Force driven vibrations of fractionally damped plates subjected to primary and internal resonances

被引：7

作者：

Shitikova, Marina, V ^{[1
]}

Kandu, Vladimir ^{[1
]}

机构：

[1] Voronezh State Tech Univ, Res Ctr Dynam Solids & Struct, Voronezh 394006, Russia

来源：

EUROPEAN PHYSICAL JOURNAL PLUS | 2019年 / 134卷 / 09期

关键词：

GEOMETRICALLY NONLINEAR VIBRATIONS; RECTANGULAR-PLATES; VISCOELASTIC PLATE; AMBIENT VIBRATION; CALCULUS; MODEL;

D O I：

10.1140/epjp/i2019-12812-x

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In the present paper, nonlinear force driven vibrations of thin plates in a viscoelastic medium have been studied, when its damping features are described by the fractional derivative Kelvin-Voigt model. The motion of the plate is governed by a set of three coupled nonlinear differential equations subjected to the different conditions of the internal resonance accompanied by the external resonance, resulting in the interaction of three modes corresponding to the mutually orthogonal displacements. Nonlinear sets of resolving equations in terms of amplitudes and phase differences have been obtained. The influence of fractional order viscosity and external vertical harmonic force on the energy exchange mechanism between the coupled modes has been analyzed.

引用

页数：18

共 33 条

[1] Force driven vibrations of fractionally damped plates subjected to primary and internal resonances
Marina V. Shitikova
Vladimir Kandu
[J]. The European Physical Journal Plus, 134
[2] Internal resonances in nonlinear fractionally damped plates of the Uflyand-Mindlin type
Shitikova, M., V
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[J]. INTERNATIONAL CONFERENCE ON CONSTRUCTION, ARCHITECTURE AND TECHNOSPHERE SAFETY (ICCATS 2020), 2020, 962
[3] Dynamic Response of Fractionally Damped Viscoelastic Plates Subjected to a Moving Point Load
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Datta, Nabanita
Sunny, Mohammed Rabius
[J]. JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME, 2020, 142 (04):
[4] Vibrations suppression of fractionally damped plates using multiple optimal dynamic vibration absorbers
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[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2020, 97 (04) : 851 - 874
[5] DESIGN FOR INTERNAL RESONANCES IN NONLINEAR TRANSVERSE VIBRATIONS OF HYPERELASTIC PLATES
Tripathi, Astitva
Bajaj, Anil K.
[J]. PROCEEDINGS OF THE ASME INTERNATIONAL MECHANICAL ENGINEERING CONGRESS AND EXPOSITION, 2013, VOL 4B, 2014,
[6] Topology optimization and internal resonances in transverse vibrations of hyperelastic plates
Tripathi, Astitva
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[7] Numerical Study of Nonlinear Vibrations of Fractionally Damped Cylindrical Shells Under the Additive Combinational Internal Resonance
Shitikova, Marina, V
Ajarmah, Basem
[J]. NEW TRENDS IN NONLINEAR DYNAMICS, VOL III: PROCEEDINGS OF THE FIRST INTERNATIONAL NONLINEAR DYNAMICS CONFERENCE (NODYCON 2019), 2020, : 285 - 293
[8] ON 1:2 INTERNAL RESONANCES IN IN-PLANE VIBRATIONS OF ELECTROSTRICTIVE PLATES
Tripathi, Astitva
Bajaj, Anil K.
[J]. PROCEEDINGS OF THE ASME INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES AND COMPUTERS AND INFORMATION IN ENGINEERING CONFERENCE, 2014, VOL 7, 2014,
[9] A New Approach for Studying Nonlinear Dynamic Response of a Thin Fractionally Damped Cylindrical Shell with Internal Resonances of the Order of ε
Shitikova, Marina V.
Rossikhin, Yury A.
[J]. SHELL AND MEMBRANE THEORIES IN MECHANICS AND BIOLOGY: FROM MACRO- TO NANOSCALE STRUCTURES, 2015, : 301 - 321
[10] Interaction of internal and external resonances during force driven vibrations of a nonlinear thin plate embedded into a fractional derivative medium
Shitikova, Marina V.
Rossikhin, Yury A.
Kandu, Vladimir
[J]. X INTERNATIONAL CONFERENCE ON STRUCTURAL DYNAMICS (EURODYN 2017), 2017, 199 : 832 - 837

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