Vibration of string lattice

Vladimir Astashev1 , Nikolay Andrianov2 , Vitaly Krupenin3

1, 2, 3Mechanical Engineering Research Institute of Russian Academy of Sciences, Moscow, Russia

1Corresponding author

Vibroengineering PROCEDIA, Vol. 8, 2016, p. 97-101.
Received 16 June 2016; accepted 30 August 2016; published 7 October 2016

Copyright © 2016 JVE International Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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A two-dimensional system oscillation with massive bodies located in lattice nodes is investigated in this paper. The results of theoretical analysis and of the performed experiments are given. Certain modes of the oscillation of lattices of different dimensions are described.

Keywords: string, lattice nodes, experimental stand, standing wave, natural frequencies, mode shapes.


The study was performed account for a grant the Russian Science Foundation (Project No. 15-19-30026).


  1. Astashev V. K., Krupenin V. L., Perevezentsev V. N., Kolik L. V., Andrianov N. A. Properties of surface layers nanostructured by autoresonant ultrasonic turning. Journal of Machinery Manufacture and Reliability, Vol. 40, Issue 5, 2011, p. 68-72. [Search CrossRef]
  2. Nagaev R. F., Khodzhaev K. Sh. Kolebaniya Mekhanicheskikh System s Periodicheskoi Strukturoi (Vibration of Mechanical Systems with Periodic Structure). FAN, Tashkent, 1973, p. 220, (in Russian). [Search CrossRef]
  3. Krupenin V. L. On the calculation of vibratory processes in lattice two-dimensional constructions. Problemy Mashinostroeniya i Nadezhnosti Mashin, Vol. 2, 2006, p. 20-26, (in Russian). [Search CrossRef]
  4. Krupenin V. L. Vibroimpact processes in two-dimensional lattice constructions. Problemy Mashinostroeniya i Nadezhnosti Mashin, Vol. 3, 2006, p. 16-22, (in Russian). [Search CrossRef]
  5. Krupenin V. L. Analysis of singularized motion equations of latticed vibroimpact 2D systems in renouncing Newton’s hypothesis. Journal of Machinery Manufacture and Reliability, Vol. 45, Issue 2, 2016, p. 104-112. [Search CrossRef]
  6. Babitsky V. I., Krupenin V. L. Vibration of Strongly Nonlinear Discontinuous Systems. Springer-Verlag, Berlin, Heidelberg, New York, 2001, p. 404. [Search CrossRef]