Earticle

A new approach to the critical speed calculation of general multi-mesh gear chain system included bevel gear is presented. A transfer matrix mode! based on Hibner's branch method is developed and the natural properties of the branched rotor system are calculated with using the ${\lambda}$-matrix formulation. A Campbell diagram, in which the excitation sources caused by the mass unbalance of the rotors, misalignment and the transmitted errors of the gearing are considered, shows that, at the neighborhood of the operating speed, there are the two critical speeds amplifying the first mode and the eighth mode.

Shell structures are widely used in a variety of engineering application, and mathematical solution of shell structures are available only for a few special cases. The solution of shell structure is more complicated when it has such condition as winkler foundation, other problems. In this study many simplified methods (analogy of beam on elastic foudation, finite element method and transfer matrix method) are applied to analyze a hemisphere-cylindrical shell structures on elastic foundation. And the transfer matrix method is extensively used for the structural analysis because of its merit in the theoretical backgroud and applicability. Therefore, this paper presents the analysis of hemisphere-cylindrical shell structure base on the transfer matrix method. The technique is attractive for implementation on a numerical solution by means of a computer program coded in FORTRAN language with a few elements. To demonstrate this fact, it gives good results which compare well with finite element method.

Dispersive characteristics of SH waves propagating with an angle θ through one-dimensional elastic/piezoelectric/piezomagnetic phononic crystal are studied in this paper. Firstly, Secondary horizontal wave (SH wave) are studied in this paper. Secondly, the transfer matrix method is used to derive the dispersion equations. The solving process is as follow. The state vectors on both sides of the sub-layer in a unit cell are connected by a matrix, and those on both sides of the interface between the adjacent sub-layers are connected by an identical matrix. Thus, a matrix connecting the state vectors of both sides of the unit cell can be gotten, and the dispersion equation will be derived with the Bloch Theory. Finally, the effect of the component ratio is considered.

Dispersive characteristics of in-plane waves propagating vertically through one-dimensional elastic/piezoelectric phononic crystal with initial stresses are studied in this paper. Firstly, in-plane waves are studied in this paper. In-plane waves are coupled by P-wave (or primary wave) and SV-wave (Secondary wave in the vertical plane). Secondly, the transfer matrix method is used to derive the dispersion equations. The solving process is as follow. The state vectors on both sides of the sub-layer in a unit cell are connected by a matrix, and those on both sides of the interface between the adjacent sub-layers are connected by an identical matrix. Thus, a matrix connecting the state vectors of both sides of the unit cell can be gotten, and the dispersion equation will be derived with the Bloch Theory. Finally, the effect of the initial stresses is considered. For in-plane waves both the normal initial stresses and the shear initial stresses are taken effect. So they are calculated respectively in this paper.

This paper presents a numerical solution for the thick cylinders made of functionally graded materials (FGMs) with a constant Poisson's ratio and an arbitrary Young's modulus. We define two fundamental solutions which are derived from an ordinary differential equation under two particular initial boundary conditions. In addition, for the single layer case, we can define the transfer matrix N. The matrix gives a relation between the values of stress and displacement at the interior and exterior points. By using the assumed boundary condition and the transfer matrix, we can obtain the final solution. The transfer matrix method also provides an effective way for the solution of multiply layered cylinder. Finally, a lot of numerical examples are present.

This paper proposes a transfer matrix method for the bending vibration of two types of tapered beams subjected to axial force, and it is applied to analyze tapered beams with an edge or multiple edge open cracks. One beam type is assumed to be reduced linearly in the cross-section height along the beam length. The other type is a tapered beam in which the cross-section height and width with the same taper ratio is linearly reduced simultaneously. Each crack is modeled as two sub-elements connected by a rotational spring, and the method can evaluate the effect of cracking on the desired number of eigenfrequencies using a minimum number of subdivisions. Among the power series available for the solutions, the roots of the differential equation are computed using the Frobenius method. The computed results confirm the accuracy of the method and are compared with previously reported results. The effectiveness of the proposed methods is demonstrated by examining specific examples, and the effects of cracking and axial loading are carefully examined by a comparison of the single and double tapered beam results.

Combining the analytical transfer matrix method with supersymmetry algebra, a new quantization condition is suggested. To demonstrate the efficiency of the new quantization condition, the eigenenergies of the Coulomb potential are analytically derived. The scattering-led phase shifts are also determined and they are the same for all Coulomb potential states. It is found that the new quantization condition is mathematically simple and exact.

