Sensitivity analysis for problems of dynamic stability

Dynamic Stability of Columns Subjected to Follower Loads: A Survey

“…Claudon and Sunakawa [117] considered sensitivity analysis for such double eigenvalue problems. Pedersen and Seyranian [118] gave a uni"ed presentation, covering especially the systems reviewed in this paper. Seyranian [119] developed sensitivity analysis for multiple eigenvalues (not just double).…”

“…Langthjem [141] studied the in#uence of internal and external damping on the optimal design. The equation of motion was discretized by using a generalized Ritz method [40,41,118]. The mass distribution was expressed in terms of orthogonal trigonometric functions.…”

The effect of small internal and external damping on the stability of distributed non-conservative systems

“…The double eigenvalue i010 has a Keldysh chain of length 2, consisting of the eigenfunction and associated eigenfunction, u0, and Ux, which satisfy the equations with boundary conditions (1. The eigenfunctions u0 and v0 are defined by Eqs (1.5) and (4.10) [36,37] Uo(X ) = ch(ax) -cos(bx) + F(asin(bx) -bsh(ax) ) (4.12)…”

On the Discretization of an Elastic Rod With Distributed Sliding Friction

“…Similar approaches for solving the approximate solutions can be found in Meirovitch and Kwak [18], and Hagedorn [19]. The proof of Galerkin's method for non-self-adjoint boundary value problems has been given by Diprima and Sani [20] and sensitivity analyses in the non-conservative problem by using adjoint variational method are presented by Prasad and Herrmann [21], and Pedersen and Seyranian [22].…”