acoustical Society of America,1956,28(2):168-178.
[15]BIOT M A.Theory of propagation of elastic waves in a fluidsaturated porous solid,Ⅱ.Higher frequency range[J].The Journal of the Acoustical Society of America,1956,28(2):179-191.
[16]周凤玺,张家齐,曹小林.梯度饱和多孔材料中弹性波的截止频率[J].浙江大学学报(工学版),2016,50(4):744-749.ZHOU Fengxi,ZHANG Jiaqi,CAO Xiaolin.Analysis of cutoff frequencies for functionally graded fluid-saturated materials[J].Journal of Zhejiang University(Engineering Science),2016,50(4):744-749.
[17]ZHOU Fengxi,CAO Xiaolin.A transverse dynamic deflection model for thin plate made of saturated porous materials[J].Zeitschrift Für Naturforschung A,2016,71(10):943-948.
[18]阿肯巴赫.弹性固体中波的传播[M].徐值信,洪锦如,译.上海:同济大学出版社,1992.