FRP加固梁模态分析的摄动解法

采用基于Ritz函数展开的直接模态摄动法,求解纤维复合材料包覆钢筋混凝土（FRP-RC）梁的模态特性.在不考虑剪切变形和转动惯量的情况下,它将FRP-RC梁的无阻尼自由振动的变系数微分方程的求解转化成一组非线性代数方程组的求解,使得求解过程得以简化.在此基础上,计算了不同加固工况下FRP-RC梁在各种约束条件下的自振频率,并与其他方法进行了对比.数值结果表明,利用直接模态摄动法不仅可以简化计算过程,而且计算结果具有较高的精度和较强的适用性.

Perturbation solution for modal characteristics of beam strengthened by FRP

In order to simplify the solution procedure, the direct modal perturbation method based on Ritz-function expansion is applied for determining the modal characteristics of fiber reinforced plastics-reinforced concrete (FRP-RC) composite beam. Neglecting the effect of shear deformation and rotation inertia, the method simplifies the complex differential equation with variable coefficients of the FRP-RC composite beam into a nonlinear algebraic equations. By the numerical examples, the natural frequencies of the composite beam under different support conditions and different strengthen patterns are calculated by using the suggested method and are used to compare with the solution obtained by other methods. The numerical result show that the suggested method is of both high accurate and better applicability.