By M. G. Donley, P. D. Spanos (auth.)
1. 1 creation As offshore oil creation strikes into deeper water, compliant structural structures have gotten more and more very important. Examples of this kind of constitution are rigidity leg platfonns (TLP's), guyed tower platfonns, compliant tower platfonns, and floating creation structures. the typical function of those structures, which distinguishes them from traditional jacket platfonns, is that dynamic amplification is minimized through designing the surge and sway usual frequencies to be below the primary frequencies of the wave spectrum. traditional jacket platfonns, however, are designed to have excessive stiffness in order that the common frequencies are better than the wave frequencies. At deeper water depths, besides the fact that, it turns into uneconomical to construct a platfonn with excessive sufficient stiffness. hence, the swap is made to the opposite facet of the wave spectrum. The low usual frequency of a compliant platfonn is accomplished by way of designing platforms which inherently have low stiffness. therefore, the utmost horizontal tours of those structures may be very huge. The low average frequency attribute of compliant structures creates new analytical demanding situations for engineers. this is why geometric stiffness and hydrodynamic strength nonlinearities may cause major resonance responses within the surge and sway modes, although the usual frequencies of those modes are outdoors the wave spectrum frequencies. excessive frequency resonance responses in different modes, comparable to the pitch mode of a TLP, also are possible.
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Extra resources for Dynamic Analysis of Non-Linear Structures by the Method of Statistical Quadratization
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.
23), only the transfer function vectors need to be computed. The force transfer function Hi1)(ro) is the same as the linear white-noise fIlter transfer function. 17). 30) where (*) denotes complex conjugation. 28) that the response quadratic transfer functions have the same properties. (t) is not gaussian. Approximate joint distributions can be obtained by an expansion of partial derivatives of a joint gaussian distribution. 31) where jT =jl + h +.. 32) clI(S) is a joint gaussian distribution given by the equation clI(S) = (21t)"N ISrl/2 exp[ - ~ ST S-l 5] where the matrix S is the covariance matrix for the state space vector.
42) where alii refers to the ith diagonal element of the respective matrix. Thus, only moments of the i th degree of freedom are needed to solve for the quadratization coefficients associated with that degree of freedom. Joint moments of the i th and jth degree of freedom may still be of interest, but would not need to be computed until after the iteration process has converged. ---Ai. 1 = 0 50 The most significant savings for this reduced method is due to the fact that considerably fewer third order moments need to be computed.
Dynamic Analysis of Non-Linear Structures by the Method of Statistical Quadratization by M. G. Donley, P. D. Spanos (auth.)