基于声子晶体周期薄板结构低频率带隙机理研究及其应用
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摘要
由于在力学性能上的优点,板壳结构广泛应用于航空航天、机械设备、交通工具以及家用电器上,其减振与降噪问题,一直是机械振动领域研究的重要问题之一。伴随着中国汽车产业的飞速发展,2010年中国汽车产销量均达到1800万辆,成为世界汽车产销量第一的国家。同时人们对汽车乘坐舒适性的要求也越来越高,车内振动与噪声的处理问题突显了出来。据研究显示,车内振动与噪声主要集中在中低频率,而车身板壳结构的振动与二次激振噪声也是车内振动与噪声源之一。通常采用大面积阻尼对板壳构件从被动减振降噪的角度进行处理,这种处理方法对于处理高频率噪声振动是很有效的,但对于中低频率振动与噪声处理效果却很有限。于是,寻找一种便捷、有效、低成本的处理方法,便是板壳结构振动领域研究的重点。
本文基于声子晶体理论,采用周期结构对薄板振动和噪声进行处理。
首先建立周期薄板结构的理论模型,根据结构连续性条件以及相关边界条件,建立方程组,同时由于结构的周期性,引入Bloch定理,这样便将方程组的求解问题转换为矩阵特征值的求解,求解得到的特征值即为弹性波频率关于周期结构各参数的函数,将其可视化,可以得到周期薄板结构的带隙频率特性。
其次,采用有限元法对周期薄板结构的带隙特性进行研究。建立周期薄板结构有限元模型,并进行动力学仿真,从而得到周期结构的带隙,对理论计算的带隙进行验证。
然后,采用实验测试的方法,得到周期薄板结构的带隙特性,对理论计算和有限元法得到的带隙进行验证。通过试验测试的方法肯定了中低频率带隙的存在。
最后,将周期薄板结构应用于车辆NVH处理上,通过对比周期薄板结构处理前后车内噪声级转速跟踪图,实现了车内声压级平均降低3dB以上结果,从而使车内振动与噪声的能量得到了很大的衰减。
Plates and shells are used widely in field of aviation, mechanical equipments, vehicles and domestic appliances, for advantage of its mechanical property. Its vibration attenuation and noise reduction is always a subject which is analyzed in mechanical vibration. With rapid expansion of automobile industry, the production and sale of automobile in china reach to 18 millions in 2010, become to the number one of automobile production and sale in the world. Meanwhile, people ask for higher and higher with ride comfort of vehicle, automobile noise and vibration become one problem which needs to start with immediately. Studies have shown that the noise and vibration interior car are concentrate in low and medium frequencies, the vibration and second vibration of car body are one main noise source. For the passive anti-vibration and noise reduction, people usually use bulk damping structure to deal its high frequency of noise and vibration, but it inefficacy in low and medium frequency. So, a method which is effective, convenient and fast and low cost is searching for now, and it is also a key point which is analyzed in field of plates and shells vibration.
Based on Phononic Crystals theory, plates and shells with periodic structure are applied to deal with noise and vibration in this thesis.
The theoretical model of periodic plate structure is built firstly, equations according to the structure continuity conditions and relevant boundary conditions are established. At the same time, Bloch theorem is introduced for the structures of periodic. Then, solve of the equations is converted to matrix eigenvalues and eigenvector solving. The eigenvalues are the function of frequency which is depends on the parameter of periodic structure, visualization it, the bandgaps frequency characteristics of periodic structure can got.
Bandgaps frequency characteristics of periodic plate structures are investigated by FEM secondly. Finite element model of periodic plate structure is established, and dynamic simulation is taken, thus, the bandgaps of periodic structures is obtained, and verified it with theoretical calculation.
Then, practical model is established, bandgaps of periodic structure is gotten by experiment, verified the bandgaps which is gotten with theoretical calculation and FEM, affirms existence of bandgaps in low and medium frequency.
Finally, the periodic plate structure is applied in vehicle NVH, compare the interior noise speed tracking, the sound acoustic pressure level is attenuated 3dB average, the sound and vibration energy interior car is attenuated strongly.
本文基于声子晶体理论,采用周期结构对薄板振动和噪声进行处理。
首先建立周期薄板结构的理论模型,根据结构连续性条件以及相关边界条件,建立方程组,同时由于结构的周期性,引入Bloch定理,这样便将方程组的求解问题转换为矩阵特征值的求解,求解得到的特征值即为弹性波频率关于周期结构各参数的函数,将其可视化,可以得到周期薄板结构的带隙频率特性。
其次,采用有限元法对周期薄板结构的带隙特性进行研究。建立周期薄板结构有限元模型,并进行动力学仿真,从而得到周期结构的带隙,对理论计算的带隙进行验证。
然后,采用实验测试的方法,得到周期薄板结构的带隙特性,对理论计算和有限元法得到的带隙进行验证。通过试验测试的方法肯定了中低频率带隙的存在。
最后,将周期薄板结构应用于车辆NVH处理上,通过对比周期薄板结构处理前后车内噪声级转速跟踪图,实现了车内声压级平均降低3dB以上结果,从而使车内振动与噪声的能量得到了很大的衰减。
Plates and shells are used widely in field of aviation, mechanical equipments, vehicles and domestic appliances, for advantage of its mechanical property. Its vibration attenuation and noise reduction is always a subject which is analyzed in mechanical vibration. With rapid expansion of automobile industry, the production and sale of automobile in china reach to 18 millions in 2010, become to the number one of automobile production and sale in the world. Meanwhile, people ask for higher and higher with ride comfort of vehicle, automobile noise and vibration become one problem which needs to start with immediately. Studies have shown that the noise and vibration interior car are concentrate in low and medium frequencies, the vibration and second vibration of car body are one main noise source. For the passive anti-vibration and noise reduction, people usually use bulk damping structure to deal its high frequency of noise and vibration, but it inefficacy in low and medium frequency. So, a method which is effective, convenient and fast and low cost is searching for now, and it is also a key point which is analyzed in field of plates and shells vibration.
