Nonlinear oscillations of a flexible fiber under gravity waves
Mechanical Engineering, Indian Institute of Technology, 801103, Patna, Bihar, India
2 Mechanical and Aerospace Engineering, Indian Institute of Technology, 502284, Hyderabad, Telangana, India
Accepted: 20 August 2022
Published online: 5 September 2022
The present work reports the analytical investigation of the hydrodynamic interaction of a vertically mounted flexible structure with the surface gravity waves. The nonlinear equation governing the transverse motion of the inextensible beam with cantilever boundary conditions is used to model the flexible structure under the gravity wave. The hydrodynamic action of the free surface of small-slope water waves on the flexible structure is considered as a linearized drag obtained with potential flow assumption. The structure’s displacement is expressed as a series of eigenfunctions of linear Euler–Bernoulli beam satisfying cantilever boundary, each of which is associated with generalized coordinates. Method of multiple scales is used as a solution procedure to derive the modulation and frequency response equation. The numerical solution of the modulation equations is compared with an analytical solution. Further, the stability of the stationary solution is examined by evaluating eigenvalues of Jacobian equations associated with first-order modulation equations. The response of the flexible structure and the stability of the stationary points are investigated. The effect of system parameters such as magnitude and frequency of the drag and structural damping on the frequency response is presented.
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