欧拉梁动力反应初边值问题的微分求积解

动荷载作用下欧拉梁动响应的计算是一个初边值问题,通常很难得到解析解,传统数值方法一般是把空间和时间分别离散进行求解,计算相对复杂,效率也不高.针对分布动荷载作用下欧拉梁的振动偏微分方程,采用传统微分求积法,在空间和时间上同时进行离散;对于所有非0阶的初/边值条件,采用嵌入法在权系数计算中予以考虑.算例的数值结果与精确解的对比证明采用传统微分求积法处理此问题是可行的,而且是高效的.对于实际工程中的其他类似问题,该方法同样适用.

Differential quadrature solution to initial-boundary-value problems for dynamic response of Euler beams

The analytical solution of the response of an Euler beam subjected to dynamic loads is essentially an initial-boundary-value problem,and that is usually difficult to be obtained. Application of traditional numerical methods to this problem is relatively complicated and inefficient, which commonly discretize spatial domain and temporal domain separately. Partial differential equations of the Euler beam for the forced vibration induced by distributed dynamic loads are solved by using the differential quadrature method to both spatial and time dimensions simultaneously as a whole. All the initial/boundary conditions of non-zero order are imposed during the formulation of the weighting coefficients for higher order derivatives. Comparison between the numerical and exact results of the presented example demonstrates the feasibility and high efficiency of the traditional differential quadrature method being applied to this problem. This method can also be applied to other analogous problems in engineering.