We present an improved transfer matrix algorithm which can be used in solving general n-band effective-mass $Schr{\ddot{o}}dinger$ equation for quantum well structures with arbitrary shaped potential profiles(where n specifies the number of bands explicitly included in the effective-mass equation). In the proposed algorithm, specific formulas are presented for the three-band (the conduction band and the two heavy- and light-hole bands) and two-band (the heavy- and light-hole bands) effective-mass eigensystems. Advantages of the present method can be taken in its simple and unified treatment for general $n{\times}n$ matrix envelope-function equations, which requires relatively smaller computation efforts as compared with existing methods of similar kind. As an illustration of application of the method, numerical computations are performed for a single GaAs/AlGaAs quantum well using both the two-band and three-band formulas. The results are compared with those obtained by the conventional variational procedure to assess the validity of the method.

Combustion instability is a major issue in design of gas turbine combustors for efficient operation with low emissions. Combustion instability is induced by the interaction of the unsteady heat release of the combustion process and the change in the acoustic pressure in the combustion chamber. In an effort to develop a technique to predict self-excited combustion instability of gas turbine combustors, a new stability analysis method based on the transfer matrix method is developed. The method views the combustion system as a one-dimensional acoustic system with a side branch and describes the heat source as the input to the system. This approach makes it possible to use the advantages of not only the transfer matrix method but also well-established classic control theories. The approach is applied to a simple gas turbine combustion system to demonstrate the validity and effectiveness of the approach.

In this study, an in-house $^{152}Eu$ calibration source was produced from a custom epoxy matrix with a density of ${\rho}=1.14g\;cm^{-3}$, which is chemically stable and durable form after its solidification. The homogeneity of $^{152}Eu$ in matrix was obtained better than 98%. For a Marinelli beaker geometry, an efficiency calibration procedure was applied to a n-type, coaxial, 78.5% relative efficient HPGe detector in the energy range of 121.7-1408.0 keV by using in-house $^{152}Eu$ calibration source. Then the measured efficiencies for Marinelli geometry were compared with the results calculated by MEFFTRAN and ANGLE softwares for the validation. Although MEFFTRAN and ANGLE have two different efficiency transfer algorithms to calculate the efficiencies, they usually need to use a reliable and accurate reference efficiency values as input data. Hence, reference efficiency values were obtained experimentally from a multinuclide standard source for the same detector-Marinelli geometry. In the present source characterization, the corrections required for self-absorption and true coincidence summing effects for $^{152}Eu$ gamma-rays were also obtained for a such close counting geometry condition. The experimental results confirmed the validity of efficiency calculations obtained by MEFFTRAN and ANGLE softwares that are calculation tools.

평면파 근사식에 기초한 지형에 의한 파랑변형 모형인 산란체법과 변환행렬법을 비교하여 특성을 분석하였다. 산란체법의 결과가 기존 엄밀해에 보다 근접하고 내재한 물리현상을 보다 명확히 설명하는 것으로 평가된다. 이들은 해석해로 계산이 빠르고 용이하며 지형이 비교적 단순한 경우에는 상당한 정밀도를 보인다.

Both scatterer method and transfer matrix method are compared to analyze their characteristics, which are wave propagation models due to topographic change based on plane wave approximation. Results from the scatterer method are closer to the results obtained by the more accurate existing models and it is appraised that the scatterer method gives the clearer explanation about physical process involved in the wave transformation. Since both methods have analytical solutions, in the computational point of view they are very fast and easy to be implemented. Both methods give a good prediction for wave scattering by relatively simple bedform.

이 논문은 연산장치에서 임의의 유효숫자를 제어함으로써 초월함수를 사용하여 유추된 전달행렬법의 세 가지 수치적 불안정성을 분석했고, 이 방법의 전형적인 불안정성은 다음과 같다. 첫째, 연산과정에서 놓친 고유진동수 문제, 둘째, 수치적 불안정성으로 인한 부정확한 결과, 셋째, 고차고유진동수의 계산적 어려움이다. 두 가지 형태의 전달행렬법을 검토했다. 하나의 전달행렬은 곧고 균일한 단면을 가진 보의 굽힘 진동에 대해 기초적인 삼각함수와 하이퍼볼릭 함수로 구성되었다($4{\times}4$ TMM). 다른 하나는 비틀린 보의 연성된 굽힘 진동에 대해 행렬의 각 요소가 지수함수로 구성되었다($8{\times}8$ TMM). 검토된 전달행렬법은 수치적 안정성을 가지고 연산장치의 오버플로($2^{1024}$)까지 220개 이상의 고유치 쌍을 계산 할 수 있다. $4{\times}4$와 $8{\times}8$ 전달행렬법을 사용하여 고유치 쌍을 계산할 수 있는 분명한 범위가 분석된 결과에서 제공되었다.

