• Liudmila Ya. BanakhEmail author
  • Mark L. Kempner
Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)


A broad class of systems in nature and engineering is represented by regular structures consisting of repeated elements or having a geometrical symmetry. A significant amount of research in various fields of science is devoted to the study of such systems.


Dispersion Equation Regular Structure Repeated Element Regular System Dynamic Compliance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 35.
    Filin, A.P., Tananajko O.D. et al.: Algorithms of Resolving Equations of Rod Systems. Strojizdat, Moscow (Russian) (1983)Google Scholar
  2. 11.
    Banakh, L.: Decomposition methods for vibration analysis of large mechanical systems. In: Proceedings of the 2nd European Nonlinear Oscillations Conference, Academy of Sci, of Czech Republic Prague, vol. 1, 73–76 (1996)Google Scholar
  3. 36.
    Fillippov, A.G.: Oscillations of Mechanical Systems. Naukova Dumka, Kiev (Russian) (1965)Google Scholar
  4. 44.
    Grodko, L.N.: About Small Oscillations of Mechanical Systems having Circular Symmetry. Izv. AN SSSR, 1, Moscow (Russian) (1967)Google Scholar
  5. 48.
    Kandidov, V.P., Chesnokov, S.S.: Application of Finite Elements Method for Calculation of Transversal Oscillations for One-dimensional Systems. Vestnik of Moscow State University, series 3, 4, (Russian) (1971)Google Scholar
  6. 26.
    Buryshkin, M.L., Gordeev, V.I.: Effective Methods and Calculation Programs for Symmetric Constructions. Budivelnik, Kiev (Russian) (1984)Google Scholar
  7. 61.
    Khammermesh, M.: The Theory of Groups and its Application to Physical Problems. Mir, Moscow (Russian) (1966)Google Scholar
  8. 9.
    Banakh, L.: Decomposition methods in oscillations of multi- dimensional systems. Doklady AN, Technical physics 337(2), 189–193, Moscow (Russian) (1994)Google Scholar
  9. 75.
    Mandelbrot, B.B.: Fractal Geometry of Nature. Institute of Computer Researches, Moscow (Russian) (2002)Google Scholar
  10. 31.
    Dondoshanskii, V.K.: Calculation of Oscillations of Elastic Systems on Electronic Computers. Mashinostroenie, Moscow-Leningrad (Russian) (1965)Google Scholar
  11. 80.
    Nagaev R.F., Chodzhaev K.Sh.: Oscillations of Mechanical Systems with Periodic Structure FAN Uzbek SSR, Tashkent (Russian) (1973)Google Scholar
  12. 71.
    Lyubarskii G.Ya.: Theory of Groups and its Application in Physics. Gostehizdat, Moscow (Russian) (1957)Google Scholar
  13. 10.
    Banakh L.: The weak interactions by mechanical systems oscillations. Doklady AN., Mechanics, 337, 336–338, Moscow (Russian) (1994)Google Scholar
  14. 92.
    Perminov, M.D., Petrov, V.D.: Research of oscillations of complicate systems by a partitions method. In: Dynamics and Durability of Elastic and Hydro-elastic Systems, Nauka, Moscow (Russian), 41–52 (1975)Google Scholar
  15. 33.
    Fedoseev, Yu., Pusakina A.: Analysis of dynamics of mechanical systems with help of symmetry groups. In: Problemy masinostrojenia i nadezhnost mashin, 1, Moscow (Russian) 26–34 (2009)Google Scholar
  16. 69.
    Landa, P.S.: Nonlinear Oscillations and Waves in Dynamical Systems. Dordrecht-Boston-London: Kluwer Academic Publ. (1996)Google Scholar
  17. 54.
    Kempner, M.L.: Application of topology methods for calculation of the connected oscillations of gasturbine engines. In: Problems of Dynamic and Durability of Engines. Leningrad (Russian) (1973)Google Scholar
  18. 70.
    Lashchennikov, B.J., Dolotkazin, D.V.: About application of a finite elements method in problems of waves distribution. The Building Mechanics and Calculation of Constructions 6, 52–54 (Russian) (1983)Google Scholar
  19. 45.
    Ivanov, V.P.: About some vibrating properties of the elastic systems, having cyclic symmetry. In: Durability and Dynamics of Aviation Engines, vol. 6, Mashinostrojenie, Moscow (Russian) pp. 113–132 (1971)Google Scholar
  20. 115.
    Zlokovich, J.: Theory of Groups and G-vector Spaces in Oscillations, Stability and a Static of Constructions. Strojizdat, Moscow (Russian) (1977)Google Scholar
  21. 64.
    Kollatz, L.: Eeigenvalues Problems. Nauka, Moscow (Russian) (1966)Google Scholar
  22. 91.
    Painter, P., Coleman, M, et al.: The theory of Vibrational Spectroscopy. A Wiley-Interscience Publication, John Wiley, New York (1986)Google Scholar
  23. 25.
