Free vibration of a cantilever tapered Timoshenko beam

• Autorzy: Cekus D.
• Języki publikacji: EN

Abstrakty

EN

In this paper the Lagrange multiplier formalism has been used to find a solution of free vibration problem of a cantilever tapered beam. The beam has been circumscribed according to the Timoshenko theory. The sample numerical calculations for the cantilever tapered beam have been carried out and compared with experimental results to illustrate the correctness of the present method.

Słowa kluczowe

EN

free vibration; Timoshenko beam; Timoshenko theory; tapered beam

PL

drgania swobodne; teoria Timoshenki

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2012
• Tom: Vol. 11, nr 4
• Strony: 11--17
• Opis fizyczny: Bibliogr. 14 poz., rys., tab.

Twórcy

autor

Cekus D.

• Institute of Mechanics and Machine Design Foundations Czestochowa University of Technology, Czestochowa, Poland,

Bibliografia

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• [2] Hsu J.H., Lai H.Y., Chen C.K., Free vibration of non-uniform Euler-Bernoulli beams with general elastically end constraints using Adomian modified decomposition method, Journal of Sound and Vibration 2008, 318, 965-981.
• [3] Yagci B., Filiz S., Romero L.L., Ozdoganlar O.B., A spectral-Tchebychev technique for solving linear and nonlinear beam equations, Journal of Sound and Vibration 2009, 321, 375-404.
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• [5] Eisenberger M., Dynamic stiffness matrix for variable cross-section Timoshenko beams, Communications in Numerical Methods in Engineering 1995, 11, 507-513.
• [6] 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.
• [7] Liao M., Zhong H., Nonlinear vibration analysis of tapered Timoshenko beams, Chaos, Solitons and Fractals 2008, 36, 1267-1272.
• [8] Attarnejad R., Semnani S.J., Shahba A., Basic displacement functions for free vibration analysis of non-prismatic Timoshenko beams, Finite Elements is Analysis and Design 2010, 46, 916-929.
• [9] 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.
• [10] Timoshenko S.P., On the transverse vibrations of bars of uniform cross section, Philosophical Magazine 1922, 6(43), 379-384.
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• [12] Posiadała B., Modelling and analysis of continuous-discrete mechanical systems, Application of the Lagrange multiplier formalism, Seria Monografie nr 136, Wydawnictwo Politechniki Częstochowskiej, Częstochowa 2007 (in Polish).
• [13] Cekus D., Use of Lagrange multiplier formalism to solve of transverse vibrations problem of stepped beams according to Timoshenko theory, Scientific Research of the Institute of Mathematics and Computer Science 2011, 2(10), 49-56.
• [14] Cowper G.R., The shear coefficient in Timoshenko’s beam theory, Journal of Applied Mechanics 1966, 33(2), 335-340.