NDLI: Parametric and internal resonance of axially accelerating viscoelastic beams with the recognition of longitudinally varying tensions

Content Provider	Springer Nature Link
Author	Tang, You Qi Zhang, Deng Bo Gao, Jia Ming
Copyright Year	2015
Abstract	In this paper, parametric and 3:1 internal resonance of axially moving viscoelastic beams on elastic foundation are analytically and numerically investigated. The beam is restricted by viscous damping force. The beam’s material obeys the Kelvin model in which the material time derivative is used. The governing equations of coupled planar vibration and the associated boundary conditions are derived from the generalized Hamilton principle. The effects of the nonhomogeneous boundary conditions due to the viscoelasticity are highlighted, while the boundary conditions are assumed to be homogeneous in previous studies. In small but finite stretching problems, the equation is simplified into a governing equation of transverse nonlinear vibration. It is a nonlinear integro-partial differential equation with time-dependent and space-dependent coefficients. The dependence of the tension on the finite axial support rigidity is also modeled. The method of multiple scales is directly applied to establish the solvability conditions. The nonlinear steady-state oscillating response along with the stability and bifurcation of the beam is investigated. A detailed study is carried out to determine the influence of the viscoelastic coefficient and the viscous damping coefficient on dynamic behavior of the system. The numerical calculations by the differential quadrature scheme confirm the approximate analytical results.
Starting Page	401
Ending Page	418
Page Count	18
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	83
Issue Number	1-2
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-08-30
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Nonlinearity Parametric and 3:1 internal resonance Axially accelerating viscoelastic beam Longitudinally varying tension Nonhomogeneous boundary condition Method of multiple scales Differential quadrature scheme Vibration, Dynamical Systems, Control Mechanics Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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