• Steel and Composite Structures
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• 제47권1호
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• pp.79-90
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• 2023

Nonlinear forced vibration properties of three-layered plates containing graphene platelets (GPL) filled skins and an auxetic core have been inquired within the present paper. Owning reduced weight as well as reduced stiffness, rectangle-shaped auxetic cores have been frequently made from novel techniques such as additive manufacturing. Here, the rectangle shape core is amplified via the graphene-filled layers knowing that the layers possess uniform and linear graphene gradations. The rectangle shape core has the equivalent material specifications pursuant to relative density value. The sandwich plate is formulated pursuant to Kirchhoff plate theory while a numerical trend has been represented to discretize the plate equations. Next, an analytical trend has been performed to establish the deflection-frequency plots. Large deflections, core density and GPL amplification have showed remarkable impacts on dynamic response of three-layered plates.

• Structural Engineering and Mechanics
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• 제90권4호
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• pp.357-370
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• 2024

Due to the fact that the mechanism of the effects of temperature and initial geometric imperfection on low-velocity impact problem of axially moving plates is not yet clear, the present paper is to fill the gap. In the present paper, the nonlinear dynamic behavior of axially moving imperfect graphene platelet reinforced metal foams (GPLRMF) plates subjected to lowvelocity impact in thermal environment is analyzed. The equivalent physical parameters of GPLRMF plates are estimated based on the Halpin-Tsai equation and the mixing rule. Combining Kirchhoff plate theory and the modified nonlinear Hertz contact theory, the nonlinear governing equations of GPLRMF plates are derived. Under the condition of simply supported boundary, the nonlinear control equation is discretized with the help of Gallekin method. The correctness of the proposed model is verified by comparison with the existing results. Finally, the time history curves of contact force and transverse center displacement are obtained by using the fourth order Runge-Kutta method. Through detailed parameter research, the effects of graphene platelet (GPL) distribution mode, foam distribution mode, GPL weight fraction, foam coefficient, axial moving speed, prestressing force, temperature changes, damping coefficient, initial geometric defect, radius and initial velocity of the impactor on the nonlinear impact problem are explored. The results indicate that temperature changes and initial geometric imperfections have significant impacts.

• Advances in nano research
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• 제10권5호
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• pp.449-460
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• 2021

Flexoelectricity is an interesting materials' property that is more touchable in small scales. This property beside the sandwich structures placed in the center of scientists' attention due to their extraordinary effects on the mechanical properties. Furthermore, in the passage of decades, more elaborated sandwich structures took into consideration results from using honeycomb core. This kind of structure, inspiring from honeycomb core, provides more stiffness to weight ratio, which plays a crucial role in different industries. In this paper, based on the Love-Kirchhoff's hypothesis, Hamilton's principle, modified couple stress theory and Fourier series analytical method, equations of motion for a sandwich plate containing a honeycomb core integrated by two face-sheets have derived and solved analytically. The equations of both face sheets have derived by flexoelectricity consideration. Moreover, it should be noticed that the whole structure rests on the visco-Pasternak foundation. Conducting current research provided an acceptable and throughout study based on flexoelectricity to address the effect of materials' characteristics, length-scale parameter, aspect, and thickness ratios and boundary conditions on the natural frequency of honeycomb sandwich plates. Also, based on the presented figures and tables, there is a close agreement between previous studies and recent work. Due to the high ratio of strength to weight, current model analyzing is capable of taking into account for different vehicles' manufacturing in a high range of industries.

• 유변학
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• 제11권1호
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• pp.18-27
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• 1999

본 연구에서는 3차원 열성형 공정 알고리듬과 이에 membrane approximation을 도입한 근사적인 알고리듬을 개발하였고, 이 알고리듬을 이용하여 몇몇 열성형계에 대한 수치모사를 수행하여 그 결과를 비교 분석하였다. 3차원 알고리듬의 경우에는 구성한 유한요소 평형 방정식에 벌칙함수를 도입하여 비압축성 조건을 만족시켜 해를 얻었으며, membrane approximation을 도입한 알고리듬의 경우에는 두께 방향의 응력을 무시하여 구성한 방정식으로부터 해를 얻었다. 구성방정식은 2nd Piola-Kirchhoff 응력 텐서와 Cauchy-Green 변형 텐서를 사용하여 표현하였고 수지의 물질 모델식으로는 2항의 Mooney-Rivlin 모델을 사용하였으며, total Lagrangian coordinate를 도입하여 지배방정식을 유한요소화함으로써 알고리듬을 구성하였다. 대상계로 선정한 사각평판 수지의 자유 부풀림 거동과 금형이 있는 경우에서의 수지의 부풀림 거동을 3차원 알고리듬과 membrane approximation 알고리듬을 각각 이용하여 분석하였으며 3차원 알고리듬의 경우 clamping 부분의 경계조건을 달리하여 결과를 비교하였다. 금형이 있는 계에 대해서는 slip 경계조건과 no-slip 경계조건을 각각 부여하여 수치모사를 수행, 수지의 변형거동과 응력분포를 비교 분석하였으며, 두께를 달리 한 수지에 대해 두께 방향의 응력을 비교 분석함으로써 membrane approximation 알고리듬의 한계에 대하여 논하였다. 한편 수지 온도 변화에 따른 성형품의 두께 분포의 변화를 살펴보기 위하여 ABS 수지를 대상으로 하여 $137.8^{\circ}C$에서 $171.1^{\circ}C$사이의 온도에서 수행한 인장실험 데이터를 수치모사에 사용하였다. 그 결과 수지의 온도가 높을수록 두께의 표준편차가감소하여 균일한 두께 분포를 얻을 수 있음을 확인하였고 이는 수지의 흐름성이 증가함으로써 나타나는 현상으로 해석할 수 있다.

