• Structural Engineering and Mechanics
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• v.45 no.1
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• pp.69-93
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• 2013

The present study deals with the dynamics of the flapwise (out-of-plane) vibrations of a rotating, internally damped (Kelvin-Voigt model) tapered Bernoulli-Euler beam carrying a heavy tip mass. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The equation of motion and the corresponding boundary conditions are derived via the Hamilton's Principle, leading to a differential eigenvalue problem. Afterwards, this eigenvalue problem is solved by using Frobenius Method of solution in power series. The resulting characteristic equation is then solved numerically. The numerical results are tabulated for a variety of nondimensional rotational speed, tip mass, tip mass offset, mass moment of inertia, internal damping parameter, hub radius and taper ratio. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained.

• Structural Engineering and Mechanics
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• v.64 no.6
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• pp.723-730
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• 2017

This paper studies on dynamic and stability behavior of a clamped-elastically restrained nanobeam under the action of a nonconservative force with an emphasis on the influence of surface properties on divergence and flutter instability. Using the Euler-Bernoulli beam theory incorporating surface effects, a governing equation for a clamped-elastically restrained nanobeam is derived according to Hamilton's principle. The characteristic equation is obtained explicitly and the force-frequency interaction curves are displayed to show the influence of the surface effects, spring stiffness of the elastic restraint end on critical loads including divergence and flutter loads. Divergence and flutter instability transition is analyzed. Euler buckling and stability of Beck's column are some special cases of the present at macroscale.

• 유체기계공업학회:학술대회논문집
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• 2000.12a
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• pp.110-115
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• 2000

The mean streamline analysis using the empirical loss correlations has been developed for performance prediction of industrial mixed-flow fan impellers in the present study. New simple, but effective, models for the additional Euler input work characteristic and an internal recirculation loss due to internal flow reversal under the low flowrate conditions are proposed in this paper. Comparison of overall performance predictions with six sets of test data of mixed-flow fans is accomplished to demonstrate the accuracy of the proposed models. Predicted performance curves by the present set of loss models agree fairly well with experimental data for a variety of mixed-flow fan impellers over the entire operating conditions. The prediction method presented herein can be used efficiently in the conceptual design phase of mixed-flow fan impellers.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.573-591
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• 2013

In this paper, we improve the error corrected Euler method(ECEM) introduced in [11] by evaluating function values only at local nodes in each time interval. As a result, one can avoid computations of Jacobian matrices on each time interval so that the algorithms become simpler to implement in solving various class of time dependent differential equations numerically. The proposed ECEM formula resembles to the Runge-Kutta method in its representations but both methods have different characteristic properties.

• Steel and Composite Structures
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• v.32 no.5
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• pp.643-655
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• 2019

Perforation and cutouts of structures are compulsory in some modern applications such as in heat exchangers, nuclear power plants, filtration and microeletromicanical system (MEMS). This perforation complicates dynamic analyses of these structures. Thus, this work tends to introduce semi-analytical model capable of investigating the dynamic performance of perforated beam structure under free and forced conditions, for the first time. Closed forms for the equivalent geometrical and material characteristics of the regular square perforated beam regular square, are presented. The governing dynamical equation of motion is derived based on Euler-Bernoulli kinematic displacement. Closed forms for resonant frequencies, corresponding Eigen-mode functions and forced vibration time responses are derived. The proposed analytical procedure is proved and compared with both analytical and numerical analyses and good agreement is noticed. Parametric studies are conducted to illustrate effects of filling ratio and the number of holes on the free vibration characteristic, and forced vibration response of perforated beams. The obtained results are supportive in mechanical design of large devices and small systems (MEMS) based on perforated structure.

• Structural Engineering and Mechanics
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• v.59 no.6
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• pp.1139-1153
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• 2016

Elastic constraints are usually simplified as "spring forces" exerted on beam ends without considering the "spring deformation". The partial differential equation governing the free vibrations of a cantilever Bernoulli-Euler beam considering the deformation of elastic constraints is firstly established, and is nondimensionalized to obtain two dimensionless factors, $k_v$ and $k_r$, describing the effects of elastically vertical and rotational end constraints, respectively. Then the frequency equation for the above Bernoulli-Euler beam model is derived using the method of separation of variables. A numerical analysis method is proposed to solve the transcendental frequency equation for the continuous change of the frequency with $k_v$ and $k_r$. Then the mode shape functions are given. Finally, effects of $k_v$ and $k_r$ on free vibration characteristics of the beam with different slenderness ratios are calculated and analyzed. The results indicate that the effects of $k_v$ are larger on higher-order free vibration characteristics than on lower-order ones, and the impact strength decreases with slenderness ratio. Under a relatively larger slenderness ratio, the effects of $k_v$ can be neglected for the fundamental frequency characteristics, while cannot for higher-order ones. However, the effects of $k_r$ are large on both higher- and lower-order free vibration characteristics, and cannot be neglected no matter the slenderness ratio is large or small.

• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.797-820
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• 2019

For every tree T, we introduce a topological invariant, called the T-cross-index, for connected graphs. The T-cross-index of a graph is a non-negative integer or infinity according to whether T is a tree basis of the graph or not. It is shown how this cross-index is independent of the other topological invariants of connected graphs, such as the Euler characteristic, the crossing number and the genus.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.605-622
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• 2018

The original mixed multiplicity theory considered the class of mixed multiplicities concerning the terms of highest total degree in the Hilbert polynomial. This paper defines a broader class of mixed multiplicities that concern the maximal terms in this polynomial, and gives many results, which are not only general but also more natural than many results in the original mixed multiplicity theory.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.1-8
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• 2018

In this paper, we study some topological structure of a compact domain in ${\mathbb{R}}^n$ in terms of the curvature conditions and develop a geometric inequality involving the volume and the integral of mean curvatures over the boundary of the compact domain.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.449-457
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• 2020

The aim of this short paper is to show some rigidity results for the actions of certain finitely presented groups by homeomorphisms. As an interesting and special case, we show that the actions of Higman-Thompson groups by homeomorphisms on a cohomology manifold with a non-zero Euler characteristic should be trivial. This is related to the wellknown Zimmer program and shows that the actions by homeomorphism could be very much different from those by diffeomorphisms.