• 한국통신학회논문지
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• 제22권12호
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• pp.2819-2827
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• 1997

유전체 구형 도파로를 quasi TE모드와 quasi TM모드에 의하여 분석한다. 전기장과 자장의 각 성분을 근사화하지 않고 또한 각 유전체 경계면에서 경계 조건을 만족시키도록 하여 유전체 구형 도파로를 분석했다. 경계 조건을 도입하여 얻어지는 행렬식을 풀어 보면 전자파의 진행 방향인 z방향에 대한 전파 상수를 구할 수 있다. 수치해석에 의하여 유전체 구형 도파로를 분석 할 경우, 종종 발생하여 프로그래밍을 복잡하게 하는 spurious 모드를이 이 분석법에는 나타나지 않았다. 그러므로 이 방법에 의해 구해진 전파 상수 값들은 유전체 구형 도파로 분석에서 많이 사용되는 유한요소법이나 유한차등법 등과 비교하는데 유용하게 사용될 수 있다.

• Advances in aircraft and spacecraft science
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• 제4권2호
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• pp.169-184
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• 2017

The optimum design of structures with frequency constraints is of great importance in the aeronautical industry. In order to avoid severe vibration, it is necessary to shift the fundamental frequency of the structure away from the frequency range of the dynamic loading. This paper develops a novel topology optimisation method for optimising the fundamental frequencies of structures. The finite element dynamic eigenvalue problem is solved to derive the sensitivity function used for the optimisation criteria. An alternative material interpolation scheme is developed and applied to the optimisation problem. A novel level-set criteria and updating routine for the weighting factors is presented to determine the optimal topology. The optimisation algorithm is applied to a simple two-dimensional plane stress plate to verify the method. Optimisation for maximising a chosen frequency and maximising the gap between two frequencies are presented. This has the application of stiffness maximisation and flutter suppression. The results of the optimisation algorithm are compared with the state of the art in frequency topology optimisation. Test cases have shown that the algorithm produces similar topologies to the state of the art, verifying that the novel technique is suitable for frequency optimisation.

• Steel and Composite Structures
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• 제30권6호
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• pp.493-516
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• 2019

This paper is dedicated to nonlinear static and free vibration analysis of Uniform Distributed Carbon Nanotube Reinforced Composite (UD-CNTRC) structures under in-plane loading. The authors have suggested an efficient six-node triangular element. Mixed Interpolation of Tensorial Components (MITC) approach is employed to alleviate the membrane locking phenomena. Moreover, the behavior of the well-known LST element is considerably improved by applying an additional linear interpolation on the strain fields. Based on the rule of mixture, the properties of CNTRC are obtained. In this study, only the uniform distributed CNTs are employed through the thickness direction of element. To achieve the natural frequencies and shape modes, the eigenvalue problem is also solved. Using Total Lagrangian Principles, large amplitude free vibration is considered based on the first normalized mode shape of structure. Different well-known plane problem benchmarks and some proposed ones are studied to validate the accuracy and capability of authors' formulations. In addition, the effects of length to the height ratio of beam, CNT's characteristics, support conditions and normalized amplitude parameter on the linear and nonlinear vibration parameters are investigated.

• 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.

• Advances in nano research
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• 제7권3호
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• pp.157-167
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• 2019

In this paper, a classical plate model is utilized to formulate the wave propagation problem of magnetostrictive sandwich nanoplates (MSNPs) while subjected to hygrothermal loading with respect to the scale effects. Herein, magnetostriction effect is considered and controlled on the basis of a feedback control system. The nanoplate is supposed to be embedded on a visco-Pasternak substrate. The kinematic relations are derived based on the Kirchhoff plate theory; also, combining these obtained equations with Hamilton's principle, the local equations of motion are achieved. According to a nonlocal strain gradient theory (NSGT), the small scale influences are covered precisely by introducing two scale coefficients. Afterwards, the nonlocal governing equations can be derived coupling the local equations with those of the NSGT. Applying an analytical solution, the wave frequency and phase velocity of propagated waves can be gathered solving an eigenvalue problem. On the other hand, accuracy and efficiency of presented model is verified by setting a comparison between the obtained results with those of previous published researches. Effects of different variants are plotted in some figures and the highlights are discussed in detail.

