Buradasınız

Çok Sayıda Elastik Mesnetli Rijit Çubuk Taşıyan Eksenel Yüklü Çok Kademeli Timoshenko Kirişinin Serbest Titreşim Analizi

Free Vibration Analysis of the Axial-Loaded Timoshenko Multiple-Step Beam Carrying Multiple Elastic-Supported Rigid Bars

Journal Name:

Publication Year:

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In this paper, the natural frequencies of the axial-loaded Timoshenko multiple-step beam carrying multiple elastic-supported rigid bars are calculated. At first, the coefficient matrices for the elastic-supported rigid bars, the step change in cross-section, left-end support and right-end support of the multiple-step beam are derived. Next, the numerical assembly technique is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the system. The natural frequencies of the beams by using secant method for the different values of axial force are presented in tables.
Abstract (Original Language): 
Bu çalışmada, çok sayıda elastik mesnetli rijit çubuk taşıyan, eksenel yüke maruz, çok kademeli Timoshenko kirişinin doğal frekansları hesaplanmıştır. İlk olarak, elastik mesnetli rijit çubukların, kiriş en kesitinin değiştiği noktaların, sol uç mesnetin ve sağ uç mesnetin kat sayılar matrisi elde edilmiştir. Sonra, nümerik toplama tekniği kullanılarak titreşen sistemin bileşik katsayılar matrisi kurulmuştur. Son olarak, bileşik katsayılar matrisinin determinantı sıfıra eşitlenerek sistemin doğal frekansları hesaplanmıştır. Farklı eksenel kuvvet değerleri için secant metodu kullanılarak hesaplanan kiriş doğal frekans değerleri tablolar halinde sunulmuştur.
182
197

REFERENCES

References: 

