Dynamic Analysis of Non-Linear Structures by the Method of by M. G. Donley, P. D. Spanos (auth.)

By M. G. Donley, P. D. Spanos (auth.)

1. 1 advent As offshore oil creation strikes into deeper water, compliant structural structures have gotten more and more very important. Examples of this sort of constitution are pressure leg platfonns (TLP's), guyed tower platfonns, compliant tower platfonns, and floating creation structures. the typical characteristic of those structures, which distinguishes them from traditional jacket platfonns, is that dynamic amplification is minimized by way of designing the surge and sway average frequencies to be under the most important frequencies of the wave spectrum. traditional jacket platfonns, however, are designed to have excessive stiffness in order that the ordinary frequencies are larger than the wave frequencies. At deeper water depths, although, it turns into uneconomical to construct a platfonn with excessive adequate stiffness. hence, the change is made to the opposite part of the wave spectrum. The low traditional frequency of a compliant platfonn is accomplished by way of designing structures which inherently have low stiffness. as a result, the utmost horizontal tours of those platforms could be very huge. The low traditional frequency attribute of compliant structures creates new analytical demanding situations for engineers. the reason is, geometric stiffness and hydrodynamic strength nonlinearities could cause major resonance responses within the surge and sway modes, although the ordinary frequencies of those modes are open air the wave spectrum frequencies. excessive frequency resonance responses in different modes, reminiscent of the pitch mode of a TLP, also are possible.

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31). 14) dupng the iteration process and compute other moments after convergence. This saves considerable computational effort. However, it is still quite costly to compute all the moments and in particular the third order moments. 40) A simplifted solution procedure is implemented for this case in the next section. 14) reduces from a 5Nx5N system to a 5x5 system where the vector X is now given by the equation -T X = (x j, x':' j, (xA2j -

34). 27). 42) where (*) denotes complex conjugation. These properties greatly reduce the computational effort and storage requirements. 40) that the response quadratic transfer functions have the same properties. 4 R~sponse Probability Distribution In general, the probability distribution of x(t) is not gaussian. In particular, the quadratic response, x(2)(t), is non-gaussian because it is a quadratic transfonnation of a gaussian process. The exact distribution of the response is not known, but there are methods available to approximate it.

The peak at the excitation frequencies is the response due to the linear force. The low frequency peak is a resonance response due to the quadratic force. The response due to the high frequency components of the quadratic force is negligible. It can be seen that the spectra obtained by simulation and quadratization are in good agreement. The quadratization method, however, is computationally much more efficient, to the extent that it reduces the requisite computation time by two orders of magnitude.

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