Journal
JOURNAL OF ENGINEERING MATHEMATICS
Volume 67, Issue 3, Pages 205-218Publisher
SPRINGER
DOI: 10.1007/s10665-009-9316-9
Keywords
Asymptotic perturbation; Axially accelerating string; Nonlinearity; Parametric vibration; Viscoelasticity
Funding
- National Outstanding Young Scientists Fund of China [90816001]
- National Natural Science Foundation of China [10725209]
- Shanghai Subject Chief Scientist Project [09XD1401700]
- Shanghai Municipal Education Commission Scientific Research [07ZZ07]
- Shanghai Leading Academic Discipline Project [Y0103]
- Changjiang Scholars and Innovative Research Team in University Program [IRT0844]
Ask authors/readers for more resources
Nonlinear parametric vibration of axially accelerating viscoelastic strings is investigated via an approximate analytical approach. The standard linear solid model using the material time derivative is employed to describe the string viscoelastic behaviors. A coordinate transformation is introduced to derive Mote's model of transverse motion from the governing equation of the stationary string. Mote's model leads to Kirchhoff's model by replacing the tension with the averaged tension over the string. An asymptotic perturbation approach is proposed to study principal parametric resonance based on the two models. The amplitude and the existence conditions of the steady-state responses are determined by locating the nonzero fixed points in the modulation equations resulting from the solvability condition. Numerical results are presented to highlight the effects of the material parameters, the axial-speed fluctuation amplitude, and the initial stress on steady-state responses.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available