摘要
本文首先采用一个线性变换将平行四边形域上的边值问题变换到矩形域。然后在王磊教授工作的基础上再次采用康托洛维奇能量近似法结合广义梁函数,导得板振动的一个常微分方程及边界条件。采用“对分法”求解了18种边界条件下不同斜度的平行四边形板,得到板的振动频率。本文所采用的方法较原有方法计算工作量大为减少,且具有相当高的精度。
A linear transformation is used to transform the boundary value problem in a parallelogram region into one in a rectangular region. By the Kantorovich approximation method with generalized beam functions, an ordinary differential equation and the boundary conditions for plate vibrations are derived. The vibration frequencies of the plates can be found with eighteen types of boundary conditions and various inclined angles. The method proposed is found to be simpler and more convenient than those in current use.
出处
《华中理工大学学报》
CSCD
北大核心
1990年第5期43-49,共7页
Journal of Huazhong University of Science and Technology
关键词
薄板
平行四边形
自由振动
康氏法
Theory of elasticity
Kantorovich method
Generalized beam function
Parallelogram thin plate
Free vibration
