声子晶体型周期复合结构禁带特性研究
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摘要
弹性波或声波在周期性复合介质中传播时,有可能会产生类似光子晶体的禁带特性;即处于禁带频率范围内的弹性波或声波将被禁止传播,于是提出了声子晶体的概念。这一概念的提出和证实,迅速引起了世界各国有关研究机构的高度关注,并积极地开展了研究。这些研究一方面是深入探索声子晶体的禁带机理和特性;另一方面是努力谋求为工程中日益迫切和苛严的振动噪声控制提供新的思路和途径。
本论文在讨论了声子晶体现有基本理论和研究方法的基础上,较深入地研究了一维、二维和三维声子晶体的某些特性及其影响因素。同时,利用声子晶体的禁带原理,尝试通过构建具有声子晶体禁带特性的周期性复合结构,用于工程结构振动噪声控制的可行性。主要研究工作包括:
(1)用波传播法对纵波在一维声子晶体中的禁带特性进行了研究,并与平面波展开法进行对比,发现波传播法能在较短计算时间内得到禁带频率。在处理粘弹性材料的频变特性时,波传播法能直接得到禁带频率,比经过迭代改进的平面波展开法要快的多。
(2)用平面波展开法对二维二元和三元薄板型声子晶体的弯曲禁带特性进行了研究。在二维三元薄板型声子晶体中得到了基于局域共振的低频禁带,分析讨论了填充率、半径比等对禁带特性的影响。采用有限元法对有限周期复合薄板结构弯曲振动的传输特性进行计算,发现弯曲振动在有限板中也受到了较大的抑制,但与禁带频率有一定的差异;并讨论了边界条件对有限周期复合薄板结构振动传输特性的影响。
(3)用平面波展开法研究了将钢立方散射体以简单立方点阵形式嵌入环氧树脂基体中形成三维声子晶体的禁带特性,分析讨论了填充率、散射体参数变化等对禁带频率的影响。发现通过调节散射体的边长比,可以得到不同方向上的禁带。
(4)用波传播法研究了钢/环氧树脂周期结构梁的禁带特性,发现剪切变形和转动惯量的考虑会使禁带频率降低,并分析讨论了梁几何物理参数对禁带频率的影响。利用声子晶体的禁带原理,在无限梁上周期性配置动力吸振器来阻止弯曲振动的传播,讨论了动力吸振器和梁参数等对禁带频率的影响。有限元仿真计算表明,禁带频率内的有限梁结构对弯曲振动也有很好的抑制作用。
(5)用波传播法导出了平面波垂直入射时一维层状声子晶体禁带特性的计算方法,探讨了构建声子晶体型周期组合板结构用于阻断人体敏感噪声谱的可行性。分析计算了由多层铅/软橡胶和钢/丁腈橡胶声子晶体构成的组合板结构的隔声性能。讨论了层数、组合方式等对隔声性能的影响。发现通过参数的合理调制和搭配,多组声子晶体组合板结构能够降低起始频率和提高禁带宽度。
(6)基于Flügge壳体理论,采用波传播法对两种不同材料组成的周期性复合管道的禁带特性进行了研究,在不同周向模态下均发现了禁带频率。分析讨论了弹性模量比、密度比、晶格常数和管厚等对禁带频率的影响。结果表明,通过参数的合理调制,设计一种能够隔阻振动的周期性复合管道结构是可行的。
本文研究成果有助于将声子晶体这一概念和原理应用到振动噪声控制中;所构建的若干声子晶体型周期复合结构及对其禁带特性的分析研究,可为工程结构振动噪声控制提供新的思路和途径。
When elastic and acoustic waves propagate in the periodic composite media, maybe some photonic crystals-like band gaps will come into being. That is to say, the propagation of vibration and sound will be forbidden when the frequencies are the range of band gaps. So the concept of phononic crystals (PCs) was brought about. The propagation of elastic and acoustic waves in PCs has received much attention in the world, and a great deal of work has been devoted to the study of band gaps of PCs. The motivation for these studies is to further understand the forming mechanism of band gaps and make great efforts to provide some new idea and approach in vibration and noise control.
Based on the research status and basic theory of PCs, the characteristics and effect factor of band gaps in one- two- and three-dimensional PCs are studied. At the same time, the feasibility of building some periodic composite structures with band gaps of PCs for vibration and noise control in engineering structures is presented by making use of the forming mechanism of band gaps of PCs. The main work is shown as following:
(1) Using the wave propagation method (WPM), the band gaps of longitudinal wave in one-dimensional PCs are studied. Results obtained using WPM are evaluated against those by plane wave expansion (PWE). It shows that the computing speed of WPM is quicker than that of PWE. Considering the changing of elastic constants with frequency of viscoelastic material, the band gaps can be obtained directly, and the computing time of WPM is far too smaller than that of PWE improved using iterative method.
