A dynamic order reduction method for fluid-structure systems

Abstract In this paper, an iterative method is proposed to reduce the order of the coupled eigenvalue problem related to fluid-structure interaction systems. In fact, it is required to solve a smaller eigenvalue problem rather than the larger one (original) to compute the natural frequencies and mode shapes of the system. To this end, all degrees of freedom (DOFs) of the system are divided into master (retained) and slave (eliminated) ones. Then, the problem is re-expressed based on the master DOFs and a transformation matrix is introduced. The results show a remarkable decline in computational costs, whereas the accuracy of the modal outputs does not significantly decrease. A stopping criterion is defined to check whether the iterative process converges. Moreover, three fluid-structure systems are analyzed, including a two-dimensional fully-filled concrete tank, a two-dimensional gravity dam-reservoir, and a three-dimensional arch dam-reservoir, to assess the correctness and performance of the presented method. Findings prove that the proposed method is able to reduce the order of the eigenvalue problem of fluid-structure systems.

[1]  Farhang Daneshmand,et al.  COUPLED FREE VIBRATION ANALYSIS OF A FLUID-FILLED RECTANGULAR CONTAINER WITH A SAGGED BOTTOM MEMBRANE , 2010 .

[2]  A. Jennings.  Mass condensation and simultaneous iteration for vibration problems , 1973 .

[3]  R. Guyan.  Reduction of stiffness and mass matrices , 1965 .

[4]  Phill-Seung Lee,et al.  A dynamic condensation method using algebraic substructuring , 2017 .

[5]  Ahmed K. Noor,et al.  Recent Advances and Applications of Reduction Methods , 1994 .

[6]  Robert L. Kidder,et al.  Reduction of structural frequency equations. , 1973 .

[7]  Huajun Li,et al.  Using incomplete modal data for damage detection in offshore jacket structures , 2008 .

[8]  Vahid Lotfi,et al.  Dynamic analysis of concrete arch dams by ideal-coupled modal approach , 2010 .

[9]  Ebrahim Sotoudehnia,et al.  A new method for damage detection of fluid-structure systems based on model updating strategy and incomplete modal data , 2019, Ocean Engineering.

[10]  M. R. Kianoush,et al.  Generalized SDOF system for dynamic analysis of concrete rectangular liquid storage tanks , 2009 .

[11]  Alexander H. Flax,et al.  Comment on "Reduction of Structural Frequency Equations" , 1975 .

[12]  Youngin Choi,et al.  Model reduction methods for cylindrical structures in reactor internals considering the fluid–structure interaction , 2016 .

[13]  R. Ohayon,et al.  Substructure variational analysis of the vibrations of coupled fluid–structure systems. Finite element results , 1979 .

[14]  Ki-Ook Kim,et al.  Convergence Acceleration of Iterative Modal Reduction Methods , 2001 .

[15]  M. Friswell,et al.  THE CONVERGENCE OF THE ITERATED IRS METHOD , 1998 .

[16]  M. Friswell,et al.  Model reduction using dynamic and iterated IRS techniques , 1995 .

[17]  Vahid Lotfi,et al.  Comparison of Three Efficient Methods for Computing Mode Shapes of Fluid-Structure Interaction Systems , 2013 .

[18]  S. A. Arjmandi,et al.  Computing mode shapes of fluid-structure systems using subspace iteration methods , 2011 .

[19]  Vahid Lotfi.  Frequency domain analysis of concrete arch dams by decoupled modal approach , 2005 .

[20]  Phill-Seung Lee,et al.  A dynamic condensation method with free interface substructuring , 2019, Mechanical Systems and Signal Processing.

[21]  R. Lin,et al.  A new iterative order reduction (IOR) method for eigensolutions of large structures , 2004 .

[22]  R. Lin,et al.  Improvement on the iterated IRS method for structural eigensolutions , 2004 .

[23]  K. Bathe.  Finite Element Procedures , 1995 .

[24]  Mohamed Menaa,et al.  Dynamic analysis of spherical shell partially filled with fluid , 2015 .

[25]  Ahmad Aftabi Sani,et al.  Free vibration analysis of gravity dam-reservoir system utilizing 21 node-33 Gauss point triangular elements , 2016 .

[26]  K. Bathe,et al.  Analysis of fluid-structure interactions. a direct symmetric coupled formulation based on the fluid velocity potential , 1985 .

[27]  Noureddine Bouhaddi,et al.  MODEL REDUCTION BY A SIMPLIFIED VARIANT OF DYNAMIC CONDENSATION , 1996 .

[28]  Klaus-Jürgen Bathe,et al.  The subspace iteration method - Revisited , 2013 .

[29]  Yuri Bazilevs,et al.  Computational Fluid-Structure Interaction: Methods and Applications , 2013 .

[30]  Seamus D. Garvey,et al.  Using Iterated IRS Model Reduction Techniques to Calculate Eigensolutions , 1997 .

[31]  Phill-Seung Lee,et al.  An iterative algebraic dynamic condensation method and its performance , 2017 .

[32]  M. R. Kianoush,et al.  The effect of earthquake frequency content on the seismic behavior of concrete rectangular liquid tanks using the finite element method incorporating soil–structure interaction , 2011 .

[33]  Anil K. Chopra,et al.  Dynamic Analysis of Arch Dams Including Hydrodynamic Effects , 1983 .