Nonlinear Parametric Resonance of a Fractional Damped Axially Moving String

被引：12

作者：

Yang, Tian-Zhi ^{[1
]}

Yang, Xiaodong ^{[2
]}

Chen, Fei ^{[3
]}

Fang, Bo ^{[1
]}

机构：

[1] Shenyang Aerosp Univ, Dept Astronaut, Shenyang 110136, Peoples R China

[2] Beijing Univ Technol, Sch Mech Engn, Shenyang 100022, Peoples R China

[3] Shenyang Aerosp Univ, Dept Engn Mech, Shenyang 110136, Peoples R China

来源：

JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME | 2013年 / 135卷 / 06期

基金：

中国国家自然科学基金;

关键词：

axially moving string; fractional derivative Kelvin constitutive relation; nonlinear parametric resonance; steady-state response; TRANSVERSE VIBRATION; STABILITY;

D O I：

10.1115/1.4024779

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

Nonlinear parametric vibration of an axially accelerating viscoelastic string is investigated. The string is constituted by the fractional Kelvin model. The principal parametric resonance is analyzed by using an asymptotic approach. The modulation equation is derived from the solvability condition. Closed-form expressions of the amplitudes and the existence conditions of steady-state responses are obtained from the modulation equation. Numerical examples are presented to highlight the effects of fractional order and other system parameters on the responses.

引用

页数：5

共 50 条

[1] Analytical Analysis on Nonlinear Parametric Vibration of an Axially Moving String with Fractional Viscoelastic Damping
Li, Ying
Tang, Ye
[J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2017, 2017
[2] PARAMETRIC EXCITATION OF AN AXIALLY MOVING STRING
MOTE, CD
[J]. JOURNAL OF APPLIED MECHANICS, 1968, 35 (01): : 171 - &
[3] On applicability of truncation method for damped axially moving string
Dehraj, Sanaullah
Sandilo, Sajad H.
Malookani, Rajab A.
[J]. JOURNAL OF VIBROENGINEERING, 2020, 22 (02) : 337 - 352
[4] ON NONLINEAR OSCILLATION OF AN AXIALLY MOVING STRING
MOTE, CD
[J]. JOURNAL OF APPLIED MECHANICS, 1966, 33 (02): : 463 - &
[5] Stability of a Nonlinear Axially Moving String
Shahruz, S. M.
El-Shaer, Ahmed H.
[J]. 2009 AMERICAN CONTROL CONFERENCE, VOLS 1-9, 2009, : 4103 - +
[6] Viscously damped transverse vibrations of an axially-moving string
Jaksic, N
Boltezar, M
[J]. STROJNISKI VESTNIK-JOURNAL OF MECHANICAL ENGINEERING, 2005, 51 (09): : 560 - 569
[7] Stability in parametric resonance of an axially moving beam constituted by fractional order material
Yang, Tian-Zhi
Fang, Bo
[J]. ARCHIVE OF APPLIED MECHANICS, 2012, 82 (12) : 1763 - 1770
[8] Stability in parametric resonance of an axially moving beam constituted by fractional order material
Tian-Zhi Yang
Bo Fang
[J]. Archive of Applied Mechanics, 2012, 82 : 1763 - 1770
[9] Principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string
Chen, LQ
Zu, JW
Wu, J
[J]. ACTA MECHANICA SINICA, 2004, 20 (03) : 307 - 316
[10] Principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string
Chen Liqun
Jean W. Zu
Wu Jun
[J]. Acta Mechanica Sinica, 2004, 20 (3) : 307 - 316

← 1 2 3 4 5 →