(2) Using PWE, the flexural vibration band gaps in thin plate PCs with two-dimensional binary and ternary units are studied. It is found that the band gaps in low frequency with local resonant mechanism exist in the thin plate PCs with ternary units. The numerical results are used to show how the width of the first full band gap depends on radius ratio, filling fraction and so on. The vibration transmission characteristics of the finite periodic thin plates are simulated by finite element method, which shows that the flexural vibration in finite periodic thin plates will be inhibited seriously in some frequencies which are different from the frequencies of band gaps. And the effect of boundary condition on vibration transmission characteristics in thin plates is also discussed.
(3) The characteristics of band gaps in three-dimensional PCs consisting of cubic steel embedded in an epoxy host periodically in simple cubic lattice are studied by using of PWE. Some numerical results are used to show how characteristics of band gaps depend on filling fraction, parameters of scatters and so on. It shows that the pseudo band gaps in some directions can be gotten by modulating the side length ratio of scatters.
(4) Using WPM, the flexural vibration band gaps in periodic beams with inconstant section are studied. It is found that the frequencies of band gaps will have some decreases when shearing deform and rotation inertia are considered. And the effects of geometric and physical parameters of beams on band gaps are discussed. Enlightened by the forming mechanism of band gaps of PCs, the impediment to propagation of flexural waves in infinite beams using dynamic vibration absorbers (DVAs) arranged periodically is investigated. And the effects on band gaps of the parameters of DVAs and beams are studied. Then the flexural vibraton transmission characteristic of a finite beam is proposed by finite element method. The numerical results show that the propagation of flexural waves will be weakened greatly in corresponding band gaps of the infinite beams.
(5) Using WPM, a method for the calculation of band gaps is deduced for the normal incident noise in one-dimensional PCs of layered plates. Then attention is turned to the feasibility of shielding the noise being sensitive to people in the case of building PCs-like composite plate structures. And the sound insulation of composite plate structures consisting of multilayer Pb-soft rubber and steel-butadience acrylnitrile rubber is presented. The results show that such composite plate structures can lower the starting frequency and widen the band gap by the reasonable modulation and collocation of parameters of PCs.
(6) Based on Flügge’s shell theory, the band gaps in pipelines composed of a set of periodically repeated elements of two types are investigated by using WPM. It is shown that the band gaps do exist in such periodic pipelines for any circumferential modes. The effects on band gaps of density ratio, stiffness ratio, lattice constant, and thickness of pipelines and so on are discussed. The numerical results show that it is feasible to design a periodic composite structure for deadening the vibration of pipelines.
The research results in the dissertation are helpful to apply the concept and principle of PCs to vibration and noise control. The band gaps of some certain PCs-like periodic composite structures presented in the dissertation will provide some new idea and approach in vibration and noise control.
本论文在讨论了声子晶体现有基本理论和研究方法的基础上,较深入地研究了一维、二维和三维声子晶体的某些特性及其影响因素。同时,利用声子晶体的禁带原理,尝试通过构建具有声子晶体禁带特性的周期性复合结构,用于工程结构振动噪声控制的可行性。主要研究工作包括:
(1)用波传播法对纵波在一维声子晶体中的禁带特性进行了研究,并与平面波展开法进行对比,发现波传播法能在较短计算时间内得到禁带频率。在处理粘弹性材料的频变特性时,波传播法能直接得到禁带频率,比经过迭代改进的平面波展开法要快的多。
(2)用平面波展开法对二维二元和三元薄板型声子晶体的弯曲禁带特性进行了研究。在二维三元薄板型声子晶体中得到了基于局域共振的低频禁带,分析讨论了填充率、半径比等对禁带特性的影响。采用有限元法对有限周期复合薄板结构弯曲振动的传输特性进行计算,发现弯曲振动在有限板中也受到了较大的抑制,但与禁带频率有一定的差异;并讨论了边界条件对有限周期复合薄板结构振动传输特性的影响。
(3)用平面波展开法研究了将钢立方散射体以简单立方点阵形式嵌入环氧树脂基体中形成三维声子晶体的禁带特性,分析讨论了填充率、散射体参数变化等对禁带频率的影响。发现通过调节散射体的边长比,可以得到不同方向上的禁带。
(4)用波传播法研究了钢/环氧树脂周期结构梁的禁带特性,发现剪切变形和转动惯量的考虑会使禁带频率降低,并分析讨论了梁几何物理参数对禁带频率的影响。利用声子晶体的禁带原理,在无限梁上周期性配置动力吸振器来阻止弯曲振动的传播,讨论了动力吸振器和梁参数等对禁带频率的影响。有限元仿真计算表明,禁带频率内的有限梁结构对弯曲振动也有很好的抑制作用。
(5)用波传播法导出了平面波垂直入射时一维层状声子晶体禁带特性的计算方法,探讨了构建声子晶体型周期组合板结构用于阻断人体敏感噪声谱的可行性。分析计算了由多层铅/软橡胶和钢/丁腈橡胶声子晶体构成的组合板结构的隔声性能。讨论了层数、组合方式等对隔声性能的影响。发现通过参数的合理调制和搭配,多组声子晶体组合板结构能够降低起始频率和提高禁带宽度。
(6)基于Flügge壳体理论,采用波传播法对两种不同材料组成的周期性复合管道的禁带特性进行了研究,在不同周向模态下均发现了禁带频率。分析讨论了弹性模量比、密度比、晶格常数和管厚等对禁带频率的影响。结果表明,通过参数的合理调制,设计一种能够隔阻振动的周期性复合管道结构是可行的。
本文研究成果有助于将声子晶体这一概念和原理应用到振动噪声控制中;所构建的若干声子晶体型周期复合结构及对其禁带特性的分析研究,可为工程结构振动噪声控制提供新的思路和途径。
When elastic and acoustic waves propagate in the periodic composite media, maybe some photonic crystals-like band gaps will come into being. That is to say, the propagation of vibration and sound will be forbidden when the frequencies are the range of band gaps. So the concept of phononic crystals (PCs) was brought about. The propagation of elastic and acoustic waves in PCs has received much attention in the world, and a great deal of work has been devoted to the study of band gaps of PCs. The motivation for these studies is to further understand the forming mechanism of band gaps and make great efforts to provide some new idea and approach in vibration and noise control.
