Natural vibration frequencies of tapered beams

• Autorzy: Rosa de M. A. , Lipiello M.
• Języki publikacji: EN

Abstrakty

EN

In this paper the free vibrations frequencies of tapered Euler-Bernoulli beams are calcu-lated, in the presence of an arbitrary number of rotationally and/or axially, elastically flexible constraints. The dynamic analysis is performed by means of the so-called cell discretization method (CDM), according to which the beam is reduced to a set of rigid bars, linked together by elastic sections, where the bending si iffness and the distributed mass of the bars is concentrated. The resulting stiffness matrix and mass matrix are easily deduced, and the generalized symmetric eingenvalue problem can be immediately solved. Various numerical comparisons allow us to show the potentialities of the proposed approach.

Słowa kluczowe

EN

free vibrations; tapered beam; elastically restrained; CDM

PL

wolne wibracje; belka; wydłużenie elastyczne

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2009
• Tom: Vol. 57, iss. 1
• Strony: 45--66
• Opis fizyczny: Bibliogr. 23 poz., wykr.

Twórcy

autor

Rosa de M. A.

autor

Lipiello M.

• Faculty of Engineering Department of Structural Engineering, (DiSGG), Potenza, Italy

Bibliografia

• 1. L. CRAVER Jr., P. JAMPALA, Transverse vibrations of a linearly tapered cantilever beam with constraining springs, J. of Sound and Vibr, 166. 521-529, 1993.
• 2. M. A. DE ROSA, N. M. AUCIELLO, Free vibrations of tapered beams with flexible ends, Comp. & Struct., 60, 197-202, 1996.
• 3. A. K. DATTA, S.N. SIL, An analysis of free undamped vibration of beams of varying cross-section, Comp. &: Struct., 59, 479-483, 1996.
• 4. S. ABRATE, Vibration of non-uniform rods and beams, J. of Sound and Vibr., 185, 703-716, 1995.
• 5. R. O. GROSSI, B. DEL V. ARENAS, A variational approach to the vibration of tapered beams with elastically restrained ends. J. of Sound and Vibr., 195, 507-511, 1996.
• 6. Y. Mou, R. P. HAN, A. H. SHAH, Exact dynamic stiffness matrix for beams of arbitrarily varying cross-sections, Int. J. Num. Methods Engrg., 40, 233-250, 1997.
• 7. D. ZHOU, Y. K. CHEUNG, The free vibrations of a type of tapered beams, Comput. Methods Appl. Mech. Engrg., 188, 203-216, 2000.
• 8. P. A. A. LAURA, R. H. GUTIERREZ, R. E. ROSSI, Free vibrations of beams of bilinearly varying thickness, Ocean Engrg, 23, 1-6, 1996.
• 9. N. M. AuciELLO, G. NOLE, Vibrations of a cantilever tapered beam with varying section properties and carrying a mass at the free end, J. of Sound and Vibr., 214, 105-119, 1998.
• 10. N. M. AuciELLO, A. ERCOLANO, Exact solution for the transverse vibration of beam, a part of which is a taper beam and other part is a uniform beam, Int. J. Solids Structures, 34, 2115-2129, 1998.
• 11. P. RUTA. Application of Chebyshev series to solution of non-prismatic beam vibration problems, J. of Sound and Vibr., 227 (2), 449-467, 1999.
• 12 P. RUTA, Dynamic stability problem of a non-prismatic rod, J. of Sound and Vibr., 250 (3), 445-464, 2002.
• 13. P. RUTA, The vibration of a non-prismatic beam on an inertial elastic half-plane, J. of Sound and Vibr., 275, 533-556, 2004.
• 14. P. RUTA, The application of Chebyshev polynomials to the solution of the non-prismatic Timoshenko beam vibration problem, J. of Sound and Vibr., 296, 243-263, 2006-
• 15. M. A. DE ROSA, Stability and dynamics of beams on Winkler elastic foundations, Earth. Engrg. Struct. Dyn., 18, 377-388, 1989.
• 16. M. A. DE ROSA, Stability and dynamic analysis of two- parameter foundation beams, (!omp. & Struct., 49, 341-349, 1993.
• 17. S. WOLFRAM, The Mathematica Book, 4rd edition, Wolfram Media Cambridge University Press, Cambridge, 1999.
• 18. W. T. THOMSON, Theory of vibration with applications, Englewood Cliff, New Jersey, I'rontice-Hall, (1972).
• 19. D. H. HODGES, Y. Y. CHUNG, X. Y. SHANG, Discrete transfer matrix method for nonuniform rotating beams, J. of Sound and Vibr., 169, 276-283, 1994.
• 20. C. S. KIM, S. M. DICKINSON, On the analysis of laterally vibrating slender beams to various complicating effects, J. of Sound and Vibr, 122, 441-455, 1988.
• 21. J. H. LAU, Vibration frequencies of tapered bars with end mass, ASME J. Appl. Mech., 51, 179-181, 1984.
• 22. S. NAGULESWARAN, A direct solution of Euler-Bernoulli wedge and cone beams, J. of Sound and Vibr., 172, 289-304, 1984.
• 23. M. C. ECE, M. AYDOGDU, V. TASKIN, Vibration of a variable cross-section beams, Mech. Res. Comm., 34, 78-84, 2007.