• 한국전산구조공학회논문집
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• 제31권6호
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• pp.331-337
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• 2018

본 논문은 MLS(moving least squares) 차분법의 1차 미분 근사함수를 바탕으로 시간에 따른 수치해석이 가능한 해석기법을 제시한다. 오직 1차 미분 근사함수로만 지배방정식을 이산화했으며, 근사함수를 조립하는 형태로 전체 시스템 방정식을 구성하여 차분법으로 이산화된 운동방정식이 유한요소법(finite element method)과 유사한 모습을 갖게 되었다. 운동방정식을 시간적분하기 위해서 중앙차분법(central difference method)을 사용하였다. 유한요소 알고리즘을 통해서 MLS 차분법과 유한요소법의 고유진동 해석을 수행하였으며, 두 해석결과를 비교하였다. 또한, 동적해석 결과를 기존의 2차 미분 근사함수를 활용한 해석결과와 함께 도시함으로써 제안된 수치기법의 정확성을 검증하였다. 1차 미분 근사함수를 조립하는 과정에서 해석결과의 떨림현상이 억제되었으며 상대적으로 균일한 응력분포를 구할 수 있었다.

• Tribology and Lubricants
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• 제36권5호
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• pp.279-289
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• 2020

In this paper, a method is proposed for establishing an approximate prediction model of rotor-dynamics through modal testing. In particular, the proposed method is applicable to systems that cannot be established according to conventional methods owing to the absence of information regarding the dimensions and material of the rotor-bearing system. The proposed method is demonstrated by employing a motor dynamometer driven by a 1 MW class induction motor without dimension and material information. The proposed method comprises a total of seven steps, wherein an initial model is established by incorporating approximate dimensions and material information, and the model is improved on the basis of the natural frequency characteristics of the system. During model improvement, the modification factor is introduced for adjusting the elastic modulus and shear modulus of the system. Analysis of critical speed and imbalance response indicates that the separation margin is 67% and the maximum vibration amplitude is less than the amplitude limit of 0.032 mm under the API 611 standard, which means that the motor dynamometer can stably operate at a rated speed of 1800 rpm. Hence, the obtained results validate the feasibility of the proposed method. Furthermore, for broad usage, it is necessary to accordingly apply and validate the proposed method for various rotor-bearing systems.

• Earthquakes and Structures
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• 제1권4호
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• pp.411-425
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• 2010

The effect of dead loads on dynamic responses of uniform elastic beams is examined by means of a governing equation which takes into account initial bending stress due to dead loads. First, the governing equation of beams which includes the effect of dead loads is briefly presented from the author's paper (Takabatake 1990). In the formulation the effect of dead loads is considered by strain energy produced by conservative initial stresses produced by the dead loads. Second, the effect of dead loads on dynamical responses produced by live loads in simply supported beams and clamped beams is confirmed by the results of numerical computations with the Galerkin method and Wilson-${\theta}$ method. It is shown that the dynamical responses, like dynamic deflections and bending moments produced by dynamic live loads, are decreased in a heavyweight beam when the effect of dead loads is included. Third, an approximate solution for dynamic deflections including the effect of dead loads is presented in closed-form. The proposed solution shows good in agreement with results of numerical computations with the Galerkin method and Wilson-${\theta}$ method. Finally, a method reflecting the effect of dead loads for dynamic responses of beams on the magnitude of live loads is presented by an example.

• Structural Engineering and Mechanics
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• 제44권4호
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• pp.521-538
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• 2012

In this study, the transverse vibrations of an axially moving flexible beams resting on multiple supports are investigated. The time-dependent velocity is assumed to vary harmonically about a constant mean velocity. Simple-simple, fixed-fixed, simple-simple-simple and fixed-simple-fixed boundary conditions are considered. The equation of motion becomes independent from geometry and material properties and boundary conditions, since equation is expressed in terms of dimensionless quantities. Then the equation is obtained by assuming small flexural rigidity. For this case, the fourth order spatial derivative multiplies a small parameter; the mathematical model converts to a boundary layer type of problem. Perturbation techniques (The Method of Multiple Scales and The Method of Matched Asymptotic Expansions) are applied to the equation of motion to obtain approximate analytical solutions. Outer expansion solution is obtained by using MMS (The Method of Multiple Scales) and it is observed that this solution does not satisfy the boundary conditions for moment and incline. In order to eliminate this problem, inner solutions are obtained by employing a second expansion near the both ends of the flexible beam. Then the outer and the inner expansion solutions are combined to obtain composite solution which approximately satisfying all the boundary conditions. Effects of axial speed and flexural rigidity on first and second natural frequency of system are investigated. And obtained results are compared with older studies.

