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Use of Lagrange multiplier formalism to solve transverse vibrations problem of stepped beams according to Timoshenko theory

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Języki publikacji
EN
Abstrakty
EN
In this paper Lagrange multiplier formalism has been used to find a solution to a free transverse vibrations problem of stepped beams. The beams have been circumscribed according to the Timoshenko theory. The sample numerical calculations for a cantilever two-stepped beam have been carried out to illustrate the validity and accuracy of the present method.
Rocznik
Strony
49--56
Opis fizyczny
Bibliogr. 18 poz., rys., tab.
Twórcy
autor
  • Institute of Mechanics and Machine Design Foundations Czestochowa University of Technical, Poland, cekus@imipkm.pcz.pl
Bibliografia
  • [1] Jang S., Bert C., Free vibration of stepped beams: exact and numerical solutions, Journal of Sound and Vibration 1989, 130, 342-346.
  • [2] Maurizi M., Belles P., Natural frequencies of one-span beams with stepwise variable cross-section, Journal of Sound and Vibration 1993, 168, 184-188.
  • [3] De Rosa M., Belles N., Maurizi M., Free vibrations of stepped beams with intermediate elastic supports, Journal of Sound and Vibration 1995, 181, 905-910.
  • [4] Popplewell N., Chang D., Free vibrations of a complex Euler-Bernoulli beam, Journal of Sound and Vibration 1996, 190, 852-856.
  • [5] Naguleswaran S., Natural frequencies, sensitivity and mode shape details of an Euler-Bernoulli beam with one-step change in cross-section and with ends on classical supports, Journal of Sound and Vibration 2002, 252, 751-767.
  • [6] Wilczak R., The use of Lagrange multiplier formalism to analyze free torsional vibrations of shafts, longitudinal vibrations of rods and lateral vibrations of beams with step change in their cross-section with additional discrete elements, Praca doktorska, Częstochowa 2006 (in Polish).
  • [7] Timoshenko S.P., On the correction for shear of the differential equation for transverse vibrations of prismatic bars, Philosophical Magazine 1921, 6(41), 744-746.
  • [8] Timoshenko S.P., On the transverse vibrations of bars of uniform cross section, Philosophical Magazine 1922, 6(43), 379-384.
  • [9] Rossi R.E., Laura P.A.A., Gutierez R.H., A note on transverse vibrations of a Timoshenko beam of non-uniform thickness clamped at one end carrying a concentrated mass at the other, Journal of Sound and Vibrations 1990, 143(3), 491-502.
  • [10] Tong X., Tabarrok B., Vibration analysis of Timoshenko beams with non-homogeneity and varying cross-section, Journal of Sound and Vibrations 1995, 186(5), 821-835.
  • [11] Farghaly S.H., Gadelrab R.M., Free vibrations of a stepped composite Timoshenko cantilever beam, Journal of Sound and Vibrations 1995, 187(5), 886-896.
  • [12] Poppllewell N., Chang D., Free vibrations of a stepped, spinning Timoshenko beam, Journal of Sound and Vibrations 1997, 203(4), 717-722.
  • [13] Kukla S., Zamojska I., Frequency analysis of axially loaded stepped beams by Green’s function method, Journal of Sound and Vibrations 2007, 300, 1034-1041.
  • [14] Kukla S., Dynamic Green’s Functions in Free Vibration Analysis of Continuous and Discrete-continuous Mechanical Systems, Serie Monografie nr 64, Wydawnictwo Politechniki Częstochowskiej, Częstochowa 1999 (in Polish).
  • [15] Dong X.-J., Meng G., Li H.-G., Ye L., Vibration analysis of a stepped laminated composite Timoshenko beam, Mechanics Research Communications 2005, 32, 572-581
  • [16] Posiadała B., Free vibrations of uniform Timoshenko beams with attachments, Journal of Sound and Vibrations 1997, 204(2), 359-369.
  • [17] Posiadała B., Modelling and Analysis of Continuous-discrete Mechanical Aystems. Application of the Lagrange Multiplier Formalism, Seria Monografie nr 136, Wydawnictwo Politechniki Częstochowskiej, Częstochowa 2007 (in Polish).
  • [18] Meirovitch L., Analytical Methods in Vibrations, The Macmillan Company, New York 1967.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPC6-0016-0006
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