CAJ | 학술논문

基于 Mathieu 方程的临界频率方程式，提出了一种改进 Mathieu 方程不稳定边界的方法，并获得了比 Bolo-tin 近似边界更精确的前三阶收敛的不稳定边界。从改进的不稳定区域边界表达式和 Bolotin 近似公式的对比中发现：两种方法获得的第一、二阶不稳定区域相差不大，但相较于 Bolotin 的第三阶不稳定区域，改进的第三阶不稳定区域整体上移，且上移幅度随着激发系数的增大而增大。当激发系数μ取0．5时，上边界上移幅度为8．61％，下边界上移幅度为11．56％。对于受低频载荷作用的动力稳定性问题，第三阶不稳定边界公式的改进具有重要的意义。
기우 Mathieu 방정적림계빈솔방정식，제출료일충개진 Mathieu 방정불은정변계적방법，병획득료비 Bolo-tin 근사변계경정학적전삼계수렴적불은정변계。종개진적불은정구역변계표체식화 Bolotin 근사공식적대비중발현：량충방법획득적제일、이계불은정구역상차불대，단상교우 Bolotin 적제삼계불은정구역，개진적제삼계불은정구역정체상이，차상이폭도수착격발계수적증대이증대。당격발계수μ취0．5시，상변계상이폭도위8．61％，하변계상이폭도위11．56％。대우수저빈재하작용적동력은정성문제，제삼계불은정변계공식적개진구유중요적의의。
An improved method about unstable boundary of Mathieu equation was proposed according to the critical frequency equation,and the first three orders convergent unstable boundary was got,which is more accurate than the Bolotin approximate boundary.Comparing the two methods,it shows that their first two orders dynamic unstable region are almost the same,the third order unstable region of the improved method moves upward compared with the Bolotin method, and the range is amplified with the growth of excitation coefficient.When the excitation coefficient μis 0.5,the upper boundary moves upward about 8.61% and the lower boundary moves upward about 11.56%.With respect the dynamic stability problem caused by low frequency loading,the improvement on the third order unstable boundary expression has great significance.