具有任意边界的弹性力学梁固有特性的解法

Solution Methods of Inherent Characteristics of Plane Beam with Arbitrary Boundary Conditions

给出了可以用于求解具有任意边界条件的弹性力学梁的固有振动特性的双向展开方法和半解析方法。这两种方法均把梁看成为平面应力问题,不对纵向位移和横向位移作任何假设,涉及到的结构刚度和质量矩阵的元素均为显式。以简支梁固有特性求解问题为例,通过对本文结果和解析解进行比较,说明了给出的半解析方法和双向展开方法的精度和效率。

A semi-analytical method and a two-direction expansion method, have been presented and used to find the natural vibration characteristics of two-dimensional beam with arbitrary boundary conditions. In these two methods there are no any assumptions on the transverse displacement and the longitudinal displacement along x-axis and z-axis directions, i.e., the beam is considered to be in a state of plane stress, and the elements of structure stiffness and mass matrix can be given explicitly. The geometrical properties of mode shapes are investigated, and the simply supported beam is taken as an example to discuss the accuracy and the efficiency of the semi-analytic method and the two-direction expansion method through comparing the results of the two methods with that of the analytical method.