• Smart Structures and Systems
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• 제12권5호
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• pp.501-521
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• 2013

This paper is concerned with static and dynamic shape control of a laminated Bernoulli-Euler beam hosting a uniformly distributed array of resistively interconnected piezoelectric patches. We present an analytical one-dimensional model for a laminated piezoelectric beam with material discontinuities within the framework of Bernoulli-Euler and extent the model by a network of resistors which are connected to several piezoelectric patch actuators. The voltage of only one piezoelectric patch is prescribed: we answer the question how to design the interconnected resistive electric network in order to annihilate lateral vibrations of a cantilever. As a practical example, a cantilever with eight patch actuators under the influence of a tip-force is studied. It is found that the deflection at eight arbitrary points along the beam axis may be controlled independently, if the local action of the piezoelectric patches is equal in magnitude, but opposite in sign, to the external load. This is achieved by the proper design of the resistive network and a suitable choice of the input voltage signal. The validity of our method is exact in the static case for a Bernoulli-Euler beam, but it also gives satisfactory results at higher frequencies and for transient excitations. As long as a certain non-dimensional parameter, involving the number of the piezoelectric patches, the sum of the resistances in the electric network and the excitation frequency, is small, the proposed shape control method is approximately fulfilled for dynamic load excitations. We evaluate the feasibility of the proposed shape control method with a more refined model, by comparing the results of our one-dimensional calculations based on the extended Bernoulli-Euler equations to three-dimensional electromechanically coupled finite element results in ANSYS 12.0. The results with the simple Bernoulli-Euler model agree well with the three-dimensional finite element results.

• Structural Engineering and Mechanics
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• 제11권4호
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• pp.357-372
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• 2001

In this paper, cantilevered tall structures are treated as cantilever bars with varying cross-section for the analysis of their free longitudinal (or axial) vibrations. Using appropriate transformations, exact analytical solutions to determine the longitudinal natural frequencies and mode shapes for a one step non-uniform bar are derived by selecting suitable expressions, such as exponential functions, for the distributions of mass and axial stiffness. The frequency equation of a multi-step bar is established using the approach that combines the transfer matrix procedure or the recurrence formula and the closed-form solutions of one step bars, leading to a single frequency equation for any number of steps. The Ritz method is also applied to determine the natural frequencies and mode shapes in the vertical direction for cantilevered tall structures with variably distributed stiffness and mass. The formulae proposed in this paper are simple and convenient for engineering applications. Numerical example shows that the fundamental longitudinal natural frequency and mode shape of a 27-storey building determined by the proposed methods are in good agreement with the corresponding measured data. It is also shown that the selected expressions are suitable for describing the distributions of axial stiffness and mass of typical tall buildings.

• International Journal of Naval Architecture and Ocean Engineering
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• 제10권3호
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• pp.393-402
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• 2018

While interacting with a sloping structure, an ice floe may fracture in different patterns. For example, it can be local bending failure or global splitting failure depending on the contact properties, geometry and confinement of the ice floe. Modelling these different fracture patterns as a natural outcome of numerical simulations is rather challenging. This is mainly because the effects of crack propagation, crack branching, multi fracturing modes and eventual fragmentation within a solid material are still questions to be answered by the on-going research in the Computational Mechanic community. In order to simulate the fracturing of ice floes with arbitrary geometries and confinement; and also to simulate the fracturing events at such a large scale yet with sufficient efficiency, we propose a semi-analytical/empirical and semi-numerical approach; but with focus on the global splitting failure mode in this paper. The simulation method is validated against data we collected during the Oden Arctic Technology Research Cruise 2015 (OATRC2015). The data include: 1) camera images based on which we specify the exact geometry of ice floes before and after an impact and fracturing event; 2) IMU data based on which the global dynamic force encountered by the icebreaker is extracted for the impact event. It was found that this method presents reasonably accurate results and realistic fracturing patterns upon given ice floes.