Based on the research status and basic theory of PCs, the characteristics and effect factor of band gaps in one- two- and three-dimensional PCs are studied. At the same time, the feasibility of building some periodic composite structures with band gaps of PCs for vibration and noise control in engineering structures is presented by making use of the forming mechanism of band gaps of PCs. The main work is shown as following:
(1) Using the wave propagation method (WPM), the band gaps of longitudinal wave in one-dimensional PCs are studied. Results obtained using WPM are evaluated against those by plane wave expansion (PWE). It shows that the computing speed of WPM is quicker than that of PWE. Considering the changing of elastic constants with frequency of viscoelastic material, the band gaps can be obtained directly, and the computing time of WPM is far too smaller than that of PWE improved using iterative method.
(2) Using PWE, the flexural vibration band gaps in thin plate PCs with two-dimensional binary and ternary units are studied. It is found that the band gaps in low frequency with local resonant mechanism exist in the thin plate PCs with ternary units. The numerical results are used to show how the width of the first full band gap depends on radius ratio, filling fraction and so on. The vibration transmission characteristics of the finite periodic thin plates are simulated by finite element method, which shows that the flexural vibration in finite periodic thin plates will be inhibited seriously in some frequencies which are different from the frequencies of band gaps. And the effect of boundary condition on vibration transmission characteristics in thin plates is also discussed.
(3) The characteristics of band gaps in three-dimensional PCs consisting of cubic steel embedded in an epoxy host periodically in simple cubic lattice are studied by using of PWE. Some numerical results are used to show how characteristics of band gaps depend on filling fraction, parameters of scatters and so on. It shows that the pseudo band gaps in some directions can be gotten by modulating the side length ratio of scatters.
(4) Using WPM, the flexural vibration band gaps in periodic beams with inconstant section are studied. It is found that the frequencies of band gaps will have some decreases when shearing deform and rotation inertia are considered. And the effects of geometric and physical parameters of beams on band gaps are discussed. Enlightened by the forming mechanism of band gaps of PCs, the impediment to propagation of flexural waves in infinite beams using dynamic vibration absorbers (DVAs) arranged periodically is investigated. And the effects on band gaps of the parameters of DVAs and beams are studied. Then the flexural vibraton transmission characteristic of a finite beam is proposed by finite element method. The numerical results show that the propagation of flexural waves will be weakened greatly in corresponding band gaps of the infinite beams.
(5) Using WPM, a method for the calculation of band gaps is deduced for the normal incident noise in one-dimensional PCs of layered plates. Then attention is turned to the feasibility of shielding the noise being sensitive to people in the case of building PCs-like composite plate structures. And the sound insulation of composite plate structures consisting of multilayer Pb-soft rubber and steel-butadience acrylnitrile rubber is presented. The results show that such composite plate structures can lower the starting frequency and widen the band gap by the reasonable modulation and collocation of parameters of PCs.
(6) Based on Flügge’s shell theory, the band gaps in pipelines composed of a set of periodically repeated elements of two types are investigated by using WPM. It is shown that the band gaps do exist in such periodic pipelines for any circumferential modes. The effects on band gaps of density ratio, stiffness ratio, lattice constant, and thickness of pipelines and so on are discussed. The numerical results show that it is feasible to design a periodic composite structure for deadening the vibration of pipelines.
The research results in the dissertation are helpful to apply the concept and principle of PCs to vibration and noise control. The band gaps of some certain PCs-like periodic composite structures presented in the dissertation will provide some new idea and approach in vibration and noise control.
引文
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