Rod stability on a movable base under the non-conservative loading

Studying mechanical systems stability exposed to the non-conservative loads often leads to the unexpected results. This is often associated with alterations in the structure design schemes. The paper presents a study of stability of the equilibrium rectilinear-form rod connected by the elastic hinge with a rigid body (base), which is elastically fixed from displacements transverse to the rod axis. The rod is loaded with potential and tracking forces. The method of expanding the solution of the disturbed motion in a series of the system oscillations eigenmodes on the loading parameters plane is used to construct boundaries of the stability region. The paper illustrates the system destabilization with alteration in the internal friction parameter of the rod material. It analyzes behavior of the characteristic indicators responsible for the system stability on straight lines intersecting the stability region in zones of the boundaries non-monotonic alteration.
EDN: FTRNSF, https://elibrary/ftrnsf

References

[1] Beck M. Die Knicklast des einseitig eingespannten, tangential gedruckten Stabes. ZAMP, 1952, vol. 3, no. 3, pp. 225–228, doi: https://doi.org/10.1007/BF02008828

[2] Pfluger A. Stabilitatsprobleme der Elastostatik. Springer, 1964. 472 p.

[3] Panovko Ya.G., Gubanova I.I. Ustoychivost i kolebaniya uprugikh sistem [Stability and oscillations of elastic systems]. Moscow, Nauka Publ., 1967. 420 p. (In Russ.).

[4] Bolotin V.V. Nekonservativnye zadachi teorii uprugoy ustoychivosti [Non-conservative problems of the theory of elastic stability]. Moscow, Fizmatgiz Publ., 1961. 340 p. (In Russ.).

[5] Guskov A.M., Panovko G.Ya. Osobennosti dinamiki mekhanicheskikh sistem pod deystviem nekonservativnykh (tsirkulyatsionnykh) sil [Features of dynamics of mechanical systems under the action of non-conservative (circulating) forces]. Moscow, Bauman MSTU Publ., 2013. 53 p. (In Russ.).

[6] Volmir A.S. Ustoychivost deformiruemykh system [Stability of deformable systems]. Moscow, Nauka Publ., 1967. 984 p. (In Russ.).

[7] Alfutov N.A. Osnovy rascheta na ustoychivost uprugikh sistem [Fundamentals of calculation for stability of elastic systems.]. Moscow, Mashinostroenie Publ., 1978. 312 p. (In Russ.).

[8] Nikolai E.L. On the stability of the rectilinear equilibrium form of a compressed and twisted rod. Izv. Leningr. politekhn. in-ta, 1928, no. 31, pp. 1–26. (In Russ.).

[9] Ziegler H. Principles of structural stability. Birkh?user Basel, 1977. 150 p. (Russ. ed.: Osnovy teorii ustoychivosti konstruktsiy. Moscow, Mir Publ., 1971. 192 p.)

[10] Elishakoff I. Resolution of the twentieth century conundrum in elastic stability. Florida Atlantic University, 2014. 352 p.

[11] Radin V.P., Samogin Yu.N., Chirkov V.P. et al. Reshenie nekonservativnykh zadach teorii ustoychivosti [Solving non-conservative problems in stability theory]. Moscow, Fizmatlit Publ., 2017. 240 p. (In Russ.).

[12] Bigoni D.N., Kirillov O.N., Misseroni D. et al. Flutter and divergence instability in the Pfluger column: experimental evidence of the Ziegler destabilization paradox. J. Mech. Phys. Solids, 2018, vol. 116, pp. 99–116, doi: https://doi.org/10.1016/j.jmps.2018.03.024

[13] Kagan-Rozentsveyg L.M. Voprosy nekonservativnoy teorii ustoychivosti [Issues in non-conservative stability theory]. Sankt-Petersburg, SPbGASU Publ., 2014. 172 p. (In Russ.).

[14] Lagozinskiy S.A., Sokolov A.I. Ustoychivost pryamolineynykh sterzhney, nagruzhennykh sledyashchimi salami [Stability of a straight rod loaded by following forces]. V: Problemy prikladnoy mekhaniki, dinamiki i prochnosti mashin [In: Problems of applied mechanicsm dynamics and strength of machines]. Moscow, Bauman MSTU Publ., 2005, pp. 244–259. (In Russ.).

[15] Bolotin V.V., Zhinzher N.I. Effects of damping on stability of elastic systems subjected to nonconservative forces. Int. J. Solids Struct., 1969, vol. 5, no. 9, pp. 965–989, doi: https://doi.org/10.1016/0020-7683(69)90082-1