• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.423-445
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• 2021

In this paper, a new form of poly-Genocchi polynomials is defined by means of polylogarithm, namely, the Apostol-type poly-Genocchi polynomials of higher order with parameters a, b and c. Several properties of these polynomials are established including some recurrence relations and explicit formulas, which are used to express these higher order Apostol-type poly-Genocchi polynomials in terms of Stirling numbers of the second kind, Apostol-type Bernoulli and Frobenius polynomials of higher order. Moreover, certain differential identity is obtained that leads this new form of poly-Genocchi polynomials to be classified as Appell polynomials and, consequently, draw more properties using some theorems on Appell polynomials. Furthermore, a symmetrized generalization of this new form of poly-Genocchi polynomials that possesses a double generating function is introduced. Finally, the type 2 Apostolpoly-Genocchi polynomials with parameters a, b and c are defined using the concept of polyexponential function and several identities are derived, two of which show the connections of these polynomials with Stirling numbers of the first kind and the type 2 Apostol-type poly-Bernoulli polynomials.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1127-1132
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• 2000

Impulsive acoustic and vibration signals within rotating machinery are often induced by irregular impacting. The detection of these impulses can be useful for fault diagnosis purposes. Recently there has been an increasing trend towards the use of higher order statistics for fault detection within mechanical systems based on the observation that impulsive signals tend to increase the kurtosis values. This paper considers the use of the third and fourth order Wigner moment spectra, called the Wigner bi- and tri- spectra receptively, for analysing such signals. Expressions for the auto-and cross-terms in these distributions are presented and discussed. It is shown that the Wigner trispectrum is a more suitable analysis tool and it performance is compared to its second order counterpart for detecting impulsive signals. These methods are also applied to measured data sets from an industrial gearbox.

• Structural Engineering and Mechanics
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• v.10 no.5
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• pp.427-440
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• 2000

The formulas for the perturbation analysis with modes of close eigenvalues are derived in this paper. Emphasis is made on the consistency of the straightforward perturbation process, given the complete terms of perturbations in the zeroth-order, which is a form of Rayleigh quotient, and in the higher-orders. By dividing the perturbation of eigenvector into two parts, the first-order perturbation with respect to the modes of close eigenvalues is moved into the zeroth-order perturbation. The normality condition is employed to compute the higher-order perturbations of eigenvector. The algorithm can be condensed to a single mode with a distinct eigenvalue, and this can accelerate the convergence of the perturbation analysis. The example confirms that the perturbation approximation obtained from the suggested procedure is in a good accuracy on the eigenvalues, eigenvectors, and normality.

• Smart Structures and Systems
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• v.13 no.4
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• pp.659-683
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• 2014

The static analysis of structures with arbitrary cross-section geometry and material lamination via a refined one-dimensional (1D) approach is presented in this paper. Higher-order 1D models with a variable order of expansion for the displacement field are developed on the basis of Carrera Unified Formulation (CUF). Classical Euler-Bernoulli and Timoshenko beam theories are obtained as particular cases of the first-order model. Numerical results of displacement, strain and stress are provided by using the finite element method (FEM) along the longitudinal direction for different configurations in excellent agreement with three-dimensional (3D) finite element solutions. In particular, a layered thin-walled cylinder is considered as first assessment with a laminated conventional cross-section. An atherosclerotic plaque is introduced as a typical structure with arbitrary cross-section geometry and studied for both the homogeneous and nonhomogeneous material cases through the 1D variable kinematic models. The analyses highlight limitations of classical beam theories and the importance of higher-order terms in accurately detecting in-plane cross-section deformation without introducing additional numerical problems. Comparisons with 3D finite element solutions prove that 1D CUF provides remarkable three-dimensional accuracy in the analysis of even short and nonhomogeneous structures with arbitrary geometry through a significant reduction in computational cost.

• Structural Engineering and Mechanics
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• v.89 no.2
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• pp.199-211
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• 2024

The loading capacity of engineering structures/components reduces after the initiation and propagation of crack eventually leads to the final failure. Hence, it becomes essential to deal with the crack and its effects at the design and simulation stages itself, by detecting the prone area of the fracture. The phase-field (PF) method has been accepted widely in simulating fracture problems in complex geometries. However, most of the PF methods are formulated with second order continuity theoryinvolving C⁰ continuity. In the present study, PF method based on fourth-order (i.e., higher order) theory, maintaining C¹ continuity has been proposed for ductile fracture simulation. The formulation includes fourth-order derivative terms of phase field variable, varying between 0 and 1. Applications of fourth-order PF theory to ductile fracture simulation resulted in novelty in this area. The proposed formulation is numerically solved using a two-dimensional finite element (FE) framework in 3-layered manner system. The solutions thus obtained from the proposed fourth order theory for different benchmark problems portray the improvement in the accuracy of the numerical results and are well matched with experimental results available in the literature. These results are also compared with second-order PF theory and a comparison study demonstrated the robustness of the proposed model in capturing ductile behaviour close to experimental observations.

