复合梁模态分析的一种里兹解法

就复合材料包覆钢筋混凝土梁(FRP-RC)提出了一种分析其振动特性的近似方法,基于摄动法的思想合理选择里兹函数,并利用最小势能原理来求解纤维复合材料包覆钢筋混凝土梁的模态特性。这一方法在等截面均匀梁的模态子空间内实施,它将FRP-RC梁无阻尼自由振动时复杂的变系数微分方程加以简化,转化成一代数方程组来求解。在此基础上,计算了该梁在不同约束条件下的自振频率,并与其它方法进行了对比。分析表明,利用本方法不仅可以简化计算过程,而且计算结果具有较高的精度,对同类问题具有适用性。

An Ritz Solution for Modal Characterstics of Composite Beam

An approach method is developed to analyze the characteristics of vibration of fiber reinforced plastics-reinforced concrete(FRP-RC)composite beam. An reasonable Ritz-function expansion,based on the idea of mode perturbation,is chosen and principle of minimum potential energy is used for determining the solution of the modal characteristics of fiber reinforced plastics-reinforced concrete composite beam.In this method,an approximate solution using the analytical mode functions of the uniform beam with undetermined coefficients is substituted into the governing differential equation which has coefficients of variables of the problem such that through a solution of the algebraic equations of the undetermined coefficients may solve the problem.By the ownnerieal examples,the natural frequencies of the composite beam under different support conditions are calculated by using the suggested method in this paper,and are used to compare with the solution obtained by other methods.The numerical results show that this method is both accurate and efficient,and better applicability.