E. Absi and J. Lerbet, Instability of elastic bodies, Mech. Res. Commun, vol.31, pp.39-44, 2004.

G. Allaire, Analyse Numérique et Optimisation: Une Introductionà la Modélisation Mathématique (Editions Ecole Polytechnique, 2005.

M. Beck, Die Knicklast des einseitig eingespannten tangential gedrückten Stabes, Z. Angew. Math. Phys, vol.3, pp.225-228, 1952.

V. V. Bolotin, Non-Conservative Problems of the Theory of Elastic Stability, 1963.

J. Carr and Z. M. Malhardeen, Beck's problem, SIAM J. Appl. Math, vol.37, issue.2, pp.261-262, 1979.

N. Challamel, F. Nicot, J. Lerbet, and F. Darve, On the stability of non-conservative elastic systems under mixed perturbations, EJECE, vol.13, issue.3, pp.347-367, 2009.

N. Challamel, F. Nicot, J. Lerbet, and F. Darve, Stability of non-conservative elastic structures under additional kinematics constraints, Engineering Structures, vol.32, pp.67-84, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00833665

E. De-langre and O. Doaré, Edge flutter of long beam under follower loads, JoMMS, vol.10, issue.3, 2015.

O. Doaré, Dissipation effect on local and global stability of fluid-conveying pipes, J. Sound Vib, vol.329, issue.1, pp.72-83, 2010.

O. Doaré, Dissipation effect on local and global fluid-elastic instabilities, Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations, pp.67-84, 2014.

O. Doaré and E. De-langre, Local and global instability of fluid-conveying pipes on elastic foundations, J. Fluid. Struct, vol.16, issue.1, pp.1-14, 2002.

I. Elishakoff, Controversy associated with the so-called "follower forces": critical overview, Appl. Mech. Rev, vol.58, issue.1-6, pp.117-142, 2005.

G. Herrmann, Dynamics and Stability of Mechanical Systems with Follower Forces, Monography, p.234, 1971.

R. Hill, Some basic principles in the mechanics of solids without a natural time, J. Mech. Phys. Solids, vol.7, pp.209-225, 1959.

R. Jurisits and A. Steindl, Mode interactions and resonances of an elastic fluid-conveying tube, PAMM, vol.11, issue.1, pp.323-324, 2011.

W. T. Koiter, Unrealistic follower forces, J. Sound Vib, vol.194, pp.636-638, 1996.

O. N. Kirillov and F. Verhulst, Paradoxes of dissipation-induced destabilization or who opened Withney's umbrella?, Z. Angew. Math. Mech, vol.90, issue.6, pp.462-488, 2010.

O. N. Kirillov, Nonconservative Stability Problems of Modern Physics, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01119742

R. J. Knops and L. E. Payne, Stability in linear elasticity, Int. J. Solids Struct, vol.4, issue.12, pp.1233-1242, 1968.

L. P. Lebedev, I. I. Vorovitch, and G. M. Gladwell, Functional Analysis. Application in Mechanics and Inverse Problems, 2003.

J. Lerbet, M. Aldowaji, N. Challamel, F. Nicot, F. Prunier et al., P-positive definite matrices and stability of nonconservative systems, Z. Angew. Math. Mech, vol.92, issue.5, pp.409-422, 2012.

J. Lerbet, O. Kirillov, M. Al-dowaji, F. Nicot, N. Challamel et al., Additional constraints may soften a non-conservative structural system: buckling and vibration analysis, Int. J. Solids Struct, vol.50, issue.2, pp.636-370, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00756558

F. Nicot, J. Lerbet, and F. Darve, Flutter and divergence instabilities of some constrained twodegree-of-freedom systems, Journal of Engineering Mechanics, vol.140, issue.1, pp.47-52, 2014.

O. N. Kirillov, N. Challamel, F. Darve, J. Lerbet, and F. Nicot, Singular divergence instability thresholds of kinematically constrained circulatory systems, Phys. Lett. A, vol.378, issue.3, pp.147-152, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00912400

J. Lerbet, M. Aldowaji, N. Challamel, O. N. Kirillov, F. Nicot et al., Geometric degree of nonconservativity, Math. and Mech. of Complex Systems, vol.2, issue.2, pp.123-139, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01321974

J. Lerbet, N. Challamel, F. Nicot, and F. Darve, Variational Formulation of Divergence Stability for constrained systems, Appl. Math. Modell, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01146839

J. Lerbet, G. Hello, N. Challamel, F. Nicot, and F. Darve, 3-Dimensional flutter kinematic structural stability nonlinear analysis: Real world applications, 2016.

J. Lerbet, N. Challamel, F. Nicot, and F. Darve, Geometric Degree of Nonconservativity: set of solutions for the linear case and extension to the differentiable non linear case, Appl. Math. Modell, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01321974

J. Lerbet, N. Challamel, F. Nicot, and F. Darve, Kinematical Structural Stability, Discrete and Continuous Dynamical Systems -Series S (DCDS-S) of, 2016.

R. Mennicken and M. Möller, Non-Self-Adjoint Boundary Eigenvalue Problems, North-Holland Mathematics Studies, vol.192, 2003.

A. A. Movchan, The direct method of Lyapunov in stability problems of elastic systems, PMM-J. Appl. Math. Mech, vol.23, issue.3, pp.686-700, 1959.

A. A. Movchan, Stability of processes with respect to two metrics, PMM-J. Appl. Math. Mech, vol.24, issue.6, pp.1506-1524, 1960.

N. N. Moiseyev and V. V. Rumyantsev, Dynamic Stability of Bodies Containing Fluid, 1968.

S. Nemat-nasser and G. Herrmann, Adjoint systems in nonconservative problems of elastic stability, AIAA J, vol.4, pp.2221-2222, 1966.

M. P. Païdoussis, Fluid-Structure Interactions: Slender Structures and Axial Flows I, 1998.

M. P. Païdoussis, Fluid-Structure Interactions: Slender Structures and Axial Flows II, 2003.

S. N. Prasad and G. Herrmann, The usefulness of adjoint systems in solving nonconservative stability problems of elastic continua, Int. J. Solids Struct, vol.5, issue.7, pp.727-735, 1969.

A. Steindl and H. Troger, One and two-parameter bifurcations to divergence and flutter in the three-dimensional motions of a fluid conveying viscoelastic tube with D4-symmetry, Advances in Nonlinear Dynamics: Methods and Applications, vol.8, pp.161-178, 1995.

A. Steindl and H. Troger, Nonlinear three-dimensional oscillations of elastically constrained fluid conveying viscoelastic tubes with perfect and broken O(2)-symmetry, Nonlinear Dyn, vol.7, issue.2, pp.165-193, 1995.

A. Steindl and H. Troger, Heteroclinic cycles in the three-dimensional postbifurcation motion of O(2)-symmetric fluid conveying tubes, Appl. Math. Comput, vol.78, issue.2-3, pp.269-277, 1996.

A. Steindl, Hopf-Takens-Bogdanov interaction for a fluid-conveying tube, PAMM, vol.16, issue.1, pp.293-294, 2016.

J. M. Thompson, Paradoxical' mechanics under fluid flow, Nature, vol.296, issue.5853, pp.135-137, 1982.

H. Troger and A. Steindl, Nonlinear Stability and Bifurcation Theory, 1991.

J. Weidmann, Linear Operators in Hilbert Spaces, 1980.

H. Ziegler, Principles of Structural Stability, 1968.