• Structural Engineering and Mechanics
• /
• v.29 no.5
• /
• pp.531-550
• /
• 2008

This paper adopts the numerical assembly method (NAM) to determine the exact solutions of natural frequencies and mode shapes of a multi-span and multi-step beam carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and springmass systems. First, the coefficient matrix for an intermediate station with various concentrated elements, cross-section change and/or pinned support and the ones for the left-end and right-end supports of a beam are derived. Next, the overall coefficient matrix for the entire beam is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact solutions for the natural frequencies of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and the associated mode shapes are obtained by substituting the corresponding values of integration constants into the associated eigenfunctions.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.2
• /
• pp.317-333
• /
• 2024

For the classes of analytic functions f defined on the unit disk satisfying ${\frac{2zf'(z)}{f(z)-f(-z)}}{\prec}{\varphi}(z)$) and ${\frac{(2zf'(z))'}{(f(z)-f(-z))'}}{\prec}{\varphi}(z)$, denoted by S^*_s(𝜑) and C_s(𝜑), respectively, the sharp bound of the n^th Taylor coefficients are known for n = 2, 3 and 4. In this paper, we obtain the sharp bound of the fifth coefficient. Additionally, the sharp lower and upper estimates of the third order Hermitian Toeplitz determinant for the functions belonging to these classes are determined. The applications of our results lead to the establishment of certain new and previously known results.

• Journal of applied mathematics & informatics
• /
• v.39 no.1_2
• /
• pp.133-143
• /
• 2021

The purpose of this paper is to introduce and study certain subclasses of analytic functions by using Ruscheweyh derivative operator. We discuss various of interesting properties such as, necessary condition, arc length problem and growth rate of coefficient of newly defined class. Also rate of growth of Hankel determinant will be estimated.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.389-404
• /
• 2023

We prove sharp bounds for Hankel determinants for starlike functions f with respect to symmetrical points, i.e., f given by $f(z)=z+{\sum{_{n=2}^{\infty}}}\,{\alpha}_nz^n$ for z ∈ 𝔻 satisfying $$Re{\frac{zf^{\prime}(z)}{f(z)-f(-z)}}>0,\;z{\in}{\mathbb{D}}$$. We also give sharp upper and lower bounds when the coefficients of f are real.

• Coupled systems mechanics
• /
• v.6 no.3
• /
• pp.317-333
• /
• 2017

The present paper is concerned with the investigation of Rayleigh waves in a homogeneous transversely isotropic magnetothermoelastic medium with two temperature, in the presence of Hall current and rotation. The formulation is applied to the thermoelasticity theories developed by Green-Naghdi theories of Type-II and Type-III. Secular equations are derived mathematically at the stress free and thermally insulated boundaries. The values of Determinant of secular equations, phase velocity and Attenuation coefficient with respect to wave number are computed numerically. Cobalt material has been chosen for transversely isotropic medium and magnesium material is chosen for isotropic solid. The effects of rotation, magnetic field and phase velocity on the resulting quantities and on particular case of isotropic solid are depicted graphically. Some special cases are also deduced from the present investigation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2013.04a
• /
• pp.141-146
• /
• 2013

This research investigates the stability analysis for the rotating and the stationary grooved journal bearing. The dynamic coefficients of the journal bearing are calculated by using FEM and the perturbation method. When journal bearing is in whirling motion, the dynamic coefficients have time-varying components as a sine wave due to the reaction force of oil film toward the center of journal even in the steady state. The solutions for the equations of motion can be assumed as the Fourier series expansion. The equations of motion can be rewritten as the linear algebraic equations with respect to the Fourier coefficients. Then, stability of the grooved journal bearing can be calculated by Hill's infinite determinant. The periodic function of dynamic coefficients is derived using Fourier Fast Transform(FFT).The stability of journal bearing is determined as rotating speed increases and the stability of rotating grooved journal bearing is compared and discussed with the stability of stationary grooved journal bearing.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.4
• /
• pp.839-850
• /
• 2020