• Structural Engineering and Mechanics
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• 제75권6호
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• pp.747-769
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• 2020

This paper provides a semi-analytical approach to investigate the variations of 3D displacement components, electric potential, stresses, electric displacements and transverse vibration frequencies in laminated piezoelectric composite plates based on the scaled boundary finite element method (SBFEM) and the precise integration algorithm (PIA). The proposed approach can analyze the static and dynamic responses of multilayered piezoelectric plates with any number of laminae, various geometrical shapes, boundary conditions, thickness-to-length ratios and stacking sequences. Only a longitudinal surface of the plate is discretized into 2D elements, which helps to improve the computational efficiency. Comparing with plate theories and other numerical methods, only three displacement components and the electric potential are set as the basic unknown variables and can be represented analytically through the transverse direction. The whole derivation is built upon the three dimensional key equations of elasticity for the piezoelectric materials and no assumptions on the plate kinematics have been taken. By virtue of the equilibrium equations, the constitutive relations and the introduced set of scaled boundary coordinates, three-dimensional governing partial differential equations are converted into the second order ordinary differential matrix equation. Furthermore, aided by the introduced internal nodal force, a first order ordinary differential equation is obtained with its general solution in the form of a matrix exponent. To further improve the accuracy of the matrix exponent in the SBFEM, the PIA is employed to make sure any desired accuracy of the mechanical and electric variables. By virtue of the kinetic energy technique, the global mass matrix of the composite plates constituted by piezoelectric laminae is constructed for the first time based on the SBFEM. Finally, comparisons with the exact solutions and available results are made to confirm the accuracy and effectiveness of the developed methodology. What's more, the effect of boundary conditions, thickness-to-length ratios and stacking sequences of laminae on the distributions of natural frequencies, mechanical and electric fields in laminated piezoelectric composite plates is evaluated.

• Advances in nano research
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• 제7권4호
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• pp.249-263
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• 2019

In the current paper, an exact solution method is carried out for analyzing the thermo-mechanical vibration of curved FG nano-beams subjected to uniform thermal environmental conditions, by considering porosity distribution via nonlocal strain gradient beam theory for the first time. Nonlocal strain gradient elasticity theory is adopted to consider the size effects in which the stress for not only the nonlocal stress field but also the strain gradients stress field is considered. It is perceived that during manufacturing of functionally graded materials (FGMs) porosities and micro-voids can be occurred inside the material. Material properties of curved porous FG nanobeam are assumed to be temperature-dependent and are supposed to vary through the thickness direction of beam which modeled via modified power-law rule. Since variation of pores along the thickness direction influences the mechanical and physical properties, porosity play a key role in the mechanical response of curved FG nano-structures. The governing equations and related boundary condition of curved porous FG nanobeam under temperature 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 nanobeam supposed to thermal loading. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality parameter, porosity volume fractions, thermal effect, gradient index, opening angle and aspect ratio on the natural frequency of curved FG porous nanobeam are successfully discussed. It is concluded that these parameters play key 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.

• 대한핵의학회지
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• 제38권6호
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• pp.486-491
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• 2004

