• Structural Engineering and Mechanics
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• 제62권3호
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• pp.345-355
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• 2017

The aim of the present study is to develop an elemental approach based on the differential quadrature method for free vibration analysis of cracked thin plate structures. For this purpose, the equations of motion are established using the classical plate theory. The well-known Generalized Differential Quadrature Method (GDQM) is utilized to discretize the governing equations on each computational subdomain or element. In this method, the differential terms of a quantity field at a specific computational point should be expressed in a series form of the related quantity at all other sampling points along the domain. However, the existence of any geometric discontinuity, such as a crack, in a computational domain causes some problems in the calculation of differential terms. In order to resolve this problem, the multi-block or elemental strategy is implemented to divide such geometry into several subdomains. By constructing the appropriate continuity conditions at each interface between adjacent elements and a crack tip, the whole discretized governing equations of the structure can be established. Therefore, the free vibration analysis of a cracked thin plate will be provided via the achieved eigenvalue problem. The obtained results show a good agreement in comparison with those found by finite element method.

• 대한기계학회논문집A
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• 제31권3호
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• pp.331-337
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• 2007

Rotating cantilever beams can be found in several practical engineering applications such as turbine blades and helicopter rotor blades. For reliable and economic design, it is necessary to estimate the dynamic characteristics of those structures accurately and efficiently since significant variation of dynamic characteristics resulted from rotational motion of the structures. Recently, Differential Transformation Method(DTM) was proposed by Zhou. This method has been applied to fluid dynamics and vibration problems, and has shown accuracy, efficiency and convenience in solving differential equations. The purpose of this study, the free vibration analysis of a rotating cantilever beam, is to seek for the reliable property of DTM and confidence in the results obtained by this method by comparing the results with that of finite element method applied to linear partial differential equations. In particular, this study is worked by supposing optional T-function values because the equations governing chordwise motion are based on two differential equations coupled with each other. This study also shows mode shapes of rotating cantilever beams for various rotating speeds.

• 정보저장시스템학회논문집
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• 제2권1호
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• pp.85-90
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• 2006

In this study, measurement of thermal conductivity of multilayer thin dielectric film has been conducted via differential $3\omega$ method. Also, verification of differential $3\omega$ method has been accomplished with various proposed criteria. The target film for the measurement is 300 nm thick silicon dioxide which is covered with upper protective layer of various thicknesses. The upper protective layer is inserted between the target film and the heater line for purpose of electrical insulator or anti-oxidation barrier since the target film may be a good electrical conductor or a well-oxidizing material. Since the verification of differential $3\omega$ method has not been conducted yet, we have shown that the measurement of thermal conductivity of thin films with upper protective layer via differential $3\omega$ method is verified to be reliable as long as the proposed preconditions of the samples are satisfied. Experimental results show that the experimental errors tend to increase with aspect ratio between thickness of the upper protective layer and width of the heater line due to heat spreading effect.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.905-915
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• 2000

In this article we discuss some aspects of operational Tau Method on delay differential equations and then we apply this method on the differential delay equation defined by $\omega(u)\;=\frac{1}{u}\;for\;1\lequ\leq2$ and $(u\omega(u))'\;=\omega(u-1)\;foru\geq2$, which was introduced by Buchstab. As Khajah et al.[1] applied the Recursive Tau Method on this problem, they had to apply that Method under the Mathematica software to get reasonable accuracy. We present very good results obtained just by applying the Operational Tau Method using a Fortran code. The results show that we can obtain as much accuracy as is allowed by the Fortran compiler and the machine-limitations. The easy applications and reported results concerning the Operational Tau are again confirming the numerical capabilities of this Method to handle problems in different applications.

