Introduction to the special issue on real world applications of intelligent tutoring systems

The idea behind creating this special issue on real world applications of intelligent tutoring systems was to bring together in a single publication some of the most important examples of success in the use of ITS technology. This will serve as a reference to all researchers working in the area. It will also be an important resource for the industry, showing the maturity of ITS technology and creating an atmosphere for funding new ITS projects. Simultaneously, it will be valuable to academic groups, motivating students for new ideas of ITS and promoting new academic research work in the area.

Delamination analysis of carbon fibre reinforced laminates: evaluation of a special step drill

Drilling of carbon fibre/epoxy laminates is usually carried out using standard drills. However, it is necessary to adapt the processes and/or tooling as the risk of delamination, or other damages, is high. These problems can affect mechanical properties of produced parts, therefore, lower reliability. In this paper, four different drills – three commercial and a special step (prototype) – are compared in terms of thrust force during drilling and delamination. In order to evaluate damage, enhanced radiography is applied. The resulting images were then computational processed using a previously developed image processing and analysis platform. Results show that the prototype drill had encouraging results in terms of maximum thrust force and delamination reduction. Furthermore, it is possible to state that a correct choice of drill geometry, particularly the use of a pilot hole, a conservative cutting speed – 53 m/min – and a low feed rate – 0.025 mm/rev – can help to prevent delamination.

Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.