This study analyzes the cause of three numerical instabilities for the transfer matrix method (TMM) by controlling the precision of the arbitrary digits in the numerical device as follows: (1) the missing natural frequency, (2) the inaccurate results, and (3) the computational difficulty of the high-order natural frequency. Two types of TMMs are examined. One TMM is composed of the trigonometric and hyperbolic functions ($4{\times}4$ TMM) for the transverse vibration of a straight beam, and the other is composed of exponential functions ($8{\times}8$ TMM) for the coupled bending vibrations of a twisted beam. TMMs with numerical stability can obtain the eigenpairs of over 220 up to the overflow ($2^{1024}$) in the numerical device. The explicit range capable of computing the eigenpairs using the $4{\times}4$ and $8{\times}8$ TMMs without any modifications is proposed in the analyzed results.

The transfer matrix method has been extensively used to analyze the vibration problem. The final stage in this method is to find out solutions which make the frequency determinant zero. However, the frequency determinant includes the exponential terms and it causes instability to calculation and increases error. Recently the frontal transfer matrix method was suggested by Okada to heighten stability and effectivity in calculation. This paper applied the frontal transfer method to both the beam and torsional system, and confirmed stability and effectivity in comparsion with the transfer matrix method and the Holzer method.

This paper presents a numerical method that can evaluate the effect of crack for the in-plane bending vibration of Timoshenko beam. The method is a transfer matrix method that the element transfer matrix is deduced from the element dynamic stiffness matrix. An edge crack is expressed as a rotational spring, and then is formulated as an independent transfer matrix. To demonstrate the accuracy of this theory, the results computed from the present are compared with those obtained from the commercial finite element analysis program. Based on these comparison results, a parametric study is performed to analyze the effects for the size and locations of crack.

For the vibration analysis of 3-dimensional piping system containing fluid flow, a transfer matrix method is presented. The fluid velocity and pressure were considered, that coupled to longitudinal and flexural vibrations. Transfer matrices and point matrices were derived from direct solutions of the differential equations of motion of pipe conveying fluids, and the variations of natural frequency with flow velocity for 3-dimensional piping system were investigated.

As the size of tanker increase, the analysis and strength prediction of the transverse web frames in a tanker have become important problems. Therefore, several papers dicussed the subject and various method of analysis have been presented. Most of these studies are based on the elastic framework analysis. Framework analysis is carried out by the matrix methods. The matrix methods used most frequently are the displacement method, force method and the transfer matrix method. In this paper, the analysis is carried out by the transfer matrix method. The program has been tested by IBM 1130 and the results of example show good agreements with those by the program of stress analysis, STRESS, which was developed in M.I.T.

This paper deals with the rotor vibration analysis of Switched Reluctance Motor(SRM) with the 6/4 poles. For this analysis, 3-dimensional mode shapes corresponding to the natural frequency and critical speed map according to rotor speed are presented by using 3D Transfer Matrix Method(TMM). The gyroscopic effect and shear deformation of rotor are considered.

For analyzing the torsional vibration of a multiple stepped gear system containing a pair of triple gears, a transfer matrix model based on Hibner's branch method is developed and the natural properties of the branched rotor system are calculated with using the $\lambda$-matrix formulation. A Campbell diagram, in which the excitation sources caused by the mass unbalances of the rotors and the transmitted errors of thegearings are considered, shows that, at the neighborhood of the operating speed, there are the four critical speeds amplifying the first mode and the fifth mode. For the surpression of the gear box vibration, two ways are suggested by referring the mode shapes.

This paper present an analysis method of crankshaft of four cylinder internal combustion engine for studying dynamic characteristics of the shaft. For simple analysis, uniform sections of journal, pin and arm parts were assumed. Transfer Matrix Method was used, considering branched part and coordinate transformation part. Natural frequencies, natural modes and transfer functions of crank shaft were investigated based upon the Timosenko beam theory: It was shown that the calculated natural frequencies, modeshapes agree well with the experimental results.