圆形或扇形薄板的横向振动问题(二)扇形薄板情形下偏微分方程的分离变量

Transverse vibration of thin plate with circular or sector shape(Ⅱ)Separation of variables of partial differential equation in the problem of transverse vibration of sector plate

从数理方程的角度探讨了扇形薄板的横振动问题,针对本征值问题中出现的4阶偏微分方程,给出了分离变量的方法.在给定的边界条件下,给出了扇形薄板横振动的固有振动频率和相应的振动模式.

The transverse vibration of sector plate is discussed from the point of view of equations of mathematical physics.The separation of variables applied to the partial differential equation in the eigenvalue problems is sketched.As an example,the eigenfrequencies and corresponding proper vibration modes are given when the boundary of sector plate is fixed.