Short communicationA new decoupling strategy for structures with frequency-dependent properties
Section snippets
Nomenclature
Lowercase and capital bold letters are respectively used to denote vectors and matrices while italic letters with indices designate their elements. The superscripts , and stand for the conjugate, the transpose and the hermitian operators. The imaginary unit is noted and stands for the circular frequency.
State space eigenproblem
First, the state variables and the state forces , with and being respectively the identity and zero matrices, are introduced. Doing so allows to recast the initial set of second-order equations into first-order equations. Indeed, it yields where are referred to as the state matrices. These definitions of the state properties are chosen among others to conserve the symmetry of the stiffness, mass and damping matrices when
Models
The methodology proposed in this paper is now used to perform the hydroelastic analysis of an end-anchored floating pontoon bridge subjected to first order wave loads [3]. This example is based on a two-dimensional finite element model of the Bergsøysund Bridge, which crosses a 300-m deep fjord in the Northwestern coast of Norway and is currently the longest of its kind.
As illustrated in Fig. 2-(a) and 2-(b), this bridge is composed of seven pontoons which are connected to each others and to
Conclusions
The present paper proposes to combine a modal state formulation with a series expansion of the frequency response matrix to decouple the governing equations of a structure with frequency-dependent properties. This procedure indeed allows to compute the power spectral densities and the second order statistics of both the displacements and the velocities based on the successive inversions of a diagonal matrix only.
This approach is also iterative. It can be stopped at any order according to the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The first and the second authors received financial support from the F.R.S.-FNRS (Belgian Fund for Scientific Research). The work of the first author at NTNU Trondheim was also funded by two research stay grants of the FWB (Fédération Wallonie-Bruxelles), Belgium and the Rotary, USA . The contribution of the Norwegian Public Road Administration is acknowledged as well by the third author.
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