Bifurcations in threedimensional motions of articulated tubes. I  Linear systems and symmetry. II  Nonlinear analysis
Abstract
Threedimensional nonlinear motions of articulated tubes are analyzed within the framework of bifurcation theory for systems with rotational symmetry. For simplicity, the case of only two tubes is treated and the analysis is restricted to those cases where the static solution breaks up into periodic motions. It is shown that the downward vertical position of equilibrium of the twosegment articulated tube system becomes unstable when the flow velocity reaches a critical value. The loss of stability is associated with two coincident pairs of complex conjugate eigenvalues crossing the imaginary axis. The nonlinear equations of motion of the system are then analyzed for bifurcating solutions near critical flow velocities, and the behavior of the system is studied in several specific cases.
 Publication:

ASME Journal of Applied Mechanics
 Pub Date:
 September 1982
 Bibcode:
 1982ATJAM..49..606B
 Keywords:

 Branching (Mathematics);
 Liquid Filled Shells;
 Pipe Flow;
 Pipes (Tubes);
 Shell Stability;
 Structural Vibration;
 Canonical Forms;
 Equations Of Motion;
 Linear Systems;
 Symmetry;
 Engineering (General)