A low-dimensional model for the planar nonlinear dynamics of a fluid-conveying cantilever is constructed using the proper orthogonal decomposition method (PODM) in the post-flutter region. Firstly, the nonlinear partial differential equation (PDE) of motion is converted into a finite set of coupled ordinary differential equations (ODEs) by a Galerkin projection scheme using the cantilever beam modes as a basis. A finite difference method based on Houbolt's scheme is used to obtain the stable solution of the nonlinear ODEs. A complex eigenvalue analysis is also carried out to determine the region of flutter instability with increasing flow velocity. Secondly, an efficient projection basis for the Galerkin scheme is constructed by using PODM for the low-dimensional representation of the original PDE describing the dynamics of the system. The important question regarding the capability of the reduced-order model to capture the principal features of the original system is addressed. Interestingly, the reduced-order basis constructed using PODM at a specific flow velocity can efficiently reproduce the system response at a range of flow rates involving limit-cycle oscillations (LCO) in the proximity of the flutter point. Furthermore, a weighted POD basis is derived subsequently in order to enhance the efficacy of the reduced-order model over a wider range of flow velocity, in the case when the LCO amplitude exhibits considerable variation beyond the flutter velocity.

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Persistent URL dx.doi.org/10.1016/S0889-9746(02)00150-0
Journal Journal of Fluids and Structures
Sarkar, A, & Païdoussis, M.P. (M. P.). (2003). A compact limit-cycle oscillation model of a cantilever conveying fluid. Journal of Fluids and Structures, 17(4), 525–539. doi:10.1016/S0889-9746(02)00150-0