    Brillyuan, L., Parodi, M.: Distribution of Waves in Periodic Structures. Inostrannaya literature, Moscow (Russian) (1959)Google Scholar
  24. 67.
    Kron, G. Kron, G.: Research of complicated systems in parts. Diakoptika. Nauka, Moscow (Russian) (1972)Google Scholar
  25. 76.
    Mandelstam, L.: The Lectures on the Oscillations Theory. Nauka, Moscow (Russian) (1972)Google Scholar
  26. 55.
    Kempner, M.L., Tselnits, D.S.: Oscillations of Systems with Cyclic Symmetry. In: Trudy MIIT, vol. 476, Moscow (Russian) 25–32 (1975)Google Scholar
  27. 27.
    Collatz L.: Eigenwertaufgoben mit technishen Anwendungen. Akademische Verlagsgesselshaft Geest & Portig K.-G., Leipzig (1963)Google Scholar
  28. 29.
    Dinkevich, S.Z.: Calculation of Cyclic Constructions. A Spectral Method. Strojizdat, Moscow (Russian) (1977)Google Scholar
  29. 108.
    Vejts, V.L., Kolovskij, M.Z., et al.: Dynamics of Controlled Machine Aggregates. Mashinostrojenie, Moscow (Russian) (1984)Google Scholar
  30. 82.
    Nayfe, A.A: Perturbation Methods. Mir, Moscow Moscow (Russian) (1976)Google Scholar
  31. 84.
    Ovsyannikov, L.B.: Group Analysis of Differential Equations. Nauka, Moscow (Russian) (1978)zbMATHGoogle Scholar
  32. 22.
    Bleich, F.: The Equations in Finite Differences for Constructions Statics, Gostechizdat, Kharkov (Russian) (1933)Google Scholar
  33. 78.
    Maslov, V.P., Rimskii-Korsakov, A.V.: Plane wave in a plate with parallel ribs. In: Vibration and Noise, Nauka, Moscow 29–38 (Russian) (1969)Google Scholar
  34. 89.
    Pain, H.J.: Physics of Vibrations and Waves. John Willey. London, (1976)zbMATHGoogle Scholar
  35. 110.
    Vulfson J.I.: Vibroactivity of Branched and Ring Structured Mechanical Drives. Hemisphere Publ. Corpor.: New York, Washington, London (1998)Google Scholar
  36. 86.
    Palmov, V.A., Pervozvanskii, A.A.: About computing features of matrix calculation methods for oscillations. Trudy LPI, 210, Dynamic and Durability of Machines, Mashgis, Moscow-Leningrad (Russian) (1960)Google Scholar
  37. 53.
    Kempner, M.L.: Dynamic compliances and stiffness methods for calculation of bending oscillations of elastic systems with many degrees of freedom. In: Transversal Oscillations and Critical Speeds, Ed. AN SSSR, Moscow (Russian) pp. 78–130 (1951)Google Scholar
  38. 37.
    Fomin,V.M.: Application of the theory groups representation to definition of frequencies and forms of oscillations for rod systems with the given symmetry group. In: Distributed Control of Processes in Medium, vol 1, pp. 144–151, Naukova Dumka, Kiev (Russian) (1969)Google Scholar
  39. 46.
    Ivanov, V.P.: Oscillations of Impellers of Turbomachines. Mashinostrojenie, Moscow (Russian) (1984)Google Scholar
  40. 113.
    Zhuravlev, V. F., Klimov, D.M.: Applied Methods in the Theory of Oscillations. Nauka, , Moscow (Russian) (1988)Google Scholar
  41. 5.
    Argiris, J.: Modern Achievements in Calculation Methods of Constructions with Application of Matrixes. Strojizdat, Moscow (Russian) (1968)Google Scholar
  42. 30.
    Dimentberg, F.M.: Flexural Vibrations of Rotating Shafts, Butterworth, London, United Kingdom (1983)Google Scholar
  43. 102.
    Smolnikov, B.A.: Calculation of free oscillations for closed frame systems with cyclic symmetry. In: Dynamics and Durability. Trudy LPI, 210, Mashgis (Russian) (1960)Google Scholar
  44. 23.
    Bolotin, V.V., Novichkov Yu. N.: The Mechanics of Multilayered Designs. Mashinostroenie, Moscow (Russian) (1980)Google Scholar
  45. 97.
    Rabinovich, M.I., Trubetskov, D.I.: Introduction in the Theory of Oscillations and Waves. Nauka, Moscow (Russian) (1984)Google Scholar
  46. 6.
    Artobolevskij, I.I., Boborovnitskij, J.I., Genkin M.D.: Introduction in Acoustic Dynamics of Machines. Nauka, Moscow (Russian) (1979)Google Scholar
  47. 32.
    Feder J.: Fractals. Plenum Press, NY (1991)Google Scholar
  48. 101.
    Seshu, S., Rid, M.B.: The Graphs and Electric Circuits. Vysshaja shkola, Moscow (Russian) (1971)Google Scholar
  49. 34.
    Filin, A.P.: Matrixes in Static of Rod Systems, Moscow (Russian) (1966)Google Scholar
  50. 100.
    Segal, A.I.: Rotating symmetry at rotating loadings. In: Researches Under the Theory of Constructions. Gostechizdat, vol. 8, pp. 27–34 Moscow (Russian) (1957)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Mechanical Engineering Research InstituteMoscowRussia
  2. 2.RehovotIsrael

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