목적: 요소분석법. 독립성분분석법 등이 PET을 이용하여 심근혈류를 비침습적으로 측정하기 위하여 사용되어 왔다. 이론적으로 뛰어나고 새로운 방법인 앙상블 독려성분분석법을 이용하여 $H_2^{15}O$ 동적 심근 PET데이터의 정량분석방법을 개발하였다. 이 연구에서 사용한 앙상블 독려성분분석법을 이용하여 환자의 혈류를 정량화 하였다. 대상 및 방법: 관동맥질환이 의심되어 관류 SPECT를 시행한 환자 20명을 대상으로 $H_2^{15}O$ 동적 심근 PET을 시행한 후 앙상블 독립성분분석법을 이용하여 심근 독립성분영상을 추출하였으며, 좌심실영역과 심근영역에 대한 영상대조도를 조사하였다. 앙상블 학습은 독립성분과 가중치 행렬에 대한 확률분포를 가정하고 베이지안 이론에 의해서 혼합자료에 대한 확률분포를 추정한다. 이렇게 추정한 혼합자료의 확률분포와 실제 분포간의 차이인 Kullback-Leibler 발산치가 최소가 되도록 독립성분과 가중치 행렬을 순차적으로 변화시켜가며 최종 해를 찾는 방식이다. 이 연구에서 사후확률분포는 동적 핵의학 영상에 적합한 비음성제약조건과 함께 수정된 가우시안 분포를 이용하여 최적화 하였다. 혈류량은 심첨부, 중벽 네 부분, 하벽 네 부분의 9개 영역으로 나누어 측정하였으며, 측정결과에 대해 관류 SPECT 소견과 관동맥조영술의 소견과 비교하였다. 결과: 전체 20명의 휴식기 및 부하기 영상에서 5명을 제외한 15명의 데이터에 대해 심근혈류를 측정할 수 있었다. $H_2^{15}O$ 동적 심근 PET에서 앙상블 독립성분분석법을 이용하여 정량화한 휴식기 혈류량은 $1.2{\pm}0.40$ ml/min/g, 부하기 혈류량은 $1.85{\pm}1.12$ml/min/g이었다. 같은 영역에 대해 두 번 측정했을 때 측정된 심근혈류값의 상관계수는 0.99로 재현성이 높았다. 분리된 독립성분영상에서 영상대조도는 좌심실에 대한 심근영역의 비는 평균 1:2.7이었다. 관동맥 조영술을 시행한 9명에서 협착이 없는 분절과 협착이 있는 분절의 혈류예비능에 유의한 차이가 있었다(P<0.01). 또한, 관동맥조영술에서 협착이 확인된 66분절의 심근관류 SPECT 소견에서 가역적 혈류감소를 보인 분절의 혈류예비능이 더 많이 감소되는 경향을 보였으나 통계적 유의성을 보이지는 않았다. 결론: 앙상블 학습을 이용한 독립성분분석방법을 이용하여 심근혈류가 측정이 되었다. 앙상블 독립성분분석법을 이용한 $H_2^{15}O$ 동적 심근 PET 분석방법이 관상동맥 질환의 분석 및 동적 핵의학 영상 데이터의 연구에 도움이 될 것으로 기대된다.

• Journal of Astronomy and Space Sciences
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• 제21권4호
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• pp.351-360
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• 2004

향후 우리나라의 화성 근접 탐사 임무를 대비한 우주선의 궤도전파 소프트웨어의 개발 및 검증을 실시하였다. 이를 위해 화성 주위를 비행하는 우주선의 동력학 모델에 대한 연구가 선행 되었으며, 탐사우주선의 모든 위치 정보는 화성 중심 좌표계를 사용하여 나타내었다. 정밀한 탐사 우주선의 위치 계산을 위하여 화성의 세차 및 장동 운동에 의한 영향도 고려하였다. 화성의 작용권구 안으로 진입한 탐사 우주선은 화성 주위에서의 다양한 섭동에 의한 영향을 받게 되는데 본 연구에서는 정밀한 동력한 모델의 계산을 위해 가능한 모든 섭동들을 고려하였다. 특히 화성의 비대칭 중력장에 의한 영향을 계산하기 위해 Jet Propulsion Laboratory(JPL)의 Mars50c 모델을 적용하였고 화성 대기 항력에 의한 영향의 경우 Mars-GRAM 2001 모델을 사용하여 계산하였다. 태양을 비롯한 다른 행성의 위치를 계산하기 위해서 JPL의 DE405 정밀 천체력을 이용하였고 화성 위성들(포보스와 다이모스)의 천체력 계산은 해석적인 방법으로 하였다. 개발 소프트웨어의 성능 검증을 위하여 Mars Global Surveyor의 화성 지도 작성을 위한 초기 궤도 요소를 사용하였으며, Satellite Tool Kit(STK)의 Astrogator모듈을 이용하여 산출된 결과와 본 논문에서 개발한 소프트웨어의 결과 값과 비교 하였다. 비교 결과 우주선의 모든 위치성분(반경방향, 궤도 진행방향 그리고 진행수직방향)은 화성 근접 탐사 우주선이 화성 주위를 12번 공전(약 1화성일)하는 동안 최대 ${\pm}5m$ 이내의 오차를 보여 주었다. 이는 본 연구를 통해서 개발된 소프트웨어의 성능에 대한 신뢰도가 매우 높다는 것을 의미한다. 따라서 개발된 알고리즘과 소프트웨어는 향후 우리나라의 화성 근접 탐사를 위한 우주선의 임무 설계시 활용 될 수 있다.