• Smart Structures and Systems
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• 제20권6호
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• pp.709-728
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• 2017

This disquisition proposes a nonlocal strain gradient beam theory for thermo-mechanical dynamic characteristics of embedded smart shear deformable curved piezoelectric nanobeams made of porous electro-elastic functionally graded materials by using an analytical method. Electro-elastic properties of embedded curved porous FG nanobeam are assumed to be temperature-dependent and vary through the thickness direction of beam according to the power-law which is modified to approximate material properties for even distributions of porosities. It is perceived that during manufacturing of functionally graded materials (FGMs) porosities and micro-voids can be occurred inside the material. Since variation of pores along the thickness direction influences the mechanical and physical properties, so in this study thermo-mechanical vibration analysis of curve FG piezoelectric nanobeam by considering the effect of these imperfections is performed. Nonlocal strain gradient elasticity theory is utilized to consider the size effects in which the stress for not only the nonlocal stress field but also the strain gradients stress field. The governing equations and related boundary condition of embedded smart curved porous FG nanobeam subjected to thermal and electric field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is utilized to achieve the natural frequencies of porous FG curved piezoelectric nanobeam resting on Winkler and Pasternak foundation. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality parameter, electric voltage, coefficient of porosity, elastic foundation parameters, thermal effect, gradient index, strain gradient, elastic opening angle and slenderness ratio on the natural frequency of embedded curved FG porous piezoelectric nanobeam are successfully discussed. It is concluded that these parameters play important roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.

• Advances in nano research
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• 제15권3호
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• pp.215-224
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• 2023

Nonlinearity plays an important role in control systems and the application of design. For this reason, in addition to linear vibrations, nonlinear vibrations of the stepped nanobeam are also discussed in this manuscript. This study investigated the vibrations of stepped nanobeams according to Eringen's nonlocal elasticity theory. Eringen's nonlocal elasticity theory was used to capture the nanoscale effect. The nanoscale stepped Euler Bernoulli beam is considered. The equations of motion representing the motion of the beam are found by Hamilton's principle. The equations were subjected to nondimensionalization to make them independent of the dimensions and physical structure of the material. The equations of motion were found using the multi-time scale method, which is one of the approximate solution methods, perturbation methods. The first section of the series obtained from the perturbation solution represents a linear problem. The linear problem's natural frequencies are found for the simple-simple boundary condition. The second-order part of the perturbation solution is the nonlinear terms and is used as corrections to the linear problem. The system's amplitude and phase modulation equations are found in the results part of the problem. Nonlinear frequency-amplitude, and external frequency-amplitude relationships are discussed. The location of the step, the radius ratios of the steps, and the changes of the small-scale parameter of the theory were investigated and their effects on nonlinear vibrations under simple-simple boundary conditions were observed by making comparisons. The results are presented via tables and graphs. The current beam model can assist in designing and fabricating integrated such as nano-sensors and nano-actuators.

• Advances in nano research
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• 제16권6호
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• pp.565-577
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• 2024

Vibration investigation of fluid-filled functionally graded cylindrical shells with ring supports is studied here. Shell motion equations are framed first order shell theory due to Sander. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the Rayleigh-Ritz procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Langrange energy functional is converted into a set of three partial differential equations. A cylindrical shell is immersed in a fluid which is a non-viscous one. These shells are stiffened by rings in the tangential direction. For isotropic materials, the physical properties are same everywhere where the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. After these, ring supports are located at various positions along the axial direction round the shell circumferential direction. The influence of the ring supports is investigated at various positions. Effect of ring supports with empty and fluid-filled shell is presented using the Rayleigh - Ritz method with simply supported condition. The frequency behavior is investigated with empty and fluid-filled cylindrical shell with ring supports versus circumferential wave number and axial wave number. Also the variations have been plotted against the locations of ring supports for length-to-radius and height-to-radius ratio. Moreover, frequency pattern is found for the various position of ring supports for empty and fluid-filled cylindrical shell. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. It is found that due to inducting the fluid term frequency result down than that of empty cylinder. It is also exhibited that the effect of frequencies is investigated by varying the surfaces with stainless steel and nickel as a constituent material. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

