多孔吸声矩形薄板声振特性分析的一种新模型  

A new model for analyzing vibroacoustic performance of a thin rectangular porous plate

作　　者：袁丽芸[1,2] 向宇[1,2] 陆静[1,2] 

机构地区：[1]广西科技大学汽车与交通学院,广西柳州545006 [2]广西科技大学广西汽车零部件与整车技术重点实验室,广西柳州545006

出　　处：《振动与冲击》2016年第13期106-113,166,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(11162001;51105083;11502056);广西自然科学基金(2015GXNSFBA139007);广西科技大学博士基金(院科博12Z09);广西重点实验室建设项目(1404544)

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,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。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。In order to make up deficiencies of the present numerical and analytical modeling of porous material,a new semi-analytical model was established for vibroacoustic analysis of a thin rectangular porous plate. In this model,by applying the elastic theory of thin plate and introducing membrane force and moment related to acoustic pressure of fluid media in a porous plate,based on 3D Biot theory,the constitutive equations and the corresponding relationship between internal force and displacement of 2D porous material plates were derived. Then,combining equilibrium equations of a porous plate with governing motion equations of fluid media inside the porous plate,using Fourier transformation and dimensionless processing to eliminate intermediate variables,a vibroacoustic governing matrix equation for the porous plate in frequency domain was established in the form of a first order ordinary differential matrix equation. It was solved with the extended homogeneous capacity high precision integration method. The coupled motion effects between in-plane vibration and transverse vibration were considered in this model,it was more close to the actual situation of a porous plate.Moreover,employing the extended homogeneous capacity high precision integration method,the computational accuracy for the vibroacoustic problem of a porous plate in medium-high frequency range could be ensured. Taking a thin rectangular porous plate with two-side simply-supported as an example,the coupled effects between in-plane vibration and bending vibration of the plate on its vibroacoustic performance were analyzed.

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 

分 类 号：TH113[机械工程—机械设计及理论]