A general frequency-domain dynamic analysis algorithm for offshore structures with asymmetric matrices

Asymmetric system matrices, especially the asymmetric damping matrix, must be considered because of the usual drastic variations between the energy absorption rates of materials in different parts of a structure. This paper proposes a general frequency-domain response estimation method for incorporating possibly asymmetric mass, stiffness and damping matrices in engineering. One achievement is that a general frequency response function (GFRF) is defined by estimating the coefficients, poles and zeros of the structure, rather than by using the eigenvalues and eigenvectors. The second is that nonzero initial conditions can also be considered in the frequency domain. Three examples are employed: a system with four degrees of freedom, a frame structure, and a tension leg platform. One can conclude the following: (1) the proposed method can provide more accurate results for estimating FRFs of the system with asymmetric matrices; (2) traditional frequency-domain method can be regarded as a special case of the approach, just aiming at estimating steady-state responses of the system with symmetric matrices; (3) transient responses of a system with asymmetric matrices can also be estimated properly and with a good efficiency, based on the discretization of the reconstructed external loadings.