Parametric Resonance of an Axially Accelerating Viscoelastic Beam with Non-Typical Boundary Conditions

L. Q. Chen; Xiaodong Yang

doi:10.1007/978-1-4020-6332-9_22

Parametric Resonance of an Axially Accelerating Viscoelastic Beam with Non-Typical Boundary Conditions

L. Q. Chen
, Xiaodong Yang

Mechanical and Aerospace Engineering

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

Abstract

Principal parametric resonance in transverse vibration is investigated for axially accelerating viscoelastic beams constrained by rotating sleeves with torsion springs. The method of multiple scales is applied to calculate the steady-state response. Expression of the amplitude of the steady-state response is derived from the solvability condition of eliminating secular terms. The stability of straight equilibrium and nontrivial steady-state response are analyzed by use of the Lyapunov linearized stability theory. Numerical examples are presented to highlight the effects of speed pulsation, viscoelasticity, and nonlinearity and the stiffness of the torsion spring. © 2007 Springer.

Original language	American English
Journal	Solid Mechanics and its Applications
DOIs	https://doi.org/10.1007/978-1-4020-6332-9_22
State	Published - Jan 1 2007

Keywords

Axially Accelerating Beam
Method of Multiple Scales
Parametric Resonance
Principal
Stability
Viscoelasticity

Disciplines

Aerospace Engineering
Mechanical Engineering

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https://doi.org/10.1007/978-1-4020-6332-9_22

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title = "Parametric Resonance of an Axially Accelerating Viscoelastic Beam with Non-Typical Boundary Conditions",

abstract = " Principal parametric resonance in transverse vibration is investigated for axially accelerating viscoelastic beams constrained by rotating sleeves with torsion springs. The method of multiple scales is applied to calculate the steady-state response. Expression of the amplitude of the steady-state response is derived from the solvability condition of eliminating secular terms. The stability of straight equilibrium and nontrivial steady-state response are analyzed by use of the Lyapunov linearized stability theory. Numerical examples are presented to highlight the effects of speed pulsation, viscoelasticity, and nonlinearity and the stiffness of the torsion spring. {\textcopyright} 2007 Springer.",

keywords = "Axially Accelerating Beam, Method of Multiple Scales, Parametric Resonance, Principal, Stability, Viscoelasticity",

author = "Chen, \{L. Q.\} and Xiaodong Yang",

year = "2007",

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doi = "10.1007/978-1-4020-6332-9\_22",

language = "American English",

journal = "Solid Mechanics and its Applications",

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T1 - Parametric Resonance of an Axially Accelerating Viscoelastic Beam with Non-Typical Boundary Conditions

AU - Chen, L. Q.

AU - Yang, Xiaodong

PY - 2007/1/1

Y1 - 2007/1/1

N2 - Principal parametric resonance in transverse vibration is investigated for axially accelerating viscoelastic beams constrained by rotating sleeves with torsion springs. The method of multiple scales is applied to calculate the steady-state response. Expression of the amplitude of the steady-state response is derived from the solvability condition of eliminating secular terms. The stability of straight equilibrium and nontrivial steady-state response are analyzed by use of the Lyapunov linearized stability theory. Numerical examples are presented to highlight the effects of speed pulsation, viscoelasticity, and nonlinearity and the stiffness of the torsion spring. © 2007 Springer.

AB - Principal parametric resonance in transverse vibration is investigated for axially accelerating viscoelastic beams constrained by rotating sleeves with torsion springs. The method of multiple scales is applied to calculate the steady-state response. Expression of the amplitude of the steady-state response is derived from the solvability condition of eliminating secular terms. The stability of straight equilibrium and nontrivial steady-state response are analyzed by use of the Lyapunov linearized stability theory. Numerical examples are presented to highlight the effects of speed pulsation, viscoelasticity, and nonlinearity and the stiffness of the torsion spring. © 2007 Springer.

KW - Axially Accelerating Beam

KW - Method of Multiple Scales

KW - Parametric Resonance

KW - Principal

KW - Stability

KW - Viscoelasticity

UR - https://scholarsmine.mst.edu/mec_aereng_facwork/2705

UR - https://doi.org/10.1007/978-1-4020-6332-9_22

U2 - 10.1007/978-1-4020-6332-9_22

DO - 10.1007/978-1-4020-6332-9_22

M3 - Article

JO - Solid Mechanics and its Applications

JF - Solid Mechanics and its Applications

ER -

Parametric Resonance of an Axially Accelerating Viscoelastic Beam with Non-Typical Boundary Conditions

Abstract

Keywords

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