Chen, D.W. 2003. The exact solutions for the natural frequencies and mode shapes of nonuniform beams carrying multiple various concentrated elements. Structural Engineering and Mechanics. (16), 153-176.
Chen, D.W. and Wu, J.S. 2002. The exact solutions for the natural frequencies and mode shapes of non-uniform beams with multiple spring-mass system. Journal of Sound and Vibration. (255), 299-322.
Gürgöze, M.
1984
. A note on the vibrations of restrained beams and rods with point masses. Journal of Sound and Vibration. (96), 461-468.
Gürgöze, M.
1985
. On the vibration of restrained beams and rods with heavy masses. Journal of Sound and Vibration. 100, 588-589.
Gürgöze,
M
. 1996. On the eigenfrequencies of a cantilever beam with attached tip mass and a spring-mass system. Journal of Sound and Vibration. (190), 149-162.
Gürgöze,
M
. 1998. On the alternative formulation of the frequency equation of a Bernoulli-Euler beam to which several spring-mass systems are attached in-span. Journal of Sound and Vibration. (217), 585-595.
Gürgöze, M.
an
d Batan, H. 1996. On the effect of an attached spring-mass system on the frequency spectrum of a cantilever beam. Journal of Sound and Vibration. (195), 163¬168.
Gürgöze,
M
. and Erol, H. 2001. Determination of the frequency response function of a cantilever beam simply supported in-span. Journal of Sound and Vibration. (247), 372-378.
Gürgöze,
M
. and Erol, H. 2002. On the frequency response function of a damped cantilever beam simply supported in-span and carrying a tip mass. Journal of Sound and Vibration. (255),
489-500.
Hamdan,
M.N
. and Jubran, B.A. 1991. Free and forced vibrations of a restrained uniform beam carrying an intermediate lumped mass and a rotary inertia. Journal of Sound and Vibration.
(150), 203-216.
Koplow, M.A., Bhattacharyya, A. and Mann, B.P. 2006. Closed form solutions for the dynamic response of Euler-Bernoulli beams with step changes in cross-section. Journal of Sound and Vibration. (295), 214-225.
Lin, H.P. and Chang, S.C. 2005. Free vibration analysis of multi-span beams with intermediate flexible constraints. Journal of Sound and Vibration. (281), 155-169.
Lin, H.Y. 2008. Dynamic analysis of a multi-span uniform beam carrying a number of various concentrated elements. Journal of Sound and
Vibration. (309), 262-275.
Lin, H.Y. 2010. An exact solution for free vibrations of a non-uniform beam carrying multiple elastic-supported rigid bars. Structural Engineering and Mechanics. (34), 399-416.
Lin, H.Y. and Tsai, Y.C. 2005. On the natural frequencies and mode shapes of a uniform multi-span beam carrying multiple point masses. Structural Engineering and Mechanics.
(21), 351-367.
Lin, H.Y. and Tsai, Y.C. 2006. On the natural frequencies and mode shapes of a multiple-step beam carrying a number of intermediate
Pamukkale University, Journal of Engineering Sciences, Vol. 18, No. 3, 2012
196
Free Vibration Analysis of the Axial-Loaded Timoshenko Multiple-Step Beam Carrying Multiple Elastic-Supported Rigid Bars
lumped masses and rotary inertias. Structural Engineering and Mechanics. (22), 701-717.
Lin, H.Y. and Tsai, Y.C. 2007. Free vibration analysis of a uniform multi-span beam carrying multiple spring-mass systems. Journal of Sound
and Vibration. (302), 442-456.
Liu, W.H., Wu, J.R. and Huang, C.C. 1998. Free vibration of beams with elastically restrained edges and intermediate concentrated masses. Journal of Sound and Vibration. (122), 193-207.
Naguleswaran, S. 2002a. 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. (252), 751-767.
Naguleswaran, S. 2002b. Vibration of an Euler-Bernoulli beam on elastic end supports and with up to three-step changes in cross-section. International Journal of Mechanical Science.
(44) , 2541-2555.
Naguleswaran, S. 2002c. Transverse vibrations of an Euler-Bernoulli uniform beam carrying several particles. International Journal of
Mechanical Science. (44), 2463-2478.
Naguleswaran, S. 2003a. Transverse vibration of an Euler-Bernoulli uniform beam on up o five resilient supports including ends. Journal of Sound and Vibration. (261), 372-384.
Naguleswaran, S. 2003b. Vibration and stability of an Euler-Bernoulli beam with up to three-step changes in cross-section and in axial force. International Journal of Mechanical Science.
(45) , 1563-1579.
Naguleswaran, S. 2004a. Transverse vibration and stability of an Euler-Bernoulli beam with step change in cross-section and in axial force. Journal of Sound and Vibration. 270, 1045-1055.
Naguleswaran, S. 2004b. Vibration of an Euler-Bernoulli stepped beam carrying a non-symmetrical rigid body at the step. Journal of Sound and Vibration. (271), 1121-1132.
Wang, J.R., Liu, T.L., Chen, D.W. 2007. Free
vibration analysis of a Timoshenko beam carrying multiple spring-mass systems with the effects of shear deformation and rotatory inertia. Structural Engineering and Mechanics.
(26), 1-14.
Wu, J.S. and Chen, C.T. 2008. A continuous-mass TMM for free vibration analysis of a non-uniform beam with various boundary conditions and carrying multiple concentrated elements. Journal of Sound and Vibration. (311),
1420-1430.
Wu, J.S. and Chen, D.W. 2001. Free vibration analysis of a Timoshenko beam carrying multiple spring-mass systems by using the numerical assembly technique. International Journal for Numerical Methods in Engineering.
(50), 1039-1058.
Wu, J.S. and Chou, H.M. 1999. A new approach for determining the natural frequencies and mode shape of a uniform beam carrying any number of spring masses. Journal of Sound and Vibration. (220), 451-468.
Yesilce, Y. 2010. Effect of axial force on the free vibration of Reddy-Bickford multi-span beam carrying multiple spring-mass systems. Journal of Vibration and Control. (16), 11-32.
Yesilce, Y. and Demirdag, O. 2008. Effect of
axial force on free vibration of Timoshenko multi-span beam carrying multiple spring-mass systems. International Journal of Mechanical
Science. (50), 995-1003.
Yesilce, Y., Demirdag, O. and Catal, S. 2008. Free vibrations of a multi-span Timoshenko beam carrying multiple spring-mass systems.
Sadhana. (33), 385-401.
Zhou, D. 1997. The vibrations of a cantilever beam carrying a heavy tip mass with elastic supports. Journal of Sound and Vibration. (206),
275-279.

Thank you for copying data from http://www.arastirmax.com