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The radiation impedance expressions of flexural vibration rectangular plate with simply supported boundary are derived, and the numerical results are obtained by using the Gauss numerical integral method. Some conclusions can be obtained on the basis of the curves of relative radiation impedances versus frequency in the different modes and those corresponding to different aspect ratios. The lower the mode, the greater the radiation impedance in the low frequency is, so are the acoustic radiated power and the quality with vibration. For a rectangular plate of certain area and mode, the more the value of r (r = a/b, aspect ratio) approximates to 1, that is, the closer the square is, the greater the radiation resistance and the radiation reactance are. The method offers a reference for determining magnitude of the radiation impedance of the rectangular plate in other complicated boundary conditions (they may be no analytical displacement solutions). The method of calculating the radiation impedance of flexural vibration can be naturally transplanted into the case of piston vibration.
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Keywords:
- simply supported boundary /
- rectangular plate /
- radiation impedance /
- the method of numerical integration
[1] Zhao G W, Xu Y M, Chen C 2006 Acta Phys. Sin. 55 3458 (in Chinese) [赵国伟, 徐跃民, 陈诚 2006 物理学报 55 3458]
[2] Wang H L, Wu Q, Meng F Y, Li L W 2007 Acta Phys. Sin. 56 2608 (in Chinese) [王海龙, 吴群, 孟繁义, 李乐伟 2007 物理学报 56 2608]
[3] Wang H L, Wu Q, Meng F Y, Li L W, Wu J 2007 Acta Phys. Sin. 57 4883 (in Chinese) [王海龙, 吴群, 孟繁义, 李乐伟, 吴健 2008 物理学报 57 4883]
[4] Sanchez-Torres A, Sanmartin J R, Donoso J M, Charro M 2010 Adv. in Space Res. 45 1050
[5] Vojnovic M, Mijic M 2005 Applied Acoustics. 66 481
[6] Wang Z F, Hu Y M, Meng Z, Ni M 2008 Acta Phys. Sin. 57 7022 (in Chinese) [王泽锋, 胡永明, 孟洲, 倪明 2008 物理学报 57 7022]
[7] Bouwkamp C J 1971 J. Sound. Vib. 17 499
[8] Ma D Y 2004 Theory of Modern Acoustic (Beijing: Science Press) p249-250 (in Chinese) [马大猷 2004 现代声学理论基础(北京:科学出版社) 第249—250页]
[9] Zhou F H 1984 Underwater Acoustic Transducer and Array (Beijing: National Defense Industry Press) p200-336 (in Chinese) [周福洪1984 水声换能器及基阵 (北京: 国防工业出版社) 第200—336页]
[10] Zhang H L 2007 Theoretical Acoustics (Beijing: Higher Education Press) p231 (in Chinese) [张海澜 2007 理论声学 (北京: 高等教育出版社) 第231页]
[11] Arase E M 1964 J. Acoust. Soc. Am. 36 1521
[12] Burneet D S, Soroka W W 1972 J. Acoust. Soc. Am. 51 1618
[13] Bank G, Wright J R 1990 J. Aud. Eng. S. 38 350
[14] Lee J, Seo I 1996 J. Sound. Vib. 198 299
[15] Sha K, Yang J, Gan W S 2005J. Sound. Vib. 282 179
[16] Li W L, Gibeling H J 2000J. Sound. Vib. 229 1213
[17] He Z Y, Zhao Y F 1981 Theoretical Basis of Acoustics (Beijing: National Defense Industry Press) p274 (in Chinese) [何祚镛, 赵玉芳 1981 声学理论基础(北京: 国防工业出版社) 第274 页]
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[1] Zhao G W, Xu Y M, Chen C 2006 Acta Phys. Sin. 55 3458 (in Chinese) [赵国伟, 徐跃民, 陈诚 2006 物理学报 55 3458]
[2] Wang H L, Wu Q, Meng F Y, Li L W 2007 Acta Phys. Sin. 56 2608 (in Chinese) [王海龙, 吴群, 孟繁义, 李乐伟 2007 物理学报 56 2608]
[3] Wang H L, Wu Q, Meng F Y, Li L W, Wu J 2007 Acta Phys. Sin. 57 4883 (in Chinese) [王海龙, 吴群, 孟繁义, 李乐伟, 吴健 2008 物理学报 57 4883]
[4] Sanchez-Torres A, Sanmartin J R, Donoso J M, Charro M 2010 Adv. in Space Res. 45 1050
[5] Vojnovic M, Mijic M 2005 Applied Acoustics. 66 481
[6] Wang Z F, Hu Y M, Meng Z, Ni M 2008 Acta Phys. Sin. 57 7022 (in Chinese) [王泽锋, 胡永明, 孟洲, 倪明 2008 物理学报 57 7022]
[7] Bouwkamp C J 1971 J. Sound. Vib. 17 499
[8] Ma D Y 2004 Theory of Modern Acoustic (Beijing: Science Press) p249-250 (in Chinese) [马大猷 2004 现代声学理论基础(北京:科学出版社) 第249—250页]
[9] Zhou F H 1984 Underwater Acoustic Transducer and Array (Beijing: National Defense Industry Press) p200-336 (in Chinese) [周福洪1984 水声换能器及基阵 (北京: 国防工业出版社) 第200—336页]
[10] Zhang H L 2007 Theoretical Acoustics (Beijing: Higher Education Press) p231 (in Chinese) [张海澜 2007 理论声学 (北京: 高等教育出版社) 第231页]
[11] Arase E M 1964 J. Acoust. Soc. Am. 36 1521
[12] Burneet D S, Soroka W W 1972 J. Acoust. Soc. Am. 51 1618
[13] Bank G, Wright J R 1990 J. Aud. Eng. S. 38 350
[14] Lee J, Seo I 1996 J. Sound. Vib. 198 299
[15] Sha K, Yang J, Gan W S 2005J. Sound. Vib. 282 179
[16] Li W L, Gibeling H J 2000J. Sound. Vib. 229 1213
[17] He Z Y, Zhao Y F 1981 Theoretical Basis of Acoustics (Beijing: National Defense Industry Press) p274 (in Chinese) [何祚镛, 赵玉芳 1981 声学理论基础(北京: 国防工业出版社) 第274 页]
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