• 전력전자학회논문지
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• 제8권2호
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• pp.107-115
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• 2003

PMSM은 높은 토크 특성과 우수한 전력 밀도, 논은 효율 때문에 산업용 빛 가정용 기기로 널리 사용되고 있다. PMSM의 우수한 제어 수행을 위해서는 회전자 위치의 정확한 정보가 필요하다. 그러나 위치 센서의 가격이 비싸고, 열악한 환경에서 신뢰도가 떨어지기 때문에 최근에는 센서리스 알고리즘에 대한 연구가 많이 진행되고 있다. 본 논문에서는 회전자 위치의 추정을 위해 쇄교 자속의 도함수를 이용한다. 수치적 미분을 행하지 않고 전압 방정식과 측정된 상전류를 이용한 수식적 미분을 통해 쇄교 자속을 구하는 a-$\beta$ 변환과 수식적 미분을 이용한 새로운 센서리스 알고리즘을 제안한다. 제안된 센서리스 속도 제어 알고리즘이 실험을 통해 증명된다.

• Structural Engineering and Mechanics
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• 제17권1호
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• pp.1-14
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• 2004

Numerical solution to linear bending analysis of circular plates is obtained by the method of harmonic differential quadrature (HDQ). In the method of differential quadrature (DQ), partial space derivatives of a function appearing in a differential equation are approximated by means of a polynomial expressed as the weighted linear sum of the function values at a preselected grid of discrete points. The method of HDQ that was used in the paper proposes a very simple algebraic formula to determine the weighting coefficients required by differential quadrature approximation without restricting the choice of mesh grids. Applying this concept to the governing differential equation of circular plate gives a set of linear simultaneous equations. Bending moments, stresses values in radial and tangential directions and vertical deflections are found for two different types of load. In the present study, the axisymmetric bending behavior is considered. Both the clamped and the simply supported edges are considered as boundary conditions. The obtained results are compared with existing solutions available from analytical and other numerical results such as finite elements and finite differences methods. A comparison between the HDQ results and the finite difference solutions for one example plate problem is also made. The method presented gives accurate results and is computationally efficient.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.667-677
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• 2002

In this paper we obtain the matrix Tau Method representation of a general boundary value problem for Fredholm and Volterra integro-differential equations of order $\nu$. Some theoretical results are given that simplify the application of the Tau Method. The application of the Tau Method to the numerical solution of such problems is shown. Numerical results and details of the algorithm confirm the high accuracy and user-friendly structure of this numerical approach.

• Structural Engineering and Mechanics
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• 제41권1호
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• pp.67-81
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• 2012

Differential Quadrature Method (DQM) is a powerful method which can be used to solve numerical problems in the analysis of structural and dynamical systems. In this study the governing equation which represents the free vibration of coupled shear walls is solved using the DQM method. A one-dimensional model has been used in this study. At the end of study various examples are presented to verify the accuracy of the method.

• 한국통신학회논문지
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• 제32권2A호
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• pp.195-202
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• 2007

A differential space-frequency block code - orthogonal frequency division multiplexing (SFBC-OFDM) scheme as a multiple-input multiple-output (MIMO) transmission technique for next-generation digital multimedia broadcasting (DMB) is proposed in this paper. A linear decoding method for differential SFBC, which performs comparably to the ML decoding method, is derived for the cases of two or four transmit antennas. A simple table lookup method is proposed to improve the efficiency of the encoding/decoding process of DSFBC for the case of non-constant modulus constellations. A DMB MIMO channel model, developed by extending the 3GPP MIMO model to fit DMB environments, is used to compare BER performances of differential space block code schemes for various channel environments. Simulation results show that the differential SFBC-16QAM scheme using either four transmit antennas with one receive antenna or two transmit antennas with two receive antennas achieves a performance gain of 12dB than that of the conventional DQPSK scheme, even with a data rate twice faster.

• Structural Engineering and Mechanics
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• 제35권5호
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• pp.645-658
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• 2010

In this study, the Differential Transform Method (DTM) is employed in order to solve the governing differential equation of a moving Bernoulli-Euler beam with axial force effect and investigate its free flexural vibration characteristics. The free vibration analysis of a moving Bernoulli-Euler beam using DTM has not been investigated by any of the studies in open literature so far. At first, the terms are found directly from the analytical solution of the differential equation that describes the deformations of the cross-section according to Bernoulli-Euler beam theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equation of the motion. The calculated natural frequencies of the moving beams with various combinations of boundary conditions using DTM are tabulated in several tables and are compared with the results of the analytical solution where a very good agreement is observed.