• The Transactions of the Korean Institute of Electrical Engineers C
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• v.53 no.10
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• pp.539-545
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• 2004

In this paper, we consider the problem of capacitance matrix calculation for strip-line and other interconnects crossings. The problem is formulated in the spectral domain using the method of moments. Sinc-functions are employed as basis functions. Conventionally, such a formulation leads to a large, non-sparse system of linear equations in which the calculation of each of the coefficient requires the evaluation of a Fourier-Bessel integral. Such calculations are computationally very intensive. In the method proposed here, we provide simplified expressions for the coefficients in the moment method matrix. Using these simplified expressions, the coefficients can be calculated very efficiently. This leads to a fast evaluation of the capacitance matrix of the structure. Computer simulations are provided illustrating the validity of the method proposed.

• Geomechanics and Engineering
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• v.6 no.3
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• pp.213-233
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• 2014

The present paper is dealing with the investigation of the stress field around the infinitely long cylindrical cavity, of a circular cross section, contained in the transversally isotropic elastic continuum. Investigation is based upon the determination of the stress function that satisfies the biharmonic equation, for the given boundary conditions and for rotationaly symmetric loading. The solution of the partial differential equation of the problem is given in the form of infinite series of Bessel's functions. Determination of the stress-strain field around cavities is a common requirement for estimation of safety of underground rock excavations.

• Structural Engineering and Mechanics
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• v.12 no.1
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• pp.85-100
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• 2001

In this paper, an analytical procedure for solving several static and dynamic problems of non-uniform beams is proposed. It is shown that the governing differential equations for several stability, free vibration and static problems of non-uniform beams can be written in the from of a unified self-conjugate differential equation of the second-order. There are two functions in the unified equation, unlike most previous researches dealing with this problem, one of the functions is selected as an arbitrary expression in this paper, while the other one is expressed as a functional relation with the arbitrary function. Using appropriate functional transformation, the self-conjugate equation is reduced to Bessel's equation or to other solvable ordinary differential equations for several cases that are important in engineering practice. Thus, classes of exact solutions of the self-conjugate equation for several static and dynamic problems are derived. Numerical examples demonstrate that the results calculated by the proposed method and solutions are in good agreement with the corresponding experimental data, and the proposed procedure is a simple, efficient and exact method.

• Structural Engineering and Mechanics
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• v.8 no.3
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• pp.243-256
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• 1999

Using appropriate transformations, the differential equation for flexural free vibration of a cantilever bar with variably distributed mass and stiffness is reduced to a Bessel's equation or an ordinary differential equation with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass. The general solutions for flexural free vibration of one-step bar with variable cross-section are derived and used to obtain the frequency equation of multi-step cantilever bars. The new exact approach is presented which combines the transfer matrix method and closed form solutions of one step bars. Two numerical examples demonstrate that the calculated natural frequencies and mode shapes of a 27-storey building and a television transmission tower are in good agreement with the corresponding experimental data. It is also shown through the numerical examples that the selected expressions are suitable for describing the distributions of stiffness and mass of typical tall buildings and high-rise structures.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.575-598
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• 2017

This paper introduces and studies a generalization of the classical Struve function of order p given by $$_aS_{p,c}(x):=\sum\limits_{k=0}^{\infty}\frac{(-c)^k}{{\Gamma}(ak+p+\frac{3}{2}){\Gamma}(k+\frac{3}{2})}(\frac{x}{2})^{2k+p+1}$$. Representation formulae are derived for $_aS_{p,c}$. Further the function $_aS_{p,c}$ is shown to be a solution of an (a + 1)-order differential equation. Monotonicity and log-convexity properties for the generalized Struve function $_aS_{p,c}$ are investigated, particulary for the case c = -1. As a consequence, $Tur{\acute{a}}n$-type inequalities are established. For a = 2 and c = -1, dominant and subordinant functions are obtained for the Struve function $_2S_{p,-1}$.

