Localization in Bernoulli-Euler beam on inhomogeneous elastic foundation

Authors

  • Dmitry A. Indeitsev St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation;
  • Timofey S. Kuklin Institute of Problems of Mechanical Engineering RAS, Bolshoy pr. V.O., 61, St. Petersburg, 199178, Russian Federation;
  • Yulia A. Mochalova Institute of Problems of Mechanical Engineering RAS, Bolshoy pr. V.O., 61, St. Petersburg, 199178, Russian Federation;

Abstract

The study concerns localization phenomenon in continuous structures of finite and infinite length. For a compressed infinite Bernoulli-Euler beam on a inhomogeneous elastic foundation it is shown that the existence of localization modes is due to a point spectrum of the corresponding boundary value problem. Similarity between buckling of the compressed beam and the localized modes of oscillations is analyzed. Dependence of localized point frequencies on the compressive load is shown. Setting the fundamental frequency to zero, one defines the localized buckling mode and the critical load, whose value is the same as that found in the static problem. Refs 9. Figs 8.

Keywords:

localization, buckling, elastic foundation, cut-off frequency

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Published

2015-02-01

How to Cite

Indeitsev, D. A., Kuklin, T. S., & Mochalova, Y. A. (2015). Localization in Bernoulli-Euler beam on inhomogeneous elastic foundation. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2(1), 112–122. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11138

Issue

Vol. 2 No. 1 (2015)

Section

Mechanics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.