Ahmed M. Elmogy^1,2,*, Amany Sarhan², Wael M. Elawady²

CMC-Computers, Materials & Continua, Vol.72, No.3, pp. 5629-5641, 2022, DOI:10.32604/cmc.2022.025247

Abstract As most real world systems are significantly nonlinear in nature, developing robust controllers have attracted many researchers for decades. Robust controllers are the controllers that are able to cope with the inherent uncertainties of the nonlinear systems. Many control methods have been developed for this purpose. Sliding mode control (SMC) is one of the most commonly used methods in developing robust controllers. This paper presents a higher order SMC (HOSMC) approach to mitigate the chattering problem of the traditional SMC techniques. The developed approach combines a third order SMC with an adaptive PID (proportional, integral, derivative) sliding surface to overcome… More >

A. I. Asnor¹, S. A. M. Yatim¹, Z. B. Ibrahim², N. Zainuddin³

CMC-Computers, Materials & Continua, Vol.67, No.1, pp. 1253-1267, 2021, DOI:10.32604/cmc.2021.014781

Abstract Many initial value problems are difficult to be solved using ordinary, explicit step-by-step methods because most of these problems are considered stiff. Certain implicit methods, however, are capable of solving stiff ordinary differential equations (ODEs) usually found in most applied problems. This study aims to develop a new numerical method, namely the high order variable step variable order block backward differentiation formula (VSVO-HOBBDF) for the main purpose of approximating the solutions of third order ODEs. The computational work of the VSVO-HOBBDF method was carried out using the strategy of varying the step size and order in a single code. The… More >

A. Alaimo¹, A. Milazzo¹, C. Orlando¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.15, No.4, pp. 137-144, 2010, DOI:10.3970/icces.2010.015.137

Abstract The axial and flexural natural frequencies of magneto-electro-elastic bimorph beam devices are analyzed in the framework of the third-order shear deformation theory (TSDT). Although the assumption of parabolic transverse shear strain distribution along the thickness leads to higher order stress resultants the use of the TSDT allows to avoid the need for shear correction factor. Moreover, since the electric and magnetic potentials strictly depend on the shear strains, a more accurate modeling of the magneto-electric coupling can be achieved by expanding the kinematical model up to the cubic term. The natural frequencies for different mechanical boundary conditions are computed by… More >

S.D. Akbarov^1,2

CMC-Computers, Materials & Continua, Vol.32, No.1, pp. 29-60, 2012, DOI:10.3970/cmc.2012.032.029

Abstract By the use of the Murnaghan potential the influence of third order elastic constants on axisymmetric longitudinal wave propagation velocity in a pre-stressed two-layered circular hollow cylinder is investigated. This investigation is carried out within the scope of the piecewise homogeneous body model by utilizing the first version of the small initial deformation theory of the Three-dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies. Numerical results are obtained and analyzed for the cases where the material of the outer hollow cylinder material is aluminum, but the material of the inner cylinder is steel (Case 1) and tungsten (Case… More >

H.B. Chen¹, Masa. Tanaka²

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.1, pp. 19-42, 2010, DOI:10.3970/cmes.2010.069.019

Abstract Highly accurate calculation of derivative values to the field variable is a key issue in numerical analysis of engineering problems. The boundary integral equations (BIEs) of potential second derivatives are of third order singularities and obviously the direct calculation of these high order singular integrals is rather cumbersome. The idea of the present paper is to use an indirect algorithm which is based on the regularized BIE formulations of the potential second derivatives, following the work of the present first author and his coworkers. The regularized formulations, numerical strategies and example tests are given for both potential first and second… More >

Hieu H. Pham¹, Tahir Ça ˇgın¹

CMC-Computers, Materials & Continua, Vol.16, No.2, pp. 175-194, 2010, DOI:10.3970/cmc.2010.016.175

Abstract We analyze the lattice dynamics of Fe in different crystal phases (bcc, fcc and hcp) by using density-functional theory. The study on equations of states indicates that bcc Fe is more stable than fcc and hcp Fe at low pressures. However, dynamical instabilities in lattice vibrations of bcc Fe predict a phase transformation from bcc to hcp at higher pressures. We reported a complete set of second-order and third-order elastic constants of Fe in these three phases. We observed a linear variation in the values of second order elastic constant as a function of increased pressures. The phonon spectra were… More >