For functions f(z) = z + a₂z² + a₃z³ + ⋯ belonging to particular classes, this paper finds sharp bounds for the initial coefficients a₂, a₃, a₄, as well as the sharp estimate for the second order Hankel determinant H₂(2) = a₂a₄ - a₂³. Two classes are treated: first is the class consisting of f(z) = z + a₂z² + a₃z³ + ⋯ in the unit disk 𝔻 satisfying $$\|\(\frac{z}{f(z)}\)^{1+{\alpha}}\;f^{\prime}(z)-1\|<{\lambda},\;0<{\alpha}<1,\;0<{\lambda}{\leq}1.$$ The second class consists of Bazilevič functions f(z) = z+a₂z²+a₃z³+⋯ in 𝔻 satisfying $$Re\{\(\frac{f(z)}{z}\)^{{\alpha}-1}\;f^{\prime}(z)\}>0,\;{\alpha}>0.$$

• Structural Engineering and Mechanics
• /
• v.22 no.6
• /
• pp.701-717
• /
• 2006

In the existing reports regarding free transverse vibrations of the Euler-Bernoulli beams, most of them studied a uniform beam carrying various concentrated elements (such as point masses, rotary inertias, linear springs, rotational springs, spring-mass systems, ${\ldots}$, etc.) or a stepped beam with one to three step changes in cross-sections but without any attachments. The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of the multiple-step Euler-Bernoulli beams carrying a number of lumped masses and rotary inertias. First, the coefficient matrices for an intermediate lumped mass (and rotary inertia), left-end support and right-end support of a multiple-step beam are derived. Next, the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions, respectively. The effects of distribution of lumped masses and rotary inertias on the dynamic characteristics of the multiple-step beam are also studied.

• Structural Engineering and Mechanics
• /
• v.21 no.3
• /
• pp.351-367
• /
• 2005

Multi-span beams carrying multiple point masses are widely used in engineering applications, but the literature for free vibration analysis of such structural systems is much less than that of single-span beams. The complexity of analytical expressions should be one of the main reasons for the last phenomenon. The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of a multi-span uniform beam carrying multiple point masses. First, the coefficient matrices for an intermediate pinned support, an intermediate point mass, left-end support and right-end support of a uniform beam are derived. Next, the overall coefficient matrix for the whole structural system is obtained using the numerical assembly technique of the finite element method. Finally, the natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the related eigenfunctions respectively. The effects of in-span pinned supports and point masses on the free vibration characteristics of the beam are also studied.

• Structural Engineering and Mechanics
• /
• v.32 no.4
• /
• pp.477-488
• /
• 2009

A slip critical joint has various values to adopt the proper slip coefficient in various conditions of faying surfaces in the following codes: AISC, AIJ and Eurocode 3. However, the Korean Building Code still regulates the unique slip coefficient, 0.45, regardless of the diverse faying conditions. In this study, the slip resistance test, including five kinds of surface treatments were conducted to obtain the proper slip coefficients available to steel plate KS SM490A. The faying surfaces were comprised of a clean mill, rust, red lead paint, zinc primer, and shot blast treatment. The candidates for high strength bolts were torque-shear bolts, torque-shear bolts with zinc coating, and ASTM A490 bolts. Based on the test results, the specimens with a shot blasted surface and rusted surface exhibited $k_s$, 0.61, and 0.5, respectively. It is recommended that the specimens with zinc primer exhibit $k_s{\geq}0.40$. The clean mill treated surface had prominently lower values, 0.27. For red lead painted treatment, the thickness of the coating affects the determinant of slip coefficient, so it is necessary to establish a minimum $k_s$ of 0.2, with a coating thickness of 65 ${\mu}m$. During 1,000 hours of relaxation, the uncoated surfaces exhibited the loss of clamping force behind 3%, while the coated surfaces within a certain limited thickness exhibited the loss of clamping within a range of 4.71% and 8.37%.