Standard

Localization in a Bernoulli-Euler beam on an inhomogeneous elastic foundation. / Indeitsev, D. A.; Kuklin, T. S.; Mochalova, Yu A.

In: Vestnik St. Petersburg University: Mathematics, Vol. 48, No. 1, 2015, p. 41-48.

Research output: Contribution to journal › Article › peer-review

Harvard

Indeitsev, DA, Kuklin, TS & Mochalova, YA 2015, 'Localization in a Bernoulli-Euler beam on an inhomogeneous elastic foundation', Vestnik St. Petersburg University: Mathematics, vol. 48, no. 1, pp. 41-48. https://doi.org/10.3103/S1063454115010069

APA

Indeitsev, D. A., Kuklin, T. S., & Mochalova, Y. A. (2015). Localization in a Bernoulli-Euler beam on an inhomogeneous elastic foundation. Vestnik St. Petersburg University: Mathematics, 48(1), 41-48. https://doi.org/10.3103/S1063454115010069

Vancouver

Indeitsev DA, Kuklin TS, Mochalova YA. Localization in a Bernoulli-Euler beam on an inhomogeneous elastic foundation. Vestnik St. Petersburg University: Mathematics. 2015;48(1):41-48. https://doi.org/10.3103/S1063454115010069

Author

Indeitsev, D. A. ; Kuklin, T. S. ; Mochalova, Yu A. / Localization in a Bernoulli-Euler beam on an inhomogeneous elastic foundation. In: Vestnik St. Petersburg University: Mathematics. 2015 ; Vol. 48, No. 1. pp. 41-48.

BibTeX

@article{38e590dfbffd4fed92bcf61789f665ae,
title = "Localization in a Bernoulli-Euler beam on an inhomogeneous elastic foundation",
abstract = "The paper is concerned with the localization phenomenon in continuous structures of finite and infinite length. An example of a compressed infinite beam is used to investigate the localization of oscillations in the area of a defect in the foundation and to examine the features of buckling of the structure for this case. It is shown that, in addition to the continuous spectrum, the existence of trapped modes is related to the appearance of a point (discrete) spectrum below the cut-off frequency of the structure. The dependence of the localized point frequencies on the compressive force is obtained. The convergence of the fundamental frequency to zero with increasing force specifies the localized buckling mode and the critical force, which agree with the solution of the corresponding static problem. The obtained results are compared with the results available for finite systems.",
keywords = "buckling, cut-off frequency, elastic foundation, localization",
author = "Indeitsev, {D. A.} and Kuklin, {T. S.} and Mochalova, {Yu A.}",
note = "Publisher Copyright: {\textcopyright} 2015, Allerton Press, Inc. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.",
year = "2015",
doi = "10.3103/S1063454115010069",
language = "English",
volume = "48",
pages = "41--48",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "1",

}

RIS

TY - JOUR

T1 - Localization in a Bernoulli-Euler beam on an inhomogeneous elastic foundation

AU - Indeitsev, D. A.

AU - Kuklin, T. S.

AU - Mochalova, Yu A.

N1 - Publisher Copyright: © 2015, Allerton Press, Inc. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2015

Y1 - 2015

N2 - The paper is concerned with the localization phenomenon in continuous structures of finite and infinite length. An example of a compressed infinite beam is used to investigate the localization of oscillations in the area of a defect in the foundation and to examine the features of buckling of the structure for this case. It is shown that, in addition to the continuous spectrum, the existence of trapped modes is related to the appearance of a point (discrete) spectrum below the cut-off frequency of the structure. The dependence of the localized point frequencies on the compressive force is obtained. The convergence of the fundamental frequency to zero with increasing force specifies the localized buckling mode and the critical force, which agree with the solution of the corresponding static problem. The obtained results are compared with the results available for finite systems.

AB - The paper is concerned with the localization phenomenon in continuous structures of finite and infinite length. An example of a compressed infinite beam is used to investigate the localization of oscillations in the area of a defect in the foundation and to examine the features of buckling of the structure for this case. It is shown that, in addition to the continuous spectrum, the existence of trapped modes is related to the appearance of a point (discrete) spectrum below the cut-off frequency of the structure. The dependence of the localized point frequencies on the compressive force is obtained. The convergence of the fundamental frequency to zero with increasing force specifies the localized buckling mode and the critical force, which agree with the solution of the corresponding static problem. The obtained results are compared with the results available for finite systems.

KW - buckling

KW - cut-off frequency

KW - elastic foundation

KW - localization

UR - http://www.scopus.com/inward/record.url?scp=84925298397&partnerID=8YFLogxK

U2 - 10.3103/S1063454115010069

DO - 10.3103/S1063454115010069

M3 - Article

AN - SCOPUS:84925298397

VL - 48

SP - 41

EP - 48

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -

ID: 75070589