Characterisation of the numerical damping in the modal analysis of the forced vibrations of piecewise linear elastic structures

Primary tabs

Erre a témakiírásra nem lehet jelentkezni.
Nyilvántartási szám: 
20/12
Témavezető neve: 
Témavezető e-mail címe:
nemeth.robert@emk.bme.hu
A témavezető teljes publikációs listája az MTMT-ben:
A téma rövid leírása, a kidolgozandó feladat részletezése: 
Nonlinear Normal Modes received increasing interest in  the vibration analysis of nonlinear structral dynamics recently. As a generalization of the linear normal modes of a multi degree of freedom system or a continuum, these vibration modes serve as a basis for many usual engineering tasks, e.g. the analysis of the resonant modes and frequencies, the analysis of the stability of the vibration. Dynamic properties of the structures play important role in structural diagnostic, thus for slender structures the effects of nonlinearities must be considered in those tasks too.
In the civil engineering praxis the nonlinearity often occurs in the form of a piecewise linear behaviour. Closing and opening gaps, slackening cables are a few examples on structural elements, which cause the separation of the structural behaviour into piecewise linear states, where the stiffness is different. Still, each separated state can be treated as a linear elastic one inside its range of interpretation, which allows the usage of modal analysis. When the stiffness of the structure changes at the boundary of the range of interpretation, the current displacement and velocity field of the structure must be transformed from one basis to the other. During a numerical calculation the transformation occurs between two finite dimensional spaces formed by the basis of the different modal shapes, thus there will be an energy loss at every state change called numerical damping. In the case of free vibration this numerical damping can be bounded between an upper and lower value based on the soultion of a generalized eigenvalue problem. In the current research the same approach must be extended to the forced vibration problems. Based on the self-similarity constraint on the vibration modes an algorithm must be formed to obtain nonlinear normal modes of periodically forced piecewise linear structures. From the further analysis of the results an equivalent coefficient of resonance must be calculated. The equivalent damping and period time of the steady-state vibration must be compared to the numerical damping and the period times of free vibration normal modes.
A téma meghatározó irodalma: 
1. R. Rand. A direct method for non-linear normal modes. International Journal of Non-Linear Mechanics, 9(5): 363-368, 1974.
2. S.W. Shaw, P.J. Holmes. A periodically forced piecewise linear oscillator. Journal of Sound and Vibration, 90(1): 129-155, 1983.
3. E. J. Doedel, J. P. Kernévez, AUTO: Software for continuation and bifurcation problems in ordinary differential equations, Applied Mathematics Report, California Institute of Technology, Pasadena CA, 1986
4. E. J. Doedel, H. B. Keller, J. P. Kernévez, Numerical Analysis and Control Of Bifurcation Problems, Part I: Bifurcation in Finite Dimensions, Int. J. Bifurcation and Chaos 1 #3. 1991, 493-520.
5. E. J. Doedel, H. B. Keller, J. P. Kernévez, Numerical Analysis and Control Of Bifurcation Problems, Part II: Bifurcation in Infinite Dimensions, Int. J. Bifurcation and Chaos 1 #4. 1991, 745-772.
6. D. Jiang, C. Pierre, S.W. Shaw. Large-amplitude non-linear normal modes of piecewise linear systems. Journal of Sound and Vibration, 272(3-5):869-891, 2004.
7. A.F. Vakakis, O.V. Gendelman, L.A. Bergman, D.M. McFarland, G. Kerschen, Y.S. Lee. Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems I-II, Springer, 2008
8. S.D. Yu. An efficient computational method for vibration analysis of unsymmetric piecewise-linear dynamical systems with multiple degrees of freedom. Nonlinear Dyn (2013) 71:493–504
9. L. Renson, G. Kerschen, B. Cochelin. Numerical computation of nonlinear normal modes in mechanical engineering. Journal of Sound and Vibration 364 (2016) 177–206.
 
A téma hazai és nemzetközi folyóiratai: 
1. Journal of Sound and Vibration
2. International Journal of Non-Linear Mechanics
3. International Journal of Bifurcation and Chaos
4. Engineering Structures
5. Computers and Structures
6. Építés- Építészettudomány
7. Periodica Polytechnica Civil Engineering.
A témavezető utóbbi tíz évben megjelent 5 legfontosabb publikációja: 
1. Lengyel, G ; Németh, RK. Symmetric free vibration of cracked arches of rigid discrete blocks. ENGINEERING STRUCTURES 162 pp. 51-59. , 9 p. (2018)
2. Lengyel, G ; Németh, R K. Symmetric free vibration of a cracked, quasi-continuous, masonry arch. MECCANICA 53 : 4-5 pp. 1071-1091. , 21 p. (2018)
3. Németh, Róbert Károly ; Geleji B., Borbála. Nonlinear Normal Modes of a Piecewise Linear Continuous Structure with a Regular State. PERIODICA POLYTECHNICA-CIVIL ENGINEERING 62 : 4 pp. 1039-1051. , 13 p. (2018)
4. A. Kocsis, R. K. Németh, B. Turmunkh. Dynamic analysis of a beam on block-and-tackle suspension system: A continuum approach. ENGINEERING STRUCTURES 101: pp. 412-426. (2015)
5. R.K Németh, A. Kocsis. Bielastic web of links: A discrete model of Csonka's beam. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 63: pp. 49-59. (2014)
 
A témavezető fenti folyóiratokban megjelent 5 közleménye: 
1. Lengyel, G ; Németh, RK. Symmetric free vibration of cracked arches of rigid discrete blocks. ENGINEERING STRUCTURES 162 pp. 51-59. , 9 p. (2018)
2. Németh, Róbert Károly ; Geleji B., Borbála. Nonlinear Normal Modes of a Piecewise Linear Continuous Structure with a Regular State. PERIODICA POLYTECHNICA-CIVIL ENGINEERING 62 : 4 pp. 1039-1051. , 13 p. (2018)
3. A. Kocsis, R. K. Németh, B. Turmunkh. Dynamic analysis of a beam on block-and-tackle suspension system: A continuum approach. ENGINEERING STRUCTURES 101: pp. 412-426. (2015)
4. R.K Németh, A. Kocsis. Bielastic web of links: A discrete model of Csonka's beam. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 63: pp. 49-59. (2014)
5. A. Kocsis, R. K. Németh, Gy. Károlyi. Spatially Chaotic Bifurcations of an Elastic Web of Links. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 20:(12) pp. 4011-4028. (2010)

A témavezető eddigi doktoranduszai

Státusz: 
elfogadott