Based on Phononic Crystals theory, plates and shells with periodic structure are applied to deal with noise and vibration in this thesis.
The theoretical model of periodic plate structure is built firstly, equations according to the structure continuity conditions and relevant boundary conditions are established. At the same time, Bloch theorem is introduced for the structures of periodic. Then, solve of the equations is converted to matrix eigenvalues and eigenvector solving. The eigenvalues are the function of frequency which is depends on the parameter of periodic structure, visualization it, the bandgaps frequency characteristics of periodic structure can got.
Bandgaps frequency characteristics of periodic plate structures are investigated by FEM secondly. Finite element model of periodic plate structure is established, and dynamic simulation is taken, thus, the bandgaps of periodic structures is obtained, and verified it with theoretical calculation.
Then, practical model is established, bandgaps of periodic structure is gotten by experiment, verified the bandgaps which is gotten with theoretical calculation and FEM, affirms existence of bandgaps in low and medium frequency.
Finally, the periodic plate structure is applied in vehicle NVH, compare the interior noise speed tracking, the sound acoustic pressure level is attenuated 3dB average, the sound and vibration energy interior car is attenuated strongly.
引文
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[6] Foumani M S,Khajepour A,Durali M. Application of Sensitivity Analysis to the Development of High Performance Adaptive Hydraulic Engine Mounts[J]. Vehicle System Dynamics,2003,39( 4) : 257-278.
[7] Adiguna H,Tiwari M,Singh R,et al. Transient Response of a Hydraulic Engine Mount[J]. Journal of Sound and Vibration,2003,268( 2) : 217-248.
[8]范让林,汪建忠,吕振华.汽车发动机悬置系统隔振性能优化[J].内燃机学报.Vol.28, No.3, 2010.
[9] Lueg.Process of Silencing Sound seillations.German Patent DRP[P],1933,No.655508
[10] Lueg.Proeess of Silencing Sound oscillations[P].US Patent,1936,No.2043416
[11] E.Yablonovitch.Inhibited spontaneous emission in solid-states physics and electronics[J]. Phys. Rev. Lett.,1987,58(20):2059-2062
[12] S.Jhon.Strong localization of photons in certain disordered dielectric superlattices[J]. Phys. Rev. Lett.,1987,58(23):2486-2489
[13] E. Yablonovitch,K.M. Leung.Photonic band structure: Non-spherical atoms in the face-centered-cubic case[J]. Physica B: Condensed Matter, Volume 175, Issues 1-3, Pages 81-86,1991
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[15] Brillouin L., Wave propagation in periodic structures [M], 2nd edition. New York: Dover Publications, 1953.
[16] M.M.Sigalas, E.N.Economou. Elastic and acoustic wave band structure[J]. Journalof sound and vibration.1992,158(2):277-382
[17] R.Martinez-Sala, Sanco J. Sound attenuation by sculpture. Natural(London)[J], 1995, 378:241
[18] Liu Z. Y., Zhang X., Mao Y. et al. Locally resonant sonic materials[J]. Sicence, 2000, 289: 1734-1736
[19]郁殿龙.声子晶体振动带隙及减振特性研究[D].长沙:国防科技大学,2005
[20] Dowling J. P.. Sonic band structure in fluids exhibiting periodic density variations[J]. J. Acoust. Soc. Am. ,1992,91(5):2539-2543
[21] M.M.Sigalas, Soucolis C. M. , Elastic wave propagation through disordered and/or absorbtive layered systems[J]. Phys. Rev. B,1995,51(5):2780-2789
[22] M.M.Sigalas. Theoretical study of three dimessional elastic band gaps with finite-diffrence time-domain method. J. App. Phys. ,2000,76(6):3122-3125
[23]王刚,温激鸿,韩小云,赵宏刚.二维声子晶体带隙计算中的时域有限差分法[J].物理学报,2003,52(8):1943-1947
[24]温激鸿,王刚,刘耀宗,郁殿龙.基于集中质量法的一维声子晶体弹性波带隙计算[J].物理学报,Vol.53,No.10,2004
[25]王刚,温激鸿,刘耀宗,郁殿龙,温熙森.大弹性常数差二维声子晶体带隙计算中的集中质量法[J] .物理学报, Vol. 54, No. 3, 2005
[26]沈林放,何赛灵,吴良.等效介质理论在光子晶体平面波展开分析方法中的应用[J].物理学报, Vol. 51 ,No. 5 ,2002
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