二维组合声子晶体薄板振动性能研究
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摘要
楼板、建筑幕墙等的振动控制,尤其是在工业建筑、精密仪器制造结构中的减振隔振意义更为突出。声子晶体结构的弹性波禁带理论为振动控制提出了新的思路,然而,近十年来这方面几乎所有的研究内容都集中在单一声子晶体结构禁带特性方面,对组合声子晶体结构禁带性能的研究几乎还是空白。本文利用有限元方法仿真分析了两种简单的组合声子晶体结构薄板,即二组元/三组元交替组合和分区组合两种声子晶体结构薄板的弯曲振动衰减及振动禁带特性。本文的主要研究内容有:
通过软件调试和对声子晶体结构薄板的振动仿真,分析验证了有限元软件ANSYS在声子晶体结构振动仿真方面的适用性,并得出这两种组合声子晶体结构薄板都存在弯曲振动禁带,得出了结构纵向周期数对有限结构薄板振动衰减幅度有影响,周期数越多振动衰减越大。
通过对交替组合声子晶体结构模型的振动仿真,分析了10Hz-2400Hz范围内的振动特性,利用振动传输特性曲线分析得到其振动带隙具有相应的二维二组元、二维三组元声子晶体结构薄板无法比拟的优点。
还仿真了分区组合声子晶体结构薄板,利用振动传输特性曲线分析得出其振动禁带受3C声子晶体分区部分影响较大。但是,禁带展现比2D3C声子晶体薄板更明显,即振动衰减现象更明显;各禁带宽度也比2D3C声子晶体薄板结构宽。
并且比较分析两种组合结构振动传输特性曲线的异同,得出在中低频区,交替组合声子晶体结构具有分区组合声子晶体没有的低频、大幅度振动衰减、较宽的衰减频段的优势。
本文也分析了两种组合结构的振动形态的特点,得出交替组合、分区组合声子晶体结构薄板的振动模态与相应的二维二组元、二维三组元声子晶体结构薄板的振动模态不同,但是与二者有关系,尤其是和二维三组元声子晶体晶胞模态关系明显。
本文的研究丰富了声子晶体薄板振动带隙理论的研究内容,也为声子晶体的应用提供了理论指导,为板类结构的振动控制提供了新的技术方法。
The vibration control of the floor, building walls and so on, Especially of the industrial structure have more prominent meaning. For vibration control theory, the elastic wave bandgap of phononic crystal structure put forward a new approach. however, over the past 10 years, almost all the research in this area have focused on the single crystal structure out of bandgap properties, and in combination phononic crystal structure bandgap properties is almost blank. Using finite element method we simulate bending vibration attenuation and vibration bandgap properties of the two kinds of simple combination of the two phononic crystal structure plate, that is, the two components/ three components mixed phononic crystal structure of the plate. The main contents are,
The software debugging and the vibration simulation of the phononic crystal structure of the plate, validate the applicability of the finite element analysis software ANSYS in phononic crystal structure, and that it existe the bending vibration plate Ban-Zone of these two combination of the two phononic crystal structure, and the influence of the vertical structure of the limited number of cycles about vibration attenuation, and more cycle greater attenuation.
Through model simulation of the alternating combination phononic crystal structure, ranging from 10Hz to 2400Hz, according to the vibration transmission characteristic curve, we get the vibration bandgap of the corresponding two -dimensional three-components and two-dimensional two-components crystal thin plate structure which have incomparable advantages.
Also simulating of the subareaed phononic crystal structure plate, we get that the vibration gap has the a greater impact on district by 3C phononic crystal part. But the bandgaps are more obvious than that 2D3C phononic crystal plate showed, or it shows more obvious vibration attenuation. And the bandgap are also wider than 2D3C structure’.
Also comparing the similarities and differences between the two combinat -ions, in the low-frequency, we drawed that alternating combination of phononic crystal structure has the advantage of low-frequency, substantially vibration attenuation, wide-band attenuation than subareaed one.
This article also analyzed the characteristics of the vibration shaps of the two combination structure. The vibration shapes of the subareaed combination plate and alternating combination plate are different to the corresponding 2D2C and 2D3C structure’vibration shapes, but they are related with the two, and in particular the 2D3C shape has relationed significantly.
This study has enriched the phononic crystal plate vibration bandgap theory, and provides a theoretical guidance for the application of phononic crystal, also a new way of vibration control technology for the plate.