• Geophysics and Geophysical Exploration
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• v.9 no.1
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• pp.73-85
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• 2006

Array observations of the vertical component of microtremors are frequently conducted to estimate a subsurface layered-earth structure on the assumption that microtremors consist predominantly of the fundamental mode Rayleigh waves. As a useful tool in the data collection, processing and analysis, the spatial autocorrelation (SPAC) method is widely used, which in practice requires a circle array consisting of M circumferential stations and one centre station (called "M-station circle array", where M is the number of stations). The present paper considers the minimum number of stations required for a circle array for efficient data collection in terms of analytical efficacy and field effort. This study first rearranges the theoretical background of the SPAC algorithm, in which the SPAC coefficient for a circle array with M infinite is solely expressed as the Bessel function, $J_0(rk)$ (r is the radius and k the wavenumber). Secondly, the SPAC coefficient including error terms independent of the microtremor energy field for an M-station circle array is analytically derived within a constraint for the wave direction across the array, and is numerically evaluated in respect of these error terms. The main results of the evaluation are: 1) that the 3-station circle array when compared with other 4-, 5-, and 9-station arrays is the most efficient and favourable for observation of microtremors if the SPAC coefficients are used up to a frequency at which the coefficient takes the first minimum value, and 2) that the Nyquist wavenumber is the most influential factor that determines the upper limit of the frequency range up to which the valid SPAC coefficient can be estimated.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.12 no.3
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• pp.116-129
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• 2000

The interaction of incident monochromatic waves with a tensioned, flexible, circular membrane submerged horizontally below free surface is investigated in the frame of three-dimensional linear hydro-elastic theory. The velocity potential is split into two parts i.e. the diffraction potential representing the scattering of incident waves by a rigid circular disk and the radiation potential describing motion induced waves by elastic responses of flexible membrane. The fluid domain is divided into three regions, and the diffraction and radiation potentials in each region are expressed by the Fourier Bessel series. The displacement of circular membrane is expanded with a set of natural functions, which satisfy the membrane equation of motion and boundary conditions. The unknown coefficients in each region are determined by applying the continuity of pressure and normal velocity at the matching boundaries. The results show that various types of wave focusing are possible by controlling the size, submergence depth, and tension of membrane.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.12
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• pp.2038-2046
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• 1997

In this paper the instability of the system which has a disk and a mass-spring-damper system interacting through a medium having stiffness and damping is analyzed. To solve the equations of motion of this systme, it is assumed that the solution consists of the eigenfunctions which are the products of the Bessel functions and sine or cosine functions. The former represents the radial characteristics of the disk and the latter represents the circumferential characteristics. Using this assumed solution and the orthogonality of the eigenfunctions, the equations of motion can be transformed into a set of equations of motion with variables dependent only on the time. After this set is changed to the state equation, the eigenvalue problem can be made. Once the eigenvalues are calculated according to the angular velocity of the disk, the dynamic characteristics ofthis system is obtained. Because the thickness of the disk and the element characteristics of the mass-spring-damper system have important effects on the stability of the system, it will be understood how these factors affect the system and then a method to ameliorate the stability of the system with a disk will be presented.

• Coupled systems mechanics
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• v.12 no.2
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• pp.127-149
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• 2023

A theoretical method is developed to analyze the free vibration of an elastic annular plate in contact with an ideal liquid. The displacement potential functions of the contained liquid are expressed as a combination of the Bessel functions that satisfy the Laplace equation and the liquid boundary conditions. The compatibility condition along the interface between the annular plate and the contained liquid is taken into account to consider the fluid-structure coupling. The dynamic displacement of the wet annular plate is assumed to be a combination of dry eigenfunctions, allowing for prediction of the natural frequencies using the Rayleigh-Ritz method. The study investigates the effect of radial liquid boundary conditions on the natural frequencies of the wet annular plate, considering four types of liquid bounding: outer container bounded, outer and inner bounded, inner bounded, and radially unbounded. The proposed theoretical method is validated by comparing the predicted wet natural frequencies with those obtained from finite element analysis, showing excellent accuracy. The results indicate that the radial liquid bounding effect on the natural frequencies is negligible for the axisymmetric vibrational mode, but relatively significant for the mode with one nodal diameter (n =1) and no nodal circle (m' = 0). Furthermore, the study reveals that the wet natural frequencies are the largest for the plate with an inner bounded cylinder among the radial liquid boundary cases, regardless of the vibration mode.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.4
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• pp.317-323
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• 2014

This study is concerned with the free vibration analysis of an inextensible uniform rope with a spring-mass system at the tip. The rope is hanged vertically in a gravitational field. This problem is related to the free vibration of an elevator rope connected to an elevator cage. The equation of motion and the corresponding boundary conditions are derived by using the Hamilton's principle. The general solution of the governing equation of motion is expressed in terms of Bessel functions. The characteristic equation was derived by applying the boundary conditions. The characteristic values which are in fact non-dimensionalized natural frequencies were obtained numerically. The effects of mass and spring constant were investigated. The numerical results show how the tip mass and spring affect the natural frequencies of the rope.