×

On the stability of a deep beam subjected to nonconservative and dissipative forces. (English) Zbl 0282.73026


MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74G60 Bifurcation and buckling
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] G. Herrmann,Stability of equilibrium of elastic systems subjected to nonconservative forces, Appl. Mech. Rev., 20, pp. 103–108, 1967.
[2] H. Ziegler,Die Stabilitàtskriterien der Elastomechanik, Ingen.-Arch., 20, pp. 49–56, 1952. · Zbl 0047.42606 · doi:10.1007/BF00536796
[3] J. J.Wu,Application of the finite element method to nonconservative stability problems with damping, Watervliet Arsenal Technical Report. WVT-7238, Watervliet, New York 12189, U.S.A., 1972.
[4] G. L. Anderson,Application of a variational method to dissipative, non-conservative problems of elastic stability, J. Sound Vib., 27, pp. 279–296, 1973. · Zbl 0309.73041 · doi:10.1016/S0022-460X(73)80346-3
[5] M. Como,Lateral buckling of a cantilever subject to a transverse follower force, Int. J. Solids Structures, 2, pp. 515–523, 1966. · doi:10.1016/0020-7683(66)90035-7
[6] M. Como,Del metodo dell’energia nella stabilità dei sistemi elastici soggetti a forze posizionali conservative e non conservative, Costruzioni in Cemento Armato, 5, pp. 1–56, 1967.
[7] G. Ballio,Sulla trave alta sollecitata da carichi di tipo non conservative, Rend. Istituto Lombardo, 101, pp. 307–330, 1967. · Zbl 0201.57705
[8] S. Nemat-Nasser andP. F. Tsai,Effect of warping rigidity on stability of a bar under eccentric follower force, Int. J. Solids Structures, 5, pp. 271–279, 1969. · doi:10.1016/0020-7683(69)90012-2
[9] G. L. Anderson,On the role of the adjoint problem in dissipative, nonconservative problems of elastic stability, Meccanica, 7, pp. 165–173, 1972. · Zbl 0251.73042 · doi:10.1007/BF02128762
[10] K. Wohlhart,Dynamische Kippstabilitàt eines Plattenstreifens unter Folgelast, Zeit, fùr Flugwissenschaften, 19, pp. 291–298, 1971.
[11] J. H. Wilkinson,The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, England, 1965. · Zbl 0258.65037
[12] J. F. G. Francis,The QR transformation, Computer J., 4, Part I, pp. 265–271, and Part II, pp. 332–345, 1961–1962. · Zbl 0104.34304 · doi:10.1093/comjnl/4.3.265
[13] B. N. Parlett,The LU and QR transformations, in ”Mathematical Methods for Digital Computers”, Ralston and Wilf, eds., Vol. II, John Wiley and Sons, New York, 1967. · Zbl 0171.36004
[14] R. H. Plaut,A new stabilization phenomenon in nonconservative systems, Zeit. angew. Math. Mech., 51, pp. 319–321, 1971. · doi:10.1002/zamm.19710510414
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.