• 대한기계학회논문집
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• 제18권7호
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• pp.1759-1772
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• 1994

In this study, we re-examined the Tate's modified Bernoulli equation to study penetration phenomena for long rod projectile into single or multi-layered finite thickness plates. We used the force equlibrium equation at mushroomed nose/target interface instead of conventional pressure equation at the stagnation point. In our penetration model, we considered the velocity dependent $R_t$ value for semi-infinite target and considered only the back face effect for finite target. To compensate for $R_t$ value according to target's thickness and back face effect, we used the spherical cavity expansion theory for semi-infinite plate and used the cylindrical cavity expansion theory for finite plate. Also we developed the experimental technique using make screen to measure the penetration duration time at each layered plate. In 3-layered laminated RHA/mild steel/ A1 7039 plate, we observed that spall had occured around the back face of A1 7039 plate by the stress wave interaction. Through the comparison between theoretical and experimental data including Lambert's results, we conform that our study has good confidences.

• 대한기계학회논문집A
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• 제23권11호
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• pp.1940-1951
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• 1999

In this paper, the equations of motion of a Bernoulli-Euler cantilever beam fixed on a moving cart and carrying a lumped mass concentrated at an arbitrary position along the beam is derived. The motion of the beam-mass-cart system is analyzed through unconstrained modal analysis, and a unified characteristic equation for calculating the natural frequencies of the system is obtained. The changes of natural frequencies and the corresponding mode shapes with respect to the changes in mass ratios of the system and to the concentrated position of the lumped mass are investigated with the frequency equation, which can be generally applied to this kind of systems. The exact and assumed-mode solutions including the dynamics of the base cart are obtained, and the open-loop responses of the system by arbitrarily designed forcing function are given by numerical simulations. The results match well with physical phenomena even at the extreme cases where the concentrated mass is attached to the bottom and to the top of the beam.

• Smart Structures and Systems
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• 제26권2호
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• pp.213-226
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• 2020

In this manuscript, static and dynamic behaviors of geometrically imperfect carbon nanotubes (CNTs) subject to different types of end conditions are investigated. The Doublet Mechanics (DM) theory, which is length scale dependent theory, is used in the analysis. The Euler-Bernoulli kinematic and nonlinear mid-plane stretching effect are considered through analysis. The governing equation of imperfect CNTs is a sixth order nonlinear integro-partial-differential equation. The buckling problem is discretized via the differential-integral-quadrature method (DIQM) and then it is solved using Newton's method. The equation of linear vibration problem is discretized using DIQM and then solved as a linear eigenvalue problem to get natural frequencies and corresponding mode shapes. The DIQM results are compared with analytical ones available in the literature and excellent agreement is obtained. The numerical results are depicted to illustrate the influence of length scale parameter, imperfection amplitude and shear foundation constant on critical buckling load, post-buckling configuration and linear vibration behavior. The current model is effective in designing of NEMS, nano-sensor and nano-actuator manufactured by CNTs.

• Structural Engineering and Mechanics
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• 제70권6호
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• pp.737-750
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• 2019

This paper investigates the static and dynamic behaviors of imperfect single walled carbon nanotube (SWCNT) modeled as a beam structure by using energy-equivalent model (EEM), for the first time. Based on EEM Young's modulus and Poisson's ratio for zigzag (n, 0), and armchair (n, n) carbon nanotubes (CNTs) are presented as functions of orientation and force constants. Nonlinear Euler-Bernoulli assumptions are proposed considering mid-plane stretching to exhibit a large deformation and a small strain. To simulate the interaction of CNTs with the surrounding elastic medium, nonlinear elastic foundation with cubic nonlinearity and shearing layer are employed. The equation governed the motion of curved CNTs is a nonlinear integropartial-differential equation. It is derived in terms of only the lateral displacement. The nonlinear integro-differential equation that governs the buckling of CNT is numerically solved using the differential integral quadrature method (DIQM) and Newton's method. The linear vibration problem around the static configurations is discretized using DIQM and then is solved as a linear eigenvalue problem. Numerical results are depicted to illustrate the influence of chirality angle and imperfection amplitude on static response, buckling load and dynamic behaviors of armchair and zigzag CNTs. Both, clamped-clamped (C-C) and simply supported (SS-SS) boundary conditions are examined. This model is helpful especially in mechanical design of NEMS manufactured from CNTs.

• Structural Engineering and Mechanics
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• 제12권6호
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• pp.657-668
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• 2001

Fiber reinforced cementitious composites are nowadays widely applied in civil engineering. The postcracking performance of this material depends on the interaction between a steel fiber, which is obliquely across a crack, and its surrounding matrix. While the partly debonded steel fiber is subjected to pulling out from the matrix and simultaneously subjected to transverse force, it may be modelled as a Bernoulli-Euler beam partly supported on an elastic foundation with non-linearly varying modulus. The fiber bridging the crack may be cut into two parts to simplify the problem (Leung and Li 1992). To obtain the transverse displacement at the cut end of the fiber (Fig. 1), it is convenient to directly solve the corresponding differential equation. At the first glance, it is a classical beam on foundation problem. However, the differential equation is not analytically solvable due to the non-linear distribution of the foundation stiffness. Moreover, since the second order deformation effect is included, the boundary conditions become complex and hence conventional numerical tools such as the spline or difference methods may not be sufficient. In this study, moment equilibrium is the basis for formulation of the fundamental differential equation for the beam (Timoshenko 1956). For the cantilever part of the beam, direct integration is performed. For the non-linearly supported part, a transformation is carried out to reduce the higher order differential equation into one order simultaneous equations. The Runge-Kutta technique is employed for the solution within the boundary domain. Finally, multi-dimensional optimization approaches are carefully tested and applied to find the boundary values that are of interest. The numerical solution procedure is demonstrated to be stable and convergent.