通过软件调试和对声子晶体结构薄板的振动仿真,分析验证了有限元软件ANSYS在声子晶体结构振动仿真方面的适用性,并得出这两种组合声子晶体结构薄板都存在弯曲振动禁带,得出了结构纵向周期数对有限结构薄板振动衰减幅度有影响,周期数越多振动衰减越大。
通过对交替组合声子晶体结构模型的振动仿真,分析了10Hz-2400Hz范围内的振动特性,利用振动传输特性曲线分析得到其振动带隙具有相应的二维二组元、二维三组元声子晶体结构薄板无法比拟的优点。
还仿真了分区组合声子晶体结构薄板,利用振动传输特性曲线分析得出其振动禁带受3C声子晶体分区部分影响较大。但是,禁带展现比2D3C声子晶体薄板更明显,即振动衰减现象更明显;各禁带宽度也比2D3C声子晶体薄板结构宽。
并且比较分析两种组合结构振动传输特性曲线的异同,得出在中低频区,交替组合声子晶体结构具有分区组合声子晶体没有的低频、大幅度振动衰减、较宽的衰减频段的优势。
本文也分析了两种组合结构的振动形态的特点,得出交替组合、分区组合声子晶体结构薄板的振动模态与相应的二维二组元、二维三组元声子晶体结构薄板的振动模态不同,但是与二者有关系,尤其是和二维三组元声子晶体晶胞模态关系明显。
本文的研究丰富了声子晶体薄板振动带隙理论的研究内容,也为声子晶体的应用提供了理论指导,为板类结构的振动控制提供了新的技术方法。
The vibration control of the floor, building walls and so on, Especially of the industrial structure have more prominent meaning. For vibration control theory, the elastic wave bandgap of phononic crystal structure put forward a new approach. however, over the past 10 years, almost all the research in this area have focused on the single crystal structure out of bandgap properties, and in combination phononic crystal structure bandgap properties is almost blank. Using finite element method we simulate bending vibration attenuation and vibration bandgap properties of the two kinds of simple combination of the two phononic crystal structure plate, that is, the two components/ three components mixed phononic crystal structure of the plate. The main contents are,
The software debugging and the vibration simulation of the phononic crystal structure of the plate, validate the applicability of the finite element analysis software ANSYS in phononic crystal structure, and that it existe the bending vibration plate Ban-Zone of these two combination of the two phononic crystal structure, and the influence of the vertical structure of the limited number of cycles about vibration attenuation, and more cycle greater attenuation.
Through model simulation of the alternating combination phononic crystal structure, ranging from 10Hz to 2400Hz, according to the vibration transmission characteristic curve, we get the vibration bandgap of the corresponding two -dimensional three-components and two-dimensional two-components crystal thin plate structure which have incomparable advantages.
Also simulating of the subareaed phononic crystal structure plate, we get that the vibration gap has the a greater impact on district by 3C phononic crystal part. But the bandgaps are more obvious than that 2D3C phononic crystal plate showed, or it shows more obvious vibration attenuation. And the bandgap are also wider than 2D3C structure’.
Also comparing the similarities and differences between the two combinat -ions, in the low-frequency, we drawed that alternating combination of phononic crystal structure has the advantage of low-frequency, substantially vibration attenuation, wide-band attenuation than subareaed one.
This article also analyzed the characteristics of the vibration shaps of the two combination structure. The vibration shapes of the subareaed combination plate and alternating combination plate are different to the corresponding 2D2C and 2D3C structure’vibration shapes, but they are related with the two, and in particular the 2D3C shape has relationed significantly.
This study has enriched the phononic crystal plate vibration bandgap theory, and provides a theoretical guidance for the application of phononic crystal, also a new way of vibration control technology for the plate.
引文
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3快素兰,张俞之,胡行方.光子晶体的能带结构、潜在应用和制备方法.无机材料学报, 2001, 16(2):193~198.
4 E. Yablonovitch. Inhibited Spontaneous Emission Insolid-Statephys-ics and Electronics. Physical Review Letters. 1987, 58(20):2059~2062.
5 S. John. Strong Localization of Photons in Certain Disordered Dielectrisu -per Lattices. Physical Review Letters. 1987, 58(20):2486~2489.
6 M. M. Sigalas, E. N. Economou. Elastic and Acoustic Wave Ban structure. Journal of Sound and Vibration. 1992, 158(2):377~382.
7 M. S. Kushwaha, P. Halevi, L. Dobrzynski, B. D. Jafarirouhani. Acoustic Band Structure of Periodic Elastic Composites. Physical Review Letters. 1993, 71(13): 2022~2025.
8 J. O. Vasseur, B. D. Jafarirouhani, L. Dobrzynski, P. A. Deymier. Complete Acoustic Bandgaps in Periodic Fibre Reinforced Compositmaterials: the Carbon/Epoxy Composite and Some Metallic System. Physical:Condensed Matterials. 1994, (6):8759~8770.
9 C. Goffaux, J. P. Vigneron. Theoreticaal Study of a Tunable Phononic Band -gap System [J]. Physical Review B. 2001, 64(7):5118.
10 M. S. Kushwaha, P. Halevt. Ultrawide Band Filter for Noise Control. Applied Physical. 1997, (36):1043~1044.
11 J. V. Sanche-Perez, D. Caballero, R. M. Sala, C. Rubio, J. S. Dehesa. Sound Attenuation by Two-Dimensional ArrayRigid Cylinders. Physical Review Letters. 1998, (80):5325~5328.
12 F. Cervera, L. Sanchis, J. V. S. Prez, R.M. Sala, Crubio, F. Mesegure. Refractive Acoustic Devices for Airborne Soun. Physical Review Letters. 2002, 88(2): 023902.
13 Suxia Yang. Ultrasound Tunneling through 3D Phononic Crystals. Physical Review Letters. 2002, 88(10):104301.
14 M. M. Sigalas, E. N. Economou. Elastic Waves in Plates with Period Callyplaced Inclusions. Applied Physical. 1994, 75(6):2845~2850.
15 M. S. Sigalas. Elastic Wave Bandgaps and Defect states in Two-Dimensio -nal composites. Journal of the Acoustical Society of America 1997, 101(3): 1256~1261.
16 M. M. Sigalas. Defect States of Acoustic Waves in a Two-Dimensional Lattice of Solid Cylinders. Applied Physical. 1998, 85(6):3026~3030.
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