非保守圆薄板的轴对称振动和稳定性

建立了受切向均布随从力作用的圆薄板在面内周边可移、不可移两种情况下的轴对称控制方程，用打靶法直接导出求解变系数常微分方程特征值问题数值解的计算式．通过数值计算，给出了周边可移、不可移的简支、固支圆板自振频率和临界载荷的特征曲线以及相应的临界发散载荷，并分析了泊松比对圆板自振频率和临界载荷的影响．

AXIALLY SYMMETRIC VIBRATION AND STABILITY OF CIRCULAR THIN PLATE SUBJECTED TO NON-CONSERVATIVE FORCES

Axially symmetric goveming equations of circular thin plate with movable and unmovable supports in the middle plane, subjected to tangentially uniformly distributed follower forces, are derived. Numerical solutions for the eigenvalue problem of the ordinary differential equation with variable coefficients are obtained by shooting method. Moreover, the characteristic curves between self- excited frequencies and critical loads and their critical divergence load of the circular plate with movable and unmovable simple supports and clamped along edges are plotted, and the effect of Possion's ratio on the self-excited frequencies and critical loads of the circular plate is analyzed.