圆弧曲梁面内自由振动的微分容积解法

DIFFERENTIAL CUBATURE METHOD FOR IN-PLANE VIBRATION ANALYSIS OF SHEAR DEFORMABLE CURVED BEAMS

用微分容积法求解圆弧曲梁在面内的自由振动问题。通过微分容积法将曲梁自由振动的控制微分方程和边界约束方程离散成为一组线性齐次代数方程组 ,这是一典型的特征值问题 ,求解这一特征值问题可以求得其自由振动的圆频率。文中采用了考虑轴向变形、剪切变形和转动效应的理论 ,并采用子空间迭代法求解频率方程。数值算例表明 ,本方法稳定收敛、精度较高 ,对圆弧曲梁问题简单、有效。

In the paper,the problem of free vibration of curved beams with uniform cross-section is studied by using a novel numerical solution technique,the differential cubature method.Through this numerical procedure,the governing equilibrium equations and boundary constraint equations are transformed into sets of homogeneous algebraic equations in terms of the displacements of each discrete point.By solving this typical eigenvalue problem using subspace iterative procedure,the numerical results of natural frequencies of the circular arch can be achieved.The simplicity,efficiency and applicability of the method are demonstrated by the convergence properties and numerical accuracy studies.The influence of transverse shear,centerline extensibility as well as rotary inertia on the natural frequencies of a circular beam are also studied.