粘贴碳纤维布梁自由振动分析的精细积分法

High precision integration method for free vibration analysis of beam with carbon fiber

基于线弹性梁理论和线粘弹性理论,根据欧拉梁的平衡方程和几何方程,结合传递矩阵法和精细积分法,推导出了粘贴碳纤维布的梁的整合一阶常微分方程组.运用新型齐次扩容精细积分法,对粘贴碳纤维布的梁的自由振动分析构建了一种半解析半数值方法.数值计算和有限元结果的比较表明,该方法正确可行.

Based on the linear elastic theories of beams and viscoelastic materials, according to Euler beam＇s equilibrium equations and geometric equations, combined with the transfer matrix method and the precise integration method, the integrated first-order ordinary differential matrix equation of debonding carbon fiber beam are derived. It consists of 8 independent firsorder differential equations and is represented by 8 variables with each variable having of homogenized precise a distinct physical meaning. The model lays a foundation for applying the technologies integration and building a semi-analytical and semi-numerical method with high efficiency and accuracy. Through the comparison of the numerical results and the results of the finite element method, it can be shown that the proposed approach is very effective and reliable.