Geodesic
Modelling of mechanical systems basing on interconnected differential and partial differential equations
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 1, pp. 22-34 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper considers a boundary-value problem for a hybrid system of differential equations, which represents a generalized mathematical model for a system of interconnected rigid bodies attached to the rod by elastic-damping links. A hybrid system of differential equations is understood as a system of differential equations composed of ordinary differential equations and partial differential equations. For the theoretical foundations of our approach to investigation of the boundary value problem for the hybrid system of differential equations we propose a method of finding eigenvalues for the boundary-value problem. The comparative analysis of the results of numerical computations conducted with the use of the proposed method and the results obtained by other techniques known from the literature have proved the validity and the universal character of the proposed approach.
Keywords: boundary value problem; hybrid system of differential equations; eigenvalues. 
@article{VYURU_2017_10_1_a1,
     author = {A. D. Mizhidon},
     title = {Modelling of mechanical systems basing on interconnected differential and partial differential equations},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {22--34},
     year = {2017},
     volume = {10},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2017_10_1_a1/}
}
TY  - JOUR
AU  - A. D. Mizhidon
TI  - Modelling of mechanical systems basing on interconnected differential and partial differential equations
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2017
SP  - 22
EP  - 34
VL  - 10
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VYURU_2017_10_1_a1/
LA  - en
ID  - VYURU_2017_10_1_a1
ER  - 
%0 Journal Article
%A A. D. Mizhidon
%T Modelling of mechanical systems basing on interconnected differential and partial differential equations
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2017
%P 22-34
%V 10
%N 1
%U http://geodesic.mathdoc.fr/item/VYURU_2017_10_1_a1/
%G en
%F VYURU_2017_10_1_a1
A. D. Mizhidon. Modelling of mechanical systems basing on interconnected differential and partial differential equations. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 1, pp. 22-34. http://geodesic.mathdoc.fr/item/VYURU_2017_10_1_a1/

[1] Barguev S. G., Mizhidon A. D., “The Definion of an Own Frequency of Trivial Mechanical System on Elastic Foundation”, Bulletin of Buryat State University. Mathematics, Informatics, 2009, no. 9, 58–63 (in Russian)

[2] Mizhidon A. D., Barguev S. G., Lebedeva N. V., “To Research of a Vibroprotection System with Elastic Basement”, Modern Technologies. System Analysis. Modeling, 2009, no. 2(22), 13–20 (in Russian)

[3] Mizhidon A. D., Barguev S. G., “About Own Fluctuations of the Cascade Type Mechanical System Established on the Elastic Core”, Bulletin of East Siberia State University of Technology and Management, 2010, no. 1, 26–32 (in Russian)

[4] Barguev S. G., Eltoshkina E. V., Mizhidon A. D., Tsytsyrenova M. Zh., “Investigation of the Possibility of Fluctuations Damping of $n$ Masses Loid on an Elastic Rod”, Modern Technologies. System Analysis. Modeling, 2010, no. 4(28), 78–84 (in Russian)

[5] Barguev S. G., Mizhidon A. D., “Solution of the Initial Boundary Problem Vibrations of the Oscillator on the Elastic Rod”, Bulletin of Buryat State University. Mathematics, Informatics, 2012, no. 2, 63–68 (in Russian)

[6] Mizhidon A. D., Barguev S. G., “Boundary Value Problem for One Hybrid System of Differential Equations”, Bulletin of Buryat State University. Mathematics, Informatics, 2013, no. 9, 130–137 (in Russian)

[7] Mizhidon A. D., Tsytsyrenova M. Zh., “A Generalized Mathematical Model of Rigid Bodies Mounted on Elastic Rod”, Bulletin of East Siberia State University of Technology and Management, 2013, no. 6, 5–12 (in Russian)

[8] Mizhidon A. D., Dabaeva M. Zh., “Accounting for Elastic Ties Damping Properties in Generalized Mathematical Model of Solids System Mounted on Elastic Rod”, Bulletin of East Siberia State University of Technology and Management, 2015, no. 2, 10–17 (in Russian) | MR

[9] Cha P. D., “Free Vibration of a Uniform Beam with Multiple Elastically Mounted Two-degree-of-freedom Systems”, Journal of Sound and Vibration, 307:1–2 (2007), 386–392 | DOI

[10] Wu J.-J., Whittaker A. R., “The Natural Frequencies and Mode Shapes of a Uniform Cantilever Beam with Multiple Two-DOF Spring-Mass Systems”, Journal of Sound and Vibration, 227:2 (1999), 361–381 | DOI

[11] Wu J.-S., Chou H.-M., “A New Approach for Determining the Natural Frequencies and Mode Shapes of a Uniform Beam Carrying Any Number of Spring Masses”, Journal of Sound and Vibration, 220:3 (1999), 451–468 | DOI

[12] Wu J.-S., “Alternative Approach for Free Vibration of Beams Carrying a Number of Two-Degree of Freedom Spring-Mass Systems”, Journal of Structural Engineering, 128:12 (2002), 1604–1616 | DOI

[13] Naguleswaran S., “Transverse Vibration of an Euler–Bernoulli Uniform Beam Carrying Several Particles”, International Journal of Mechanical Sciences, 44:12 (2002), 2463–2478 | DOI | Zbl

[14] Naguleswaran S., “Transverse Vibration of an Euler–Bernoulli Uniform Beam on up a Five Resilient Supports Including End”, Journal of Sound and Vibration, 261:2 (2003), 372–384 | DOI

[15] Kukla S., Posiadala B., “Free Vibrations of Beams with Elastically Mounted Masses”, Journal of Sound and Vibration, 175:4 (1994), 557–564 | DOI | Zbl

[16] Su H., Banerjee J. R., “Exact Natural Frequencies of Structures Consisting of Two Part Beam-Mass Systems”, Structural Engineering and Mechanics, 19:5 (2005), 551–566 | DOI

[17] Lin H.-Y., Tsai Y.-C., “Free Vibration Analysis of a Uniform Multi-Span Beam Carrying Multiple Spring-Mass Systems”, Journal of Sound and Vibration, 302:3 (2007), 442–456 | DOI

[18] Wu J.-S., Chen D.-W., “Dynamic Analysis of Uniform Cantilever Beam Carrying a Number of Elastically Mounted Point Masses with Dampers”, Journal of Sound and Vibration, 229:3 (2000), 549–578 | DOI

[19] Vladimirov V. S., Generalized Solutions in Mathematical Physics, Nauka, M., 1976, 280 pp. | MR