Reut and Beck columns: effects of end gravity forcé, translation and rotational inertias

Luis G. Arboleda Monsalve; David G. Zapata Medina; J. Darío Aristizabal Ochoa

doi:10.17533/udea.redin.14229

Autores/as

Luis G. Arboleda Monsalve Universidad del Noroeste
David G. Zapata Medina Universidad del Noroeste
J. Darío Aristizabal Ochoa Universidad Nacional de Colombia

DOI:

https://doi.org/10.17533/udea.redin.14229

Palabras clave:

columnas, pandeo, estabilidad dinámica, estabilidad estática, flameo, fuerzas no conservativas, columnas de Beck y Reut

Resumen

La estabilidad de las columnas de Reut y Beck sometidas a cualquier combinación de fuerzas axiales comprensivas de gravedad y no conservadoras (línea fija de seguidor) se presenta utilizando la formulación dinámica. El método propuesto consiste en los efectos de la fuerza de gravedad final, las inercias de traslación y rotación a lo largo del miembro. Los resultados analíticos están destinados a capturar el límite en el rango de aplicabilidad del método estático o de Euler en el análisis de estabilidad de columnas delgadas y definir la transición de la inestabilidad estática (con frecuencia cero) a la inestabilidad dinámica ("flutter"). Finalmente, se presenta la comparación entre las ecuaciones de estabilidad características de las columnas delgadas de Reut y Beck.

|Resumen

= 187 veces | PDF

= 63 veces|

Descargas

Los datos de descargas todavía no están disponibles.

Biografía del autor/a

J. Darío Aristizabal Ochoa, Universidad Nacional de Colombia

Escuela de Minas.

Citas

V. Bolotin. Non-conservative Problems of the Theory of Elastic Stability. 1st Ed. The Macmillan Company. New York, USA. 1963. pp .234.

Y. Panovko, I. Gubanova. Stability and Oscillations of Elastic Systems: Paradoxes, Fallacies, and New Concepts. 1st ed. Ed Springer. New York, USA. 1965. pp. 291.

V. Feodosyev. Selected Problems and Questions in Strength of Materials. Ed. MIR Publishers. Moscow, Russian. 1977. pp. 265-269.

M. Langthjem, Y. Sugiyama. “Dynamic stability of columns subjected to follower loads: a survey”. J. of Sound and Vibration. Vol. 238. 2000. pp. 809-851. DOI: https://doi.org/10.1006/jsvi.2000.3137

Y. Sugiyama, S. Ryu, M. Langthjem. “Beck’s column as the ugly duckling”. J. of Sound and Vibration. Vol. 254. 2002. pp. 407-410. DOI: https://doi.org/10.1006/jsvi.2002.5003

I. Elishakoff. “Controversy associated with the so-called “follower forces”: critical overview”. Applied Mechanics Reviews. Vol. 58. 2005. pp. 117-142. DOI: https://doi.org/10.1115/1.1849170

Y. Sugiyama, K. Katayama, S. Kinoi. “Flutter of cantilevered column under rocket thrust.” J. of Aerospace Engineering ASCE. Vol. 8. 1995. pp. 9-15. DOI: https://doi.org/10.1061/(ASCE)0893-1321(1995)8:1(9)

S. Ryu, Y. Sugiyama. “Computational dynamics approach to the effect of damping on stability of a cantilevered column subjected to a follower force”. Computers and Structures. Vol. 81. 2003. pp. 265-271. DOI: https://doi.org/10.1016/S0045-7949(02)00436-4

L. Kwasniewski. “Numerical verification of post-critical Beck’s column behavior”. International J. of Non-Linear Mechanics. Vol. 45. 2010. pp. 242-255. DOI: https://doi.org/10.1016/j.ijnonlinmec.2009.11.007

K. Sato. “Instability of a clamped-elastically restrained Timoshenko column carrying a tip load subjected to a follower force”. J. of Sound and Vibration. Vol. 194. 1996. pp. 623-630. DOI: https://doi.org/10.1006/jsvi.1996.0381

Q. Zuo, H. Schreyer. “Flutter and divergence instability of nonconservative beams and plates”. International J. of Solids and Structures. Vol. 33. 1996. pp. 1355-1367. DOI: https://doi.org/10.1016/0020-7683(95)00097-6

W. Glabisz. “Vibration and stability of the beam with elastic supports and concentrated masses under conservative and nonconservative forces”. Computers and Structures. Vol. 70. 1999. pp. 305-313. DOI: https://doi.org/10.1016/S0045-7949(98)00181-3

I. Elishakoff, N. Impollonia. “Does a partial elastic foundation increase the flutter velocity of a pipe conveying fluid?”. J. of Applied Mechanics. ASME. Vol. 68. 2001. pp. 206-212. DOI: https://doi.org/10.1115/1.1354206

A. Kounadis. “Nonclassical stability problems: Instability of slender tubes under pressure”. J. of Aerospace Engineering. ASCE. Vol. 14. 2001. pp. 6-11. DOI: https://doi.org/10.1061/(ASCE)0893-1321(2001)14:1(6)

S. Andersen, J. Thomsen. “Post-critical behavior of Beck’s column with a tip mass”. International J. of Non-Linear Mechanics. Vol. 37. 2002. pp. 135-151. DOI: https://doi.org/10.1016/S0020-7462(00)00102-5

B. Rao, G. Rao. “Post-critical behavior of Euler and Beck columns resting on an elastic foundation”. J. of Sound and Vibration. Vol. 276. 2004. pp. 1150-1158. DOI: https://doi.org/10.1016/j.jsv.2003.11.007

F. Detinko. “Lumped damping and stability of Beck column with a tip mass”. International J. of Solids and Structures. Vol. 40. 2003. pp. 4479-4486. DOI: https://doi.org/10.1016/S0020-7683(03)00298-1

E. Viola, A. Marzani. “Crack effect on dynamic stability of beams under conservative and non-conservative forces”. Engineering Fracture Mechanics. Vol. 71. 2004. pp. 699-718. DOI: https://doi.org/10.1016/S0013-7944(03)00019-5

J. Aristizabal. “Static stability of beam-columns under combined conservative and nonconservative end forces: effects of semirigid connections”. J. of Engineering Mechanics. ASCE. Vol. 131. 2005. pp. 473-484. DOI: https://doi.org/10.1061/(ASCE)0733-9399(2005)131:5(473)

J. Hernandez, J. Aristizabal. “Static and dynamic stability of an elastically restrained Beck column with an attached end mass”. J. of Sound and Vibration. Vol. 312. 2008. pp. 789-800. DOI: https://doi.org/10.1016/j.jsv.2007.11.014

D. Zapata, L. Arboleda, J. Aristizabal. “Static stability formulas of a weakened Timoshenko column: effects of shear deformations”. J. of Engineering Mechanics. ASCE. Vol. 136. 2010. pp. 1528-1536. DOI: https://doi.org/10.1061/(ASCE)EM.1943-7889.0000193

R. Clough, J. Penzien. Dynamics of Structures. 2nd Ed. McGraw – Hill Book Co. New York, USA. 1993. pp. 783

A. Chopra. Dynamics of Structures: Theory and Applications to Earthquake Engineering. 2nd ed. Prentice Hall. New Jersey, USA. 2000. pp. 844.

S. Timoshenko, J. Gere. Theory of Elastic Stability. Engineering Societies Monographs. 2nd ed. Ed. McGraw–Hill Book Company. New York, USA. 1961. pp. 55-59.