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- Title
Vibration of an axially moving string with nonclassical boundary conditions subjected to harmonic excitation based on the method of multiple scales.
- Authors
Wu, Yuanfeng; Chen, Enwei; Zhu, Weidong; He, Yuteng; Lu, Yimin; Chen, Pin
- Abstract
This paper investigates the vibration of an axially moving string with symmetrical nonclassical boundary conditions subjected to harmonic excitation. Instead of conventional fixed boundary, the boundary is modeled as a combination of a damper, a linear stiffness, and a cubic nonlinear stiffness to study the first primary resonance of the axially moving string. By applying the extended Hamilton principle, the governing equation and boundary conditions are obtained. The method of multiple scales (MMS) and the modal revision method are then utilized to perturb the governing equation and nonlinear boundary conditions into linear equations at different time scales. This enables analysis of transverse vibration at each corresponding time scale and an approximate analytical solution. The differential quadrature method (DQM) is adopted to demonstrate the feasibility and correctness of the employed method in this paper. Finally, a parametric study is carried out to indicate the effect of boundary parameters on the vibration response, taking into account rarely studied nonlinear boundaries.
- Subjects
MULTIPLE scale method; DIFFERENTIAL quadrature method; NONLINEAR equations; LINEAR equations; ANALYTICAL solutions; HAMILTON-Jacobi equations
- Publication
Nonlinear Dynamics, 2024, Vol 112, Issue 6, p4169
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-023-09115-0