四角点支承四边自由矩形板自振分析新方法  

A new analysis method for free vibration of a rectangular plate with 4-free-edges and 4 corner point supports

作　　者：许琪楼[1] 

机构地区：[1]郑州大学工学院,郑州450002

出　　处：《振动与冲击》2013年第3期83-86,共4页Journal of Vibration and Shock

摘　　要：四角点支承四边自由矩形板振形函数表达式由四边自由板所固有的基本振形和角点力所激发的附加振形组成。振形函数须满足振动微分方程和板挠度与角点力间的微分关系。为表示矩形板双向振动规律,基本振形在二个坐标轴方向分别有各自的表达式,并符合对应方向边界所限定的变形和受力特征:在对应自由边界上振幅不为零而剪力分布为零值,在自由角点处对应的四个角点力均为零值。而附加振形在角点处的振幅与角点力要符合板弯曲理论中的微分关系,在四个自由边界上对应的剪力分布均为零值。这种方法克服了现有解法中的理论缺陷,计算理念更合理。The vibration modal shape function expressions of a rectangular plate with 4-free-edges and four comer point supports are composed of two parts including the basic modal shapes of the plate with 4-free-edges and the addition ones caused by the four comer forces. The vibration modal shape functions must satisfy the vibration differential equation and the differential relation between the comer force and the bending deflection. Here, to indicate the bi-directional vibration, each basic modal shape had an alone expression along the two coordinate axes respectively, they had the load- deformation characteristics limited by the relevant edges. The features were the zero shear force and the non-zero amplitude at the relevant free edges and the zero comer forces at the four free comers. The addition modal shapes had to satisfy the differential relation between the comer force and the bending deflection at the four comer points, and the relevant shear force was zero and the relevant amplitude was not zero at the four free edges. The proposed method overcame the theoretical drawbacks of the current solving methods and seemed to be more reasonable.

关 键 词：弹性振动 矩形板 角点支承 基本振形 附加振形 

分 类 号：O326[理学—一般力学与力学基础] O327[理学—力学]