A State Space Method For Modal Analysis Of Underwater Structure

The fluid loading effect must be concerned when to establish the coupled fluid-structure system equation to study the vibration of strucure in water . The fluid-loaded term in the coupled equation is related to frequency so the system is about a nonlinear eigen system. The solution of this system is time consuming by using the common interaction method, so to develop a new method to solve these problems in a effective way have been long of interest.A new state-space coupling method is presented for the solution of natural frequencies and mode shapes of underwater structure. This method is based on standard boundary element and finite element discretizations of the acoustic and structural domains, respectively. This method expands the frequency-dependent boundary element coefficient matrix in the boundary element integral in a power series on circular frequency, after factoring out the frequency term of the boundary element coefficient matrix, the boundary element coefficient matrices are confined to a frequency-independent part. The boundary coefficient matrices are therefore frequency-independent and can be coupled with the structure matrix into a canonical state-space form after designing the state space variable to yield the fluid-loaded modes via the general eigensystem analysis. Solution of this system produces a series of complex eigenvalues and eigenvectors. Natural frequencies and resonance of a fluid-loaded sphere shell structure are calculated to demonstrate the method, also some skills to reduce the time for solution are discussed in this paperCompared with the proposed state space method by previous authors which have to obtain the acoustic impedance matrix by matrix versus operation, The present method avoid that operation, time is saved. The modal response of the spherical shell obtained by this two method are presented, the results also shows that the present method in this paper is effective and right.