随从力作用下含裂纹的粘弹性压电层合板的稳定性研究

项目名称： 随从力作用下含裂纹的粘弹性压电层合板的稳定性研究

项目编号： No.11202159

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 王砚

作者单位： 西安理工大学

项目金额： 26万元

中文摘要： 研究在随从力作用下含裂纹的粘弹性压电层合板非线性振动特性及稳定性。粘贴在板表面的压电材料对板结构的作用是一种典型的随从力，以粘贴在板的上下表面的压电材料和粘弹性板构成的层合板为研究对象，从二维粘弹性本构关系出发，建立粘弹性板中裂纹的计算模型；推导时域内含裂纹粘弹性压电层合板在随从力作用下的非线性运动微分方程，建立微分方程和边界条件的弱积分形式，用基于NURBS基函数的无网格方法建立不同粘弹性模型的含裂纹粘弹性压电层合板在随从力作用下的离散控制方程。通过数值计算，给出随从力下含裂纹粘弹性压电层合板在大变形条件下广义特征值及解的特性与系统参数的变化曲线，得到板的振幅与非线性基频的关系，分析裂纹参数、板厚比、压电参数、材料粘性以及随从力对板的非线性动力特性及稳定性的影响。运用压电材料的压电效应增强结构的稳定性，为高精度的无损探伤及智能控制提供理论依据。

中文关键词： 粘弹性；压电层合板；裂纹；随从力；稳定性

英文摘要： This project addresses the nonlinear vibration characteristic and stability of the viscoelastic piezoelectric laminated composite plate with crack and subjected to follower forces. The active force of surface bonded piezoelectric materials to the plate is the typical follower force. The research object is the laminated composite plate of the viscoelastic plate with surface bonded piezoelectric sheet. Based on the two-dimensional viscoelastic constitutive relation, the computational modeling of crack in the viscoelastic plate is established. The nonlinear differential equation of motion of the viscoelastic piezoelectric laminated composite plate containing the all-over part-through crack and subjected to uniformly distributed tangential follower forces are established in time domain. The weak integral form of the differential equations and the boundary conditions are obtained. The discrete control equation of the viscoelastic piezoelectric laminated composite plate with crack and subjected to follower forces are obtained by the element free method based in NURBS basis function. By number calculating the curves of the generalized complex eigenvalue and the characteristics of the solution of the viscoelastic piezoelectric laminated composite plate with crack versus the system parameters are plotted in large deform

英文关键词： Viscoelastic；piezoelectric composite plate；cracks；follower forces；stability