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The method of entropy has been useful in evaluating inconsistency on human judgments. This paper illustrates an entropy-based decision support system called e-FDSS to the solution of multicriterion risk and decision analysis in projects of construction small and medium enterprises (SMEs). It is optimized and solved by fuzzy logic, entropy, and genetic algorithms. A case study demonstrated the use of entropy in e-FDSS on analyzing multiple risk criteria in the predevelopment stage of SME projects. Survey data studying the degree of impact of selected project risk criteria on different projects were input into the system in order to evaluate the preidentified project risks in an impartial environment. Without taking into account the amount of uncertainty embedded in the evaluation process; the results showed that all decision vectors are indeed full of bias and the deviations of decisions are finally quantified providing a more objective decision and risk assessment profile to the stakeholders of projects in order to search and screen the most profitable projects. CE Database subject headings: Artificial intelligence; Construction industry; Decision support systems; Entropy; Risk management. Author keywords: Artificial intelligence; Construction industry; Decision support systems; Entropy; Risk. DOI: 10.1061/(ASCE)0887-3801(2010)24:1(81)

The paper applies the power series method to find the dynamic stiffness for the dynamics axial-moment buckling analyses of linear framed structures. Since the formulation is exact in classical sense, one element is good enough for the entire beam. The dynamic stiffness thus obtained can be decomposed into the stiffness, mass and initial stress matrices at a particular frequency, a particular axial force and a particular initial moment. The given axial force and moment can be nonuniformly distributed. The interaction diagrams in classical loading conditions of uniform moment, moment due to concentrated and distributed lateral force are given explicitly. The effects of warping rigidity, torsion rigidity, axial tension and compression are investigated in detail. The static and dynamic interaction buckling of a two-section I-beam structure is studied. Finally, we conclude that the three dimensional interaction diagram of the dynamic biaxial moment buckling can be obtained simply by rotating the three dimensional interaction diagram of the dynamic mono-axial moment buckling about the frequency axis if the bimoments are appropriately scaled. It is shown that application for non-uniform section is not suitable due to convergent problem. The method is very efficient that many interaction diagrams are produced for the first time. DOI: 10.1061/(ASCE)0733-9399(2009)135:8(852) CE Database subject headings: I beams; Buckling; Stability; Frames; Structural dynamics; Thin wall sections; Finite element method; Stiffness.

This paper employs the atomic-scale finite element method (AFEM) to study critical strain of axial buckling for carbon nanotubes (CNTs). Brenner et al. 'second-generation' empirical potential is used to model covalent bonds among atoms. The computed energy curve and critical strain for (8, 0) single-walled CNT (SWNT) agree well with molecular dynamics simulations. Both local and global buckling are achieved, two corresponding buckling zones are obtained, and the global buckling behavior of SWNT with a larger aspect ratio approaches gradually to that of a column described by Euler's formula. For double-walled CNTs with smaller ratio of length to outer diameter, the local buckling behavior can be explained by conventional shell theory very well. AFEM is an efficient way to study buckling of CNTs. [DOI: 10.1115/1.2198548]

In financial decision-making processes, the adopted weights of the objective functions have significant impacts on the final decision outcome. However, conventional rating and weighting methods exhibit difficulty in deriving appropriate weights for complex decision-making problems with imprecise information. Entropy is a quantitative measure of uncertainty and has been useful in exploring weights of attributes in decision making. A fuzzy and entropy-based mathematical approach is employed to solve the weighting problem of the objective functions in an overall cash-flow model. The multiproject being undertaken by a medium-size construction firm in Hong Kong was used as a real case study to demonstrate the application of entropy. Its application in multiproject cash flow situations is demonstrated. The results indicate that the overall before-tax profit was HK$ 0.11 millions lower alter the introduction of appropriate weights. In addition, the best time to invest in new projects arising from positive cash flow was identified to be two working months earlier than the nonweight system. DOI: 10.1061/(ASCE)0733-9364(2006)132:10(1099) CE Database subject headings: Decision making; Entropy; Financial management: Fuzzy sets; Weighing devices.

Abstract: In this paper, the nonlinear dynamics of the disturbed Hamiltonian systems of a suspended gyrostat with five degrees of freedom are investigated in detail. The periodic motions of the [...]

An analytical trapezoidal hierarchical element for the transverse vibration of Mindlin plates resting on two-parameter foundations is presented. Legendre orthogonal polynomials are used as enriching shape functions to avoid the shear-locking problem and to improve considerably the computational efficiency. Element matrices are integrated in closed form eliminating the numerical integration errors conventionally found. With the [C.sup.0] continuity requirement, the element can be used to analyze any triangular and polygonal plates without difficulty, while the Kirchhoff p-version elements requiring [C.sup.1] continuity are not as versatile. The computed natural frequencies for rectangular, skew, trapezoidal, triangular, annular, and polygonal plates on two-parameter foundations show that the convergence of the proposed element is very fast compared to the conventional linear finite elements with respect to the number of degrees of freedom used. Many numerical examples are given. CE Database subject headings: Plates; Finite element method; Vibration; Foundations.

An experimental test rig is built to verify the dynamics of a multi-bearing rotor. It consists of two flexibly coupled shafts and is connected to a motor at one end via a flexible coupling. Each of the shafts is supported at the ends by two hydrodynamic bearings and is attached with two disks with equal and unequal masses, respectively. The mathematical model of the test rig is developed and is simulated numerically. The non-stationary dynamic responses of the system during speed-up with a constant angular acceleration are shown, respectively, by the non-stationary bifurcation diagrams, the selected time flows, and the spectrum cascades. Experiments are then carried out on the test rig. Generally, the numerical results are verified qualitatively by the experiments. Both results indicate that the non-synchronous whirls of the two shafts influence each other when flexibly coupled together. In particular, a new phenomenon is found for the four-bearing rotor system: the pre-existing non-synchronous whirl/whip resulted from the instability of one shaft can activate the onset of oil instability of another shaft. In the theoretical simulation, this phenomenon represents the rapid increase of the non-synchronous whirl orbit, whereas in the experiment, it represents the simultaneous existence of two whirl/whip frequencies in the spectra. [DOI 10.1115/1.1898336] Keywords: Rotor, Multi-bearing, Experiment, Non-synchronous Whirl, Oil Instability