• 한국음향학회지
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• 제20권5호
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• pp.100-109
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• 2001

부레를 가진 어류의 산란 강도를 조사하기 위하여 길이가 다른 참돔 (red seabream, pagrus major)을 이용한 음향 실험을 실시하였다. 대상 어류를 살아 있는 상태로 - (1) 망 내에 각각 넣은 후, (2) 자유 유영 상태로 놓은후 - 3개의 음향센서 (38, 120, 200kHz)를 이용하여 길이에 따른 산란강도를 측정하였다. 실험 결과 길이에 따른 참돔의 산란 강도는 각 주파수별로 TS/sub 38㎑/＝20 log/sub 10(l)/ -66.41, TS/sub 120㎑/＝20 log/sub lo(1)/ -71.80, TS/sub 200㎑/＝20 log/sub 10(1)/ -73.94로 나타났다. 실험 결과와 이론 모델을 비교하기 위하여 어류의 형태를 근거로 한 Helmholtz-Kirchhoff 음선 근사법을 사용한 결과, 산란강도는 어류 몸체보다는 부레에 의한 효과가 95%이상으로 나타났다. 한편, 수신된 산란강도 자료를 이용한 확률밀도 함수로부터 어류의 행태에 따른 산란강도 변위는 망 내의 산란체에서는 가우스 확률밀도함수 (Gaussian PDF)로, 자유 유영 상태에서는 레일리 확률밀도함수 (Rayleigh PDF) 특성을 나타냈다.

• 대한전자공학회논문지SD
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• 제42권5호
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• pp.9-14
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• 2005

본 논문은 순수한 고주파 (radio-frequency: rf) 모드의 반사형과 투과형 고주파 단일전자 트랜지스터 (RF-SET) 동작의 새로운 시뮬레이션 기법을 소개한다. 이 기법은 RF-SET 회로를 주파수 영역에서 self-consistent 방법으로 키리히호프 법칙에 기반한 미분 방정식의 해를 구한다. 또한, 이 기법은 정상상태와 시변 단일전자 트랜지스터 전류 모델들 두 가지를 포함한다. 순수한 rf 모드 반사형 RF-SET의 반사파와 순수한 rf 모드 투과형 RF-SET의 투과파를 계산한다. 정상상태 단일전자 트랜지스터 전류 모델을 포함한 RF-SET 계산의 정확성은 [참고문헌 2]에서 소개된 방법으로 확인한다. GHz 이상의 고주파에서 시변 단일전자 트랜지스터 전류 모델을 포함한 RF-SET 계산 결과는 정상상태 단일전자 트랜지스터 전류 모델을 포함해서 RF-SET를 계산한 결과들과 상당한 차이가 있음을 확인했다. GHz 이상 고주파에서 RF-SET 동작 분석은 정확한 시변 단일전자 트랜지스터의 전류 모델이 요구된다.

• 한국소음진동공학회논문집
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• 제15권3호
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• pp.251-258
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• 2005

The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings (HDB) in an HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Reynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigen value problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 추계학술대회논문집
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• pp.572-578
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• 2003

The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings in a HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Raynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigenvalue problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

• Structural Engineering and Mechanics
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• 제44권4호
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• pp.431-448
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• 2012

In this paper, the first-order shear deformation theory (FSDT) (Mindlin) for continuum incorporating surface energy is exploited to study the static behavior of ultra-thin functionally graded (FG) plates. The size-dependent mechanical response is very important while the plate thickness reduces to micro/nano scales. Bulk stresses on the surfaces are required to satisfy the surface balance conditions involving surface stresses. Unlike the classical continuum plate models, the bulk transverse normal stress is preserved here. By incorporating the surface energies into the principle of minimum potential energy, a series of continuum governing differential equations which include intrinsic length scales are derived. The modifications over the classical continuum stiffness are also obtained. To illustrate the application of the theory, simply supported micro/nano scaled rectangular films subjected to a transverse mechanical load are investigated. Numerical examples are presented to present the effects of surface energies on the behavior of functionally graded (FG) film, whose effective elastic moduli of its bulk material are represented by the simple power law. The proposed model is then used for a comparison between the continuum analysis of FG ultra-thin plates with and without incorporating surface effects. Also, the transverse shear strain effect is studied by a comparison between the FG plate behavior based on Kirchhoff and Mindlin assumptions. In our analysis the residual surface tension under unstrained conditions and the surface Lame constants are expected to be the same for the upper and lower surfaces of the FG plate. The proposed model is verified by previous work.