随从力作用下含裂纹的粘弹性压电层合板的稳定性研究

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 deformation state. The relation between the amplitude and nonlinear fundamental frequency under different conditions of large deformation was derived. The effects of the crack parameters, thickness ratio, the piezoelectric parameter, the material viscosity and the follower forces on the vibration characteristics and stability of the plates are analyzed. And further discusses the dynamic systems with these parameters change presents of bifurcation and chaos phenomena.Use the potential of piezoelectric materials to strengthen structure stability. This will provide the theoretical basis for high accuracy nondestructive inspection and intelligent control.

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。

研究了压电层合粘弹性板及其运动压电层合粘弹性板在切向随从力作用下的动力稳定性，并且分析了基于在非均匀张力作用下无矩运动薄板的动力稳定性。构造了非线性弹性柔性壳的应力张量的一种新的近似模型, 基于非线性方程的求解基础，根据大挠度的 Von Karman 理论，得到以应力函数和挠度函数表示的粘弹性板在随从力作用下非线性运动偏微分方程组及其控制方程，编写了数值计算程序，进行计算和分析，分析解的收敛性。建立粘弹性板中裂纹的计算模型；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，给出广义特征值及解的特性与系统参数的变化曲线，以及得到大变形的各种条件下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动力特性及稳定性的影响。研究建立利用新的信息载体在粘弹性结构系统间的相互作用。为健康监测及稳定控制提供理论依据。.发表了15篇论文，还有4篇正在审稿中，3篇论文正在撰写中，其中被SCI检索8篇。参加学术会议7次。2013年2月至8月，项目负责人在美国University of South Carolina访问交流。随从力作用下运动粘弹性动力学研究，获得陕西省教育厅科技二等奖。出版著作一部。初步建立动态测试综合试验平台。培养硕士研究生7名，已毕业2名。