EXISTENCE AND BIFURCATION OF MINIMAL NORMAL MODES

被引:18
作者
JOHNSON, TL
RAND, RH
机构
[1] Gas Turbine Division, General Electric Company, Schenectady
[2] Department of Theoretical and Applied Mechanics, Cornell University, Ithaca
关键词
D O I
10.1016/0020-7462(79)90024-6
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
Minimal normal modes (MNMs) are defined as non-linear normal modes which give a true minimum to Jacobi's Principle of Least Action. It is shown that for a certain class of two degree of freedom non-linear conservative systems, MNMs generically occur in pairs. The nature of both generic and non-generic bifurcations of MNMs is derived and illustrative examples are given. © 1979.
引用
收藏
页码:1 / 12
页数:12
相关论文
共 17 条
[1]  
Rosenberg, On non-linear vibrations of systems with many degrees of freedom, Advances in Applied Mechanics, pp. 155-242, (1966)
[2]  
Rand, A direct method for non-linear normal modes, Int. J. Non-Linear Mech., 9, pp. 363-368, (1974)
[3]  
Johnson, Ph.D. thesis, (1978)
[4]  
Bolza, Lectures on the Calculus of Variations, (1904)
[5]  
Whittaker, Analytical Dynamics, pp. 250-253, (1937)
[6]  
Chillingworth, Differential Topology with a View to Applications, (1976)
[7]  
Chillingworth, Differential Topology with a View to Applications, (1976)
[8]  
Poston, Stewart, Taylor Expansions and Catastrophes, pp. 28-33, (1976)
[9]  
Yen, On the normal modes of non-linear dual-mass systems, Int. J. Non-Linear Mech., 9, pp. 45-53, (1974)
[10]  
Month, Rand, The stability of bifurcating the periodic solutions in a two-degree-of-freedom nonlinear system, Journal of Applied Mechanics, 44, pp. 782-784, (1977)