基于新修正偶应力理论的Mindlin层合板自由振动分析  

FREE VIBRATION ANALYSIS OF A LAMINATED COMPOSITE MINDLIN PLATE BASED ON NEW MODIFIED COUPLE STRESS THEORY

作　　者：陈万吉[1] 任鹤飞[1] 

机构地区：[1]沈阳航空航天大学辽宁省飞行器复合材料结构分析与仿真重点实验室,辽宁沈阳110136

出　　处：《工程力学》2016年第12期31-37,43,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(11202039;11572204)

摘　　要：该文基于各向异性修正偶应力理论建立一个Mindlin层合板（跨厚比10-20的中厚板）自由振动模型。该理论偶应力曲率张量不对称,但偶应力弯矩对称。利用Hamilton原理推导振动微分方程和边界条件。新模型可退化为修正偶应力层合薄板振动模型和经典Mindlin层合板振动模型。以正交铺设简支方板为例计算了偶应力模型的自振频率,分析偶应力Mindlin层合板的自由振动尺度效应。算例表明,该文建立的新修正偶应力层合板模型能够用于分析细观尺度下Mindlin层合板的自由振动及尺度效应。A free vibration model for a composite laminated Mindlin plate（span-depth ratio at 10-20） is established based on new modified couple stress theory for anisotropic material. In this theory, the curvature tensor is asymmetric, while the couple stress bending moment is symmetry. A Hamiltonian principle is employed to derive the governing equations of motion and boundary conditions. This new model can be reduced to the model for a composite laminated thin plate based on modified couple stress theory, and also to the model for a composite laminated Mindlin plate based on classical theory. An example of natural frequencies analysis with a cross-ply simple supported square-plate is used to show the scale effects of natural frequencies. Numerical results show that the present model can capture the scale effects of the free vibration of a micro-scale composite laminated Mindlin plate.

关 键 词：新修正偶应力理论 Mindlin层合板 尺度效应 自由振动 材料长度尺寸参数 

分 类 号：O33[理学—一般力学与力学基础]