• Advances in concrete construction
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• 제9권1호
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• pp.43-54
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• 2020

This paper presents an innovative stress-function variational approach in formulating the interfacial shear and normal stresses in an externally bonded concrete joint using carbon fiber-reinforced plastic (CFRP) plies. The joint is subjected to surface traction loadings applied at both ends of the concrete substrate layer. By introducing two interfacial shear and normal stress functions on the CFRP-concrete interface, based on Euler-Bernoulli beam idea and static stress equations of equilibrium, the entire stress fields of the joint were determined. The complementary strain energy was minimized in order to solve the governing equation of the joint. This yields an ordinary differential equation from which the interfacial normal and shear stresses were proposed explicitly, satisfying all the multiple traction boundary conditions. Lamination theory for composite materials was also employed to obtain the interfacial stresses. The proposed approach was validated by the analytic models in the literature as well as through a comprehensive computational code generated by the authors. Furthermore, a numerical verification was carried out via the finite element software ABAQUS. In the end, a scaling analysis was conducted to analyze the interfacial stress field dependence of the joint upon effective issues using the devised code.

• 한국수자원학회논문집
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• 제36권3호
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• pp.481-494
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• 2003

암거흐름은 지형 및 수리조건에 따라 복잡하고, 다양한 흐름특성을 나타내고 있으며, 이로인해 암거설계는 주로 모노그래프를 이용한 설계방식을 채택하고 있는 실정이다. 이는 개수로 암거의 경우 입구부에서의 수심을 산정하여야 하는 어려움과 복잡한 흐름특성 때문인 것으로 사료된다. 본 연구에서는 사각형 암거 입구부에서의 수심을 베르누이 방정식을 이용하여 결정하였으며, 이를 적용하여 여러 가지 형태의 흐름특성에 따른 암거 설계기준식을 개발하였다. 또한 설계항목을 암거경사${\cdot}$유량${\cdot}$폭${\cdot}$높이로 구분하여 각각의 경우에 대하여 양해법 산정식을 개발하였다.

• 한국소음진동공학회논문집
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• 제25권12호
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• pp.822-829
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• 2015

A transfer matrix method has been developed to determine the more accurate natural frequencies for the bending vibration of Bernoulli-Euler beam with linearly reduced width and a concentrated tip mass. The proposed method can be computed an infinite number of the natural frequencies using a single element. Using the differential equation, shear force, and bending moment in which can be deduced by the diverse variational principles, a transfer matrix is formulated. The roots of the differential equation are computed by the Frobenius method. The effect of the concentrated mass for the natural frequencies of width-tapered beams is examined through a parametric study, and to show the accuracy of the proposed method, the computed results compared with those obtained from commercial finite element analysis program(ANSYS).

• 한국정밀공학회지
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• 제32권4호
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• pp.369-375
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• 2015

This paper presents ejection of high viscosity fluids with magnetostrictive inkjet printhead(Magjet), which is not common with any other printhead. The MagJet uses a magnetostrictive material, Terfenol-D rod with 10-mm in diameter and 50-mm in length, as an actuation mechanism. It has been known that high viscosity is often an obstacle in ejecting small and mono-disperse droplets. We calculated required pressure with fluidic inertia (Bernoulli equation) and viscous loss (Hagen Poiseuille equation). The required pressure for ejecting a droplet is 1300kPa. The generated force and displacement with Terfenol-D rod are estimated to be 480N (2600kPa) and $28{\mu}m$, respectively. It was enough that Magjet eject high viscosity fluid (Max 1000cP). The experiments are performed to eject the high viscosity fluid with Magjet. The ejection of high viscosity fluids is successful with the aid of Terfenol-D's high performance.

• 한국안전학회지
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• 제20권2호
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• pp.158-161
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• 2005

액화석유가스 용기용 과류차단 밸브의 개발에 관한 연구이다. 이 밸브는 베르누이 방정식과 뉴턴의 법칙을 응용하여 개발하였다. 이것은 기존의 밸브 하단에 모듈을 삽입함으로써 과류가 발생하면 모듈이 상승하여 모듈상단의 헤드에 부착된 차단변이 가스의 통로를 폐쇄함으로써 작동된다. 최근 가스 사용이 증가됨으로써 이에 따라 가스사고가 많이 발생되고 있다. 따라서 한국에서는 과류밸브의 사용을 의무화하고 있지만 아직 개발되지 않고 있다. 본 연구는 LP가스 용기용 밸브의 과류 발생시 자동 차단되는 밸브이다. 본 밸브가 채택된다면 많은 가스 사고로부터 벗어 날 수 있을 것이다.