Search results for "complex variable techniques"

Variational approach for analysis of harmonic vibration and stabiligy of moving panels

2014

In this paper, the stability of a simply supported axially moving elastic panel (plate undergoing cylindrical deformation) is considered. A complex variable technique and bifurcation theory are applied. As a result, variational equations and a variational principle are derived. Analysis of the variational principle allows the study of qualitative properties of the bifurcation points. Asymptotic behaviour in a small neighbourhood around an arbitrary bifurcation point is analyzed and presented. It is shown analytically that the eigenvalue curves in the (ω, V0) plane cross both the ω and V0 axes perpendicularly. It is also shown that near each bifurcation point, the dependence ω(V0) for each m…