二阶振动系统的解耦条件及算法研究  

Decouplin coupling and algorithm of a quadratic system

作　　者：沈继红[1] 胡波[2] 王侃[2] 金鑫[1] 

机构地区：[1]哈尔滨工程大学理学院,哈尔滨150001 [2]哈尔滨工程大学自动化学院,哈尔滨150001

出　　处：《振动与冲击》2012年第18期89-92,156,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(11601063)

摘　　要：针对二阶振动系统的解耦问题,给出了二阶振动系统可解耦的条件及其相应证明。针对可解耦的二阶振动系统,提出同谱构造解耦算法。数值试验中验证了解耦条件的正确性,实现了一个二自由度质量弹簧系统的同谱解耦,并与近似解耦算法的谱特征进行了对比。结果表明:解耦条件判断简便且适合所有质量矩阵非奇异的二阶振动系统,同谱构造解耦算法实现完全同谱。In order to solve the decoupling problem of a quadratic vibration system, the diagonalizable condition for a quadratic vibration system and its corresponding proof were given, and an isospectral construction decoupling algorithm was proposed here. Numerical test was presented to verify the accuracy of decoupling condition and to realize isospectral deeoupling of a two-degree-of-freedom mass-spring system and to compare its eigenvalues with decoupling approximations. The results showed thatthe decoupling method is simple and the decoupled system is isospectral as the original system, and the decoupling condition is suitable to all quadratic vibration systems with nonsingular mass matrix.

关 键 词：二阶振动系统 解耦条件 同谱解耦 质量弹簧系统 

分 类 号：O29[理学—应用数学] N945[理学—数学]