非局部弹性杆固有频率的Ritz法求解

采用Ritz法求解了非局部弹性直杆的固有频率问题。非局部弹性理论与经典弹性理论相对应,区别在于非局部理论中,一点的应力与该点以及其周围区域的应变都有关,并采用核函数来表征这种相关性。基于Eringen提出的非局部弹性模型,针对三种给定核函数,用Ritz法进行了直杆的动力学分析。并针对两种边界条件给出直杆的固有频率,与其它方法比较,该方法具有可以针对多种核函数求解,精度可控,易于编程等优点。

Ritz Method for the Frequencies of Nonlocal Elastic Bar

Ritz method was adopted to study the natural frequency of nonlocal elastic bar.Nonlocal elastic theory,different from classic elastic theory,was presented that the stress of a point is related to the strain of the area around the point,and such a relationship is illustrated by kernel function.Based on Eingen's nonlocal elastic model,a dynamics analysis of nonlocal elastic bar was created by Ritz method with three different kernel functions and the natural frequencies of the bar with two different boundary conditions were supplied.Compared with other methods,this one can deal with different kernel functions.Moreover,its numerical precision is controllable and programming is very convenient.