考虑芯层横向变形的粘弹性复合材料夹层板结构的声振特性分析

VIB-ACOUSTIC ANALYSIS OF VISCOELASTIC COMPOSITE SANDWICH PLATES WITH TRANSVERSELY DEFORMABLE CORE

夹层板结构具有很高的比强度和比刚度。若芯层采用粘弹性阻尼材料,夹层板结构还具有良好的隔振和隔声特性,因此在工程结构中得到广泛应用。以往的夹层板理论大多忽略了芯层的横向正应变和横向正应力,在分析芯层较厚的夹层板或者夹层结构的高频振动问题时由于不能体现芯层的横向压缩变形,往往显得不够合理。针对这一不足,构造了一个复合材料夹层板单元:夹层板的上下面板采用基于一阶剪切变形理论的Mindlin假定以及层合板理论进行分析;采用文献[6,7]中提出的Timoshenko层合厚梁理论构造了单元每边的转角和剪应变场,消除了Mindlin板单元当板厚变小时的剪切锁死问题;假定芯层的位移沿厚度方向线性变化,并用上下面板的自由度表示,最终形成以上下面板自由度表示的系统总的运动方程。该单元不仅考虑了芯层的横向剪切变形,还考虑了芯层的横向压缩变形。数值计算结果表明:无论对于静力问题、动力问题还是声辐射等问题,考虑芯层的横向压缩变形是合理的,也是有必要的。

The great advantages of sandwich structure are its high stiffness to weight ratio and strength to weight ratio. If the core is made of high damping viscoelastic material, sandwich structure offers further advantages such as high energy absorption capacity and acoustic insulation. Therefore, viscoelastic sandwich structures are widely used in engineering, such as ship and aerospace industry. Most of the sandwich plate theories developed in the past did not take account of the effect of transverse normal deformation of the core. When such sandwich plate theories are applied to analyse those sandwich plates with thick core or under high frequency vibration, reasonable results could not be gained because of the ignoring of transverse normal deformation. The purpose of the paper is to develop a finite element formulation to include the effect of transverse normal deformation, in addition to the transverse shear deformation in the core. The face plates of the sandwich construction are modeled by plate element based on the Mindlin's assumptions and laminated plate theory. The tangential rotation and shear stains along each element side are determined by Timoshenko laminated composite beam theory to avoid the shear locking problem of Mindlin plate element. The displacements in the core are assumed to vary linearly through the thickness and are expressed in terms of the displacements of two face plates. Thus, the governing equation of the system is expressed in terms of the face plates' displacements. Numerical results show that the consideration of transverse normal deformation in the core is necessary and reasonable whether for static analysis, modal analysis or vib-acoustic analysis.