A numerical method to solve higher-order fractional differential equations

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method

An entropy-based financial decision support system (e-FDSS) for project analysis in construction SMEs

Uncertainty contributes a major part in the accuracy of a decision-making process while its inconsistency is always difficult to be solved by existing decision-making tools. Entropy has been proved to be useful to evaluate the inconsistency of uncertainty among different respondents. The study demonstrates an entropy-based financial decision support system called e-FDSS. This integrated system provides decision support to evaluate attributes (funding options and multiple risks) available in projects. Fuzzy logic theory is included in the system to deal with the qualitative aspect of these options and risks. An adaptive genetic algorithm (AGA) is also employed to solve the decision algorithm in the system in order to provide optimal and consistent rates to these attributes. Seven simplified and parallel projects from a Hong Kong construction small and medium enterprise (SME) were assessed to evaluate the system. The result shows that the system calculates risk adjusted discount rates (RADR) of projects in an objective way. These rates discount project cash flow impartially. Inconsistency of uncertainty is also successfully evaluated by the use of the entropy method. Finally, the system identifies the favourable funding options that are managed by a scheme called SME Loan Guarantee Scheme (SGS). Based on these results, resource allocation could then be optimized and the best time to start a new project could also be identified throughout the overall project life cycle

Symplectic Integration and Nonlinear Dynamic Symmetry Breaking of Frames

An accurate beam finite element is used to solve nonlinear vibration of arched beams and framed structures. The nonlinear governing equations of a skeletal structure are integrated numerically using symplectic integration schemes so that the Poincaré integral invariant of a Hamiltonian flow are preserved during the evolution. The element stiffness matrices are not required to be assembled into global form, because the integration is completed on an element level so that many elements can be handled in core by a small computer. Testing examples include arched beams and frames with and without damping in free and forced vibration. The dynamic symmetry breaking phenomena are noted at the dynamic buckling point

Toeplitz Jacobian Method for Nonlinear Double-Periodic Excitations

The Toeplitz Jacobian matrix method is an efficient algorithm for computing the steady state solutions of nonlinear periodic vibration. In this paper, the method is generalized by using multiple time scales to double-periodic solutions in a multi-frequency excited system. The method is combined with a standard multi-dimensional FFT algorithm to accurately simulate the nonlinear oscillators with widely separated frequencies. The continuation technique can also be incorporated with the Newton–Raphson iteration to further increase its efficiency, and to achieve the complete frequency response characteristics

A Dynamic Branch-Switching Method for Parametrically Excited Systems

The branch-switching algorithm in static is applied to steady state dynamic problems. The governing ordinary differential equations are transformed to nonlinear algebraic equations by means of harmonic balance method using multiple frequency components. The frequency components of the (irrational) nonlinearity of oscillator are obtained by Fast Fourier Transform and Toeplitz Jacobian method (FFT/TJM). All singularities, folds, flips, period doubling and period bubbling, are computed accurately in an analytical manner. Coexisting solutions can be predicted without using initial condition search. The consistence of both stability criteria in time and frequency domains is discussed. A highly nonlinear parametrically excited system is given as example. All connected solution paths are predicted

Dynamic Stiffness Analysis of Curved Thin-Walled Beams

The natural vibration problem of curved thin-walled beams is solved by the dynamic stiffness method. The dynamic stiffness of a curved open thin-walled beam is given. The computed natural frequencies of the beam are compared with those obtained by a completely analytical method to show the high accuracy of the present method. The interaction of in-plane and out-of-plane modes is emphasized

Two diagnostic models for PLC controlled flexible manufacturing systems

Original article can be found at: http://www.sciencedirect.com/science/journal/08906955 Copyright Elsevier Ltd.The control of flexible manufacturing systems (FMS’s) is generally characterised by logical and sequential functions under the auspices of a programmable logic controller (PLC). Operational faults associated with control processes are often confusing to maintenance personnel at workshop level. This has resulted in the development of automatic diagnosis techniques. In this paper two generic diagnostic models based on the logical function chart and sequential control process of the PLC are developed. With the two complementary models, the major operational faults of PLC controlled FMS’s can be diagnosed. Application of the models to a typical FMS is presented.Peer reviewe

Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing’s Equation

A method is proposed for calculating the normal form coefficients of the degenerate Hopf bifurcation system and the steady periodic solutions of a nonlinear vibration system. The results obtained by this method are the same as those obtained by the classical one. The present method is much simpler and can easily be implemented: that is, given the coefficients of the governing equations, the response is obtained directly by substitution