Follower forces: Leipholz's researches into generalized variational principles

1990 ◽  
Vol 17 (3) ◽  
pp. 287-293 ◽  
Author(s):  
G. M. L. Gladwell

Classical variational principles, for conservative systems, are associated with the names of Lagrange and Hamilton. Generalized variational principles for nonconservative systems were introduced by various authors and in various physical contexts in the period 1945 – 1966. This review traces their development and their use, by Leipholz, in the period 1971 – 1986. Key words: follower forces, variational principles, generalized, nonconservative, adjoint systems, stability, divergence, flutter.

AIAA Journal ◽  
1969 ◽  
Vol 7 (7) ◽  
pp. 1254-1260 ◽  
Author(s):  
B. E. GREENE ◽  
R. E. JONES ◽  
R. W. McLAY ◽  
D. R. STROME

Author(s):  
Lifu Liang ◽  
Liming Dai ◽  
Qingyong Guo

According to the corresponding relations between generalized forces and generalized displacements, the basic equations of elasto-dynamics in phase space are multiplied by corresponding virtual quantities, integrated and then added algebraically. By considering the character of fellow body and surface forces, the generalized quasi-variational principles of non-conservative systems are established in elasto-dynamics in phase space. By doing inverse Laplace transformation, the convolutional generalized quasi-variational principles of non-conservative systems of elasto-dynamics are established in original space. Applying the generalized quasi-complementary energy principle to the mechanical vibration problem of two kinds of variables, the authors of this paper present a calculation method for solving two kinds of variables simultaneously: the internal force and the displacement of a typical fellow force system.


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