谐振子密度偏差引起的频率裂解的分析

摘要

In order to study the frequency cracking caused by the nonuniform of density distribution,the dynamics equations of resonator under the nonuniform of density distribution were established by way of Bubonov—Galerkin method which is common used for solution of differential equations,the state equation was established by the dynamics equations,and then the system characteristic equations were derived.According to the system characteristic equations,two second order natural frequency caused by the density nonuniformity around the hemispherical of vibration system and the expression of frequency cracking were solved.%为研究半球谐振子密度不均匀引起的频率裂解,首先利用解微分方程的布勃诺夫-加廖尔金法建立了谐振子环向密度分布不均匀的动力学方程,根据动力学方程建立了振动系统的状态方程,进而推导了系统的特征方程,根据特征方程解出了在谐振子存在环向密度不均匀的前提下,振动系统存在的两个二阶固有频率,最后求解了固有频率裂解的表达式.