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Non-linear normal modes in dynamics-continuous systems

Result description

The paper presents a continuation of an effort started last year, when the authors briefly informed about the Non-linear normal modes (NNM) concerning the version dealing with discrete systems. Although many features of the continuous formulation from the mathematical viewpoint are similar to the discrete case, a couple of specifics should be highlighted from the viewpoint of a real applicability of this tool to investigate particular dynamic systems. Three approaches are mentioned in the paper and the Galerkin-Petrov based procedure is outlined in more details. As a particular subject the cantilever prismatic beam is discussed. Non-linear normal modes for several amplitudes are shown to demonstrate the dependence of their shapes on the actual effective amplitude. Comparison with adequate linear counterpart is done.

Keywords

nonlinear dynamic systemsnon-linear normal modesdiscretizationmulti-scale method

The result's identifiers

Alternative languages

  • Result language

    angličtina

  • Original language name

    Non-linear normal modes in dynamics-continuous systems

  • Original language description

    The paper presents a continuation of an effort started last year, when the authors briefly informed about the Non-linear normal modes (NNM) concerning the version dealing with discrete systems. Although many features of the continuous formulation from the mathematical viewpoint are similar to the discrete case, a couple of specifics should be highlighted from the viewpoint of a real applicability of this tool to investigate particular dynamic systems. Three approaches are mentioned in the paper and the Galerkin-Petrov based procedure is outlined in more details. As a particular subject the cantilever prismatic beam is discussed. Non-linear normal modes for several amplitudes are shown to demonstrate the dependence of their shapes on the actual effective amplitude. Comparison with adequate linear counterpart is done.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

    JM - Structural engineering

  • OECD FORD branch

Result continuities

Others

  • Publication year

    2016

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Article name in the collection

    Engineering Mechanics 2016

  • ISBN

    978-80-87012-59-8

  • ISSN

    1805-8248

  • e-ISSN

  • Number of pages

    4

  • Pages from-to

    414-417

  • Publisher name

    Institute of Thermomechanics CAS, v. v. i.

  • Place of publication

    Prague

  • Event location

    Svratka

  • Event date

    May 9, 2016

  • Type of event by nationality

    EUR - Evropská akce

  • UT code for WoS article

    000379986700100

Result type

D - Article in proceedings

D

CEP

JM - Structural engineering

Year of implementation

2016