• Journal of the Korean Institute of Telematics and Electronics T
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• v.36T no.2
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• pp.21-31
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• 1999

This paper presents a new possibility of calculating optimal control for large scale which consist of non-linear dynamic sub-systems using two level hierarchical structures method. And the proposed method is based on the idea of block pulse transformation to simplify the algorithm and its calculation. This algorithm used an expansion around the equilibrium point of the system to fix the second and higher order terms. These terms are compensated for iteratively at the second level by providing a prediction for the states and controls which form of a part of the higher order terms. In this new approach the quadratic penalty terms are not used in the cost function. This allows convergence over a longer time horizon and also provides faster convergence. And the method is applied to the problem of optimization of the synchronous machine. Results show that the new approach is superior to conventional numerical method or other previous algorithm.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.5B
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• pp.493-496
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• 2009

In this study, we derive the extended mild-slope equation in terms of the velocity potential using the Euler-Lagrange equation. First, we follow Kim and Bai (2004) who derive the complementary mild-slope equation in terms of the stream function using the Euler-Lagrange equation and we compare their equation to the existing extended mild-slope equations of the velocity potential. Second, we derive the extended mild-slope equation in terms of the velocity potential using the Euler-Lagrange equation. In the developed equation, the higher-order bottom variation terms are newly developed and found to be the same as those of Massel (1993) and Chamberlain and Porter (1995). The present study makes wide the area of coastal engineering by developing the extended mild-slope equation with a way which has never been used before.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.6
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• pp.2446-2462
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• 2016

In this paper, a frequency domain Expectation-Maximization (EM)-based channel estimation algorithm for Space Time Block Coded-Orthogonal Frequency Division Multiplexing (STBC-OFDM) systems is investigated to support higher data rate applications in wireless communications. The computational complexity of the frequency domain EM-based channel estimation is increased when higher order constellations are used because of the ascending size of the search set space. Thus, a search set reduction algorithm is proposed to decrease the complexity without sacrificing the system performance. The performance results of the proposed algorithm is obtained in terms of Bit Error Rate (BER) and Mean Square Error (MSE) for 16QAM and 64QAM modulation schemes.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.217-224
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• 2005

A higher order zig-zag shell theory is developed to refine the predictions of the mechanical and thermal behaviors partially coupled. The in-plane displacement fields are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field through the thickness. Smooth parabolic distribution through the thickness is assumed in the out-of-plane displacement in order to consider transverse normal deformation and stress. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface conditions of transverse shear stresses. Thus the proposed theory has only seven primary unknowns and they do not depend upon the number of layers. In the description of geometry and deformation of shell surface, all rigorous exact expressions are used. Through the numerical examples of partially coupled analysis, the accuracy and efficiency of the present theory are demonstrated. The present theory is suitable in the predictions of deformation and stresses of thick composite shell under mechanical and thermal loads combined.

• Smart Structures and Systems
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• v.16 no.5
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• pp.853-872
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• 2015

Numerical analysis of large amplitude free vibration behaviour of laminated composite spherical shell panel embedded with the piezoelectric layer is presented in this article. For the investigation purpose, a general nonlinear mathematical model has been developed using higher order shear deformation mid-plane kinematics and Green-Lagrange nonlinearity. In addition, all the nonlinear higher order terms are included in the present mathematical model to achieve any general case. The nonlinear governing equation of freely vibrated shell panel is obtained using Hamilton's principle and discretised using isoparametric finite element steps. The desired nonlinear solutions are computed numerically through a direct iterative method. The validity of present nonlinear model has been checked by comparing the responses to those available published literature. In order to examine the efficacy and applicability of the present developed model, few numerical examples are solved for different geometrical parameters (fibre orientation, thickness ratio, aspect ratio, curvature ratio, support conditions and amplitude ratio) with and/or without piezo embedded layers and discussed in details.