• Advances in Computational Design
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• 제5권4호
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• pp.363-380
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• 2020

In this paper, a cylindrical shell is immersed in a non-viscous fluid using first order shell theory of Sander. These equations are partial differential equations which are solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the Rayleigh-Ritz procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. Throughout the computation, simply supported edge condition is used. Expressions for modal displacement functions, the three unknown functions are supposed in such way that the axial, circumferential and time variables are separated by the product method. Comparison is made for empty and fluid-filled cylindrical shell with circumferential wave number, length- and height-radius ratios, it is found that the fluid-filled frequencies are lower than that of without fluid. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

• Wind and Structures
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• 제20권5호
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• pp.643-660
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• 2015

The wind tunnel test of large-scale sectional model and computational fluid dynamics (CFD) are employed for the purpose of studying the aerodynamic appendices and mechanism on suppression for the vortex-induced vibration (VIV). This paper takes the HongKong-Zhuhai-Macao Bridge as an example to conduct the wind tunnel test of large-scale sectional model. The results of wind tunnel test show that it is the crash barrier that induces the vertical VIV. CFD numerical simulation results show that the distance between the curb and crash barrier is not long enough to accelerate the flow velocity between them, resulting in an approximate stagnation region forming behind those two, where the continuous vortex-shedding occurs, giving rise to the vertical VIV in the end. According to the above, 3 types of wind fairing (trapezoidal, airfoil and smaller airfoil) are proposed to accelerate the flow velocity between the crash barrier and curb in order to avoid the continuous vortex-shedding. Both of the CFD numerical simulation and the velocity field measurement show that the flow velocity of all the measuring points in case of the section with airfoil wind fairing, can be increased greatly compared to the results of original section, and the energy is reduced considerably at the natural frequency, indicating that the wind fairing do accelerate the flow velocity behind the crash barrier. Wind tunnel tests in case of the sections with three different countermeasures mentioned above are conducted and the results compared with the original section show that all the three different countermeasures can be used to control VIV to varying degrees.

• Composites Research
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• 제13권2호
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• pp.30-39
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• 2000

고급복합재료(advanced composite material)는 여러 가지 훌륭한 장점에도 불구하고 건설기술자에게는 그 이론이 너무 복잡하여 건설구조에 대한 응용이 지연되고 있다. [$\alpha$/$\beta$/$\beta$/$\gamma$/$\alpha$/$\alpha$/$\beta$]r, $\alpha$=-$\beta$, $\gamma$=$0^{\circ}$또는 $90^{\circ}$와 같은 몇 가지 배향각을 갖은 적층판은, r이 증가함에 따라, $B_{i,j}$ 강성이 0으로 접근한다(1995). 또한 건설구조물은 그 치수가 크고 r이 증가해도 지간 대 두께비가 충분히 커서, 횡방향 변형율($varepsilon_{xz}$, $varepsilon_{yz}$)의 영향이 무시될 수 있다. 이 경우 판의 지배방정식은 간단한 특별직교 이방성 판의 지배방정식으로 변화된다. 김덕현은 토목구조물에 흔히 적용될 수 있는 이러한 배향각을 가진 적층판의 지배방정식을 취급이 간단한 특별직교 이방성 판의 경우로 변경시킨 다음 해석을 더 간단히 진행할 수 있도록 기술자들이 유사 등방성 상수(quasi-isotropic constant)를 사용하여 낯익은 등방성판의 방정식으로 답을 구하고 그가 개발한 "수정계수(correction factor)"를 사용하여 "정확한"해를 구하는 방법을 발표한 바 있다(1991).이 논문에는 [$\alpha$/$\beta$/$\beta$/$\gamma$/$\alpha$/$\alpha$/$\beta$]r 배향각을 갖는 적층판을, 일반기술자들이 이해하기 쉬운 본 논문의 방법으로 해석하는 방법을 제시하고 기술자들의 참고자료로 사용될 수 있는 여러 가지 경우에 대한 고유진동수의 계산결과가 제공되고 있다. 고유진동수의 계산결과가 제공되고 있다.