多孔吸声矩形薄板声振特性分析的一种新模型

袁丽芸1,2,向宇1,2,陆静1,2

振动与冲击 ›› 2016, Vol. 35 ›› Issue (13) : 106-113.

PDF(1299 KB)
PDF(1299 KB)
振动与冲击 ›› 2016, Vol. 35 ›› Issue (13) : 106-113.
论文

多孔吸声矩形薄板声振特性分析的一种新模型

  • 袁丽芸1,2,向宇1,2,陆静1,2
作者信息 +

A new model for analysis on the vibroacoustic performance of a thin rectangular porous plate

  • Yuan Liyun1,2, Xiang Yu1,2, Lu Jing 1,2
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文章历史 +

摘要

为了弥补现有多孔吸声材料在数值建模以及解析建模上的不足,本文建立了一种全新的多孔材料矩形薄板声振特性分析的半解析模型。利用薄板理论,引入与流体声压相关的薄膜力和力矩分量,由三维的Biot理论本退化导出了二维多孔材料矩形薄板的本构关系和内力—位移关系。然后,结合多孔板的骨架的平衡方程和多孔薄板内部流体的运动方程,通过Fourier变换和无量纲化处理,消去中间变量后建立了频域内多孔矩形薄板的声振控制方程,并写为一阶常微分矩阵形式,可采用高精度的齐次扩容精细积分法进行求解。该模型充分考虑了薄板面内振动与弯曲振动的相互耦合,比现有的解析模型更加接近多孔板的真实振动。同时,采用了一种高精度的齐次扩容精细积分法进行求解,可以在中高频段保证其精确性。文中以两端简支的多孔矩形薄板为例,分析了薄板面内振动与弯曲振动的耦合作用对声振特性的影响。

Abstract

In order to make up the deficiency of the present numerical and analytical models of porous material, a new semi-analytical model is established for the vibroacoustic analysis on a thin rectangular porous plate. In this model, by applying the elastic theory of thin plate, and introducing the membrane resultant force and moment which are relative with the acoustic pressure of the fluid media in the porous plate, according to Biot theory in the 3 dimension case, the constitutive equations and the corresponding relationship between the internal force and displacement of the porous material in 2 dimension case is obtained. Then, combining the equilibrium equations for the frame with the motion governing equation for the fluid media, through Fourier expression expansion and dimensionless manipulation on every variable in these equations, and eliminating the intermediate variables, a vibroacoustic governing matrix equation for the porous plate in frequency domain is acquired. It is expressed in the form of a first order ordinary differential matrix equation, and can be solved in precise by the extended homogeneous capacity high precision integration method. Coupling motion effect between the in-plane direction with the transverse direction is considered in the present model, which is more close to the actual case for the porous plate. Moreover, employing the extended homogeneous capacity high precision integration method, the computational accuracy for the vibroacoustic problem of a porous plate in the medium-high frequency range can be ensured. Taking a thin rectangular porous plate with the two boundaries simply-supported as an example, the coupling effect on the vibroacoustic performance is demonstrated.
 

关键词

多孔吸声薄板 / Biot理论 / 薄板理论 / 一阶常微分矩阵控制方程 / 齐次扩容精细积分法。

Key words

thin rectangular porous plate / Biot theory / thin plate elastic theory / one first order ordinary differential matrix equation / extended homogeneous capacity high precision integration method.

引用本文

导出引用
袁丽芸1,2,向宇1,2,陆静1,2. 多孔吸声矩形薄板声振特性分析的一种新模型[J]. 振动与冲击, 2016, 35(13): 106-113
Yuan Liyun1,2, Xiang Yu1,2, Lu Jing 1,2. A new model for analysis on the vibroacoustic performance of a thin rectangular porous plate[J]. Journal of Vibration and Shock, 2016, 35(13): 106-113

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