环状平膜片挠曲变形数学模型及其试验验证  

Mathematic models of deformation of deflection for circular flat diaphragm and their experimental verification

作　　者：张化岚[1] 孙宝元[1] 

机构地区：[1]大连理工大学机械工程学院,辽宁大连116024

出　　处：《大连理工大学学报》2005年第3期366-369,共4页Journal of Dalian University of Technology

基　　金：国家科技型中小企业创新基金资助项目(00C26222121163).

摘　　要：为描述环状平膜片挠度与载荷的关系,在经典弹性薄板理论、卡尔曼大挠度理论和薄膜理论下为环状平膜片分别建立了3种挠度-载荷数学模型.与试验结果比较表明,小挠度下,薄膜理论曲线与试验结果相差很大,经典理论和大挠度理论曲线与试验结果符合较好,说明膜片主要靠剪切内力平衡外载,剪切效应不能忽略;大挠度下,大挠度理论曲线最接近试验结果,最大误差为17.94%,经修正后结果令人满意,说明此时剪应力变化较小,膜片主要靠张力平衡外载.Three mathematic models of deflection-load for circular flat diaphragm are established based on classical theory of elastic thin plate, von Karman's theory of large deflection and membrane theory. Experimental results show that under small deflection, membrane theoretical curve departs from test curve, and classical theoretical curve and large deflection theoretical curve both fit well with test curve. The load is balanced by shear stress, and the shear effect can not be neglected. Under large deflection, large deflection theoretical curve approaches to test curve, its error value is 17.94%, and the amended result is satisfactory. Under large deflection, the shear stress changes a little, the membrane is balanced by strain.

关 键 词：数学模型 平膜片 试验验证 挠曲变形 环状 弹性薄板理论 试验结果 理论曲线 大挠度理论 结果比较 薄膜理论 经典理论 内力平衡 剪切效应 最大误差 应力变化 张力平衡 卡尔曼 小挠度 载荷 外载 

分 类 号：O141.4[理学—数学] TP212[理学—基础数学]