• International Journal of Precision Engineering and Manufacturing
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• 제3권2호
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• pp.33-44
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• 2002

The problem of eigenvalues and eigenvectors is obtained from a v-notched crack in pseudo-isotropic dissimilar materials by the traction free boundary and the perfect bonded conditions at interface. The complex stress function of the two-term William's type is used. The eigenvalues are solved by a commercial numerical program, MATHEMATICA. Stress singularities for v-notched cracks in pseudo-isotropic dissimilar materials are discussed. The RWCIM(Reciprocal Work Contour Integral Method) is applied to the determination of eigenvector coefficients associated with eigenvalues with egenvalues. The RWCIM algorithm is also coded by the MATHEMATICA.

• Structural Engineering and Mechanics
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• 제24권4호
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• pp.395-410
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• 2006

This paper reports the result of an investigation into wave propagation in orthotropic laminated piezoelectric cylindrical shells in hydrothermal environment. A dynamic model of laminated piezoelectric cylindrical shell is derived based on Cooper-Naghdi shell theory considering the effects of transverse shear and rotary inertia. The wave characteristics curves are obtained by solving an eigenvalue problem. The effects of layer numbers, thickness of piezoelectric layers, thermal loads and humid loads on the wave characteristics curves are discussed through numerical results. The solving method presented in the paper is validated by the solution of a classical elastic shell non-containing the effects of transverse shear and rotary inertia. The new features of the wave propagation in laminated piezoelectric cylindrical shells with various laminated material, layer numbers and thickness in hydrothermal environment and some meaningful and interesting results in this paper are helpful for the application and the design of the ultrasonic inspection techniques and structural health monitoring.

• Structural Engineering and Mechanics
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• 제48권1호
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• pp.103-124
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• 2013

This paper studies the static and dynamic characteristics of composite plates subjected to an arbitrary periodic load in hygrothermal environments. The material properties of composite plates are depended on the temperature and moisture. The governing equations of motion of Mathieu-type are established by using the Galerkin method with reduced eigenfunction transforms. A periodic load is taken to be a combination of axial pulsating load and bending stress in the example problem. The regions of dynamic instability of laminated composite plates are determined by solving the eigenvalue problems based on Bolotin's method. The effects of temperature rise and moisture concentration on the dynamic instability of laminated composite plates are investigated and discussed. The influences of various parameters on the instability region and dynamic instability index are also investigated. The numerical results reveal that the influences of hygrothermal effect on the dynamic instability of laminated plates are significant.

• 충청수학회지
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• 제21권3호
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• pp.339-345
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• 2008

We prove the existence of the positive solution for the nonlinear system of suspension bridge equations with Dirichlet boundary condition and periodic condition $$\{u_{tt}+u_{xxxx}+av^+=1+{\epsilon}_1h_1(x,t)\text{ in }(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,\\v_{tt}+v_{xxxx}+bu^+=1+{\epsilon}_2h_2(x,t)\text{ in }(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,$$ where $u^+={\max}\{u,0\},\;{\epsilon}_1,\;{\epsilon}_2$ are small numbers and $h_1(x,t)$, $h_2(x,t)$ are bounded, ${\pi}$-periodic in t and even in x and t and ${\parallel}h_1{\parallel}={\parallel}h_2{\parallel}=1$.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2005년도 춘계 학술발표회 논문집
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• pp.335-342
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• 2005

Using higher order Mindlin plates and piezoelectric materials, eigenvalue problems are considered. Since piezoelectric crystal resonators produce a proper amount of electric signal for a thickness-shear frequency, the objective is to decouple the thickness-shear mode from the others. Design variables are the bulk material densities corresponding to the mass of masking plates for electrodes. The design sensitivity expressions for the thickness-shear frequency and mode shape vector are derived using direct differentiation method(DDM). Using the developed design sensitivity analysis (DSA) method, we formulate a topology optimization problem whose objