Optimal bounded control of first-passage failure of quasi-integrable Hamiltonian systems with wide-band random excitation

The optimal bounded control of quasi-integrable Hamiltonian systems with wide-band random excitation for minimizing their first-passage failure is investigated. First, a stochastic averaging method for multi-degrees-of-freedom (MDOF) strongly nonlinear quasi-integrable Hamiltonian systems with wide-band stationary random excitations using generalized harmonic functions is proposed. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximizinig reliability and maximizing mean first-passage time are formulated based on the averaged It$\ddot{\rm o}$ equations by applying the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraints. The relationship between the dynamical programming equations and the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for the conditional mean first-passage time of optimally controlled system is discussed. Finally, the conditional reliability function, the conditional probability density and mean of first-passage time of an optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation. The application of the proposed procedure and effectiveness of control strategy are illustrated with an example.

Study on current-random wave forces acting on a framework

The forces of random wave plus current acting on a simplified offshore platform (jacket) model have been studied numerically and experimentally. The numerical results are in good agreement with experiments. The mean force can be approximated as a function of equivalent velocity parameter and the root-mean-square force as a function of equivalent significant wave height parameter.

The ensemble statistics of the band-averaged energy of a random system

This paper is concerned with the response statistics of a dynamic system that has random properties. The frequency-band-averaged energy of the system is considered, and a closed form expression is derived for the relative variance of this quantity. The expression depends upon three parameters: the modal overlap factor m, a bandwidth parameter B, and a parameter α that defines the nature of the loading (for example single point forcing or rain-on-the-roof loading). The result is applicable to any single structural component or acoustic volume, and a comparison is made here with simulation results for a mass loaded plate. Good agreement is found between the simulations and the theory. © 2003 Published by Elsevier Ltd.

Flows with Inertia in a Three-Dimensional Random Fiber Network

A fiber web is modeled as a three-dimensional random cylindrical fiber network. Nonlinear behavior of fluid flowing through the fiber network is numerically simulated by using the lattice Boltzmann (LB) method. A nonlinear relationship between the friction factor and the modified Reynolds number is clearly observed and analyzed by using the Fochheimer equation, which includes the quadratic term of velocity. We obtain a transition from linear to nonlinear region when the Reynolds numbers are sufficiently high, reflecting the inertial effect of the flows. The simulated permeability of such fiber network has relatively good agreement with the experimental results and finite element simulations.

The ensemble statistics of the energy of a random system subjected to harmonic excitation

This paper is concerned with the ensemble statistics of the response to harmonic excitation of a single dynamic system such as a plate or an acoustic volume. Random point process theory is employed, and various statistical assumptions regarding the system natural frequencies are compared, namely: (i) Poisson natural frequency spacings, (ii) statistically independent Rayleigh natural frequency spacings, and (iii) natural frequency spacings conforming to the Gaussian orthogonal ensemble (GOE). The GOE is found to be the most realistic assumption, and simple formulae are derived for the variance of the energy of the system under either point loading or rain-on-the-roof excitation. The theoretical results are compared favourably with numerical simulations and experimental data for the case of a mass loaded plate. © 2003 Elsevier Ltd. All rights reserved.

Computer Simulation Of Random Sphere Packing In An Arbitrarily Shaped Container

Most simulations of random sphere packing concern a cubic or cylindric container with periodic boundary, containers of other shapes are rarely studied. In this paper, a new relaxation algorithm with pre-expanding procedure for random sphere packing in an arbitrarily shaped container is presented. Boundaries of the container are simulated by overlapping spheres which covers the boundary surface of the container. We find 0.4 similar to 0.6 of the overlap rate is a proper value for boundary spheres. The algorithm begins with a random distribution of small internal spheres. Then the expansion and relaxation procedures are performed alternately to increase the packing density. The pre-expanding procedure stops when the packing density of internal spheres reaches a preset value. Following the pre-expanding procedure, the relaxation and shrinking iterations are carried out alternately to reduce the overlaps of internal spheres. The pre-expanding procedure avoids the overflow problem and gives a uniform distribution of initial spheres. Efficiency of the algorithm is increased with the cubic cell background system and double link data structure. Examples show the packing results agree well with both computational and experimental results. Packing density about 0.63 is obtained by the algorithm for random sphere packing in containers of various shapes.

Experimental investigation on low-temperature fatigue crack propagation in offshore structural steel A131 under random sea ice loading

An apparatus of low-temperature controlling for fatigue experiments and its crack measuring system were developed and used for offshore structural steel A131 under conditions of both low temperature and random sea ice. The experimental procedures and data processing were described, and a universal random data processing software for FCP under spectrum loading was written. Many specific features of random ice-induced FCP which differed with constant amplitude FCP behaviours were proposed and temperature effect on ice-induced FCP was pointed out with an easily neglected aspect in designing for platforms in sea ice emphasized. In the end, differences of FCP behaviours between sea ice and ocean wave were presented.

Prediction of mixed-mode cracking direction in random, short-fibre composite-materials

The prediction of cracking direction in composite materials is of significance to the design of composite structures. This paper presents several methods for predicting the cracking direction in the double grooved tension-shear specimen which gives mixed-mode cracking. Five different criteria are used in this analysis: two of them have been used by other investigators and the others are proposed by the present authors. The strain energy density criterion proposed by G.C. Sih is modified to take account of the influence of the anisotropy of the strength on the direction of crack. The two failure criteria of Tsai-Hill and Norris are extended to predict the crack orientation. The stress distributions in the near-notch zone are calculated by using the 8-node quadrilateral isoparametric finite element method. The predictions of all the criteria except one are in good agreement with the experimental measurement. In addition, on the basis of the FEM results, the size of the zone in which the singular term is dominant is estimated.

The fatigue life estimation of notched specimens under random loading

The LY12-cz aluminium alloy sheet specimens with a central hole were tested under constant amplitude loading, Rayleigh narrow band random loading and a typical fighter broad band random loading. The fatigue life was estimated by means of the nominal stress and the Miner's rule. The stress cycles were distinguished by the rainflow count, range count and peak value count, respectively. The comparison between the estimated results and the test results was made. The effects of random loading sequence and small load cycles on fatigue life were also studied.