On the theory of natural vibrations of fluid-filled structures (Q2759543)

Equation of free vibrations of a structure in contact with fluid is written out in the form \([K-\omega^2(M_e+M_l)]W =0\), where \(K\), \(M_e\) and \(M_l\) are matrices of stiffness, masses of structure and added mass of fluid; \(\omega\) is eigenfrequency, and \(W\) is the matrix whose columns are eigenvectors. In the finite element method proposed for the solution of this problem, components of vectors \(W\) are amplitude displacements of nodal points of the finite element grid. For determination of elements of matrix \(M_l\), the pressure acting on the structure is found from the solution of hydrodynamic problem for ideal inviscid fluid. The latter problem is reduced to a singular integral equation. The resulting formulation of the vibration problem is given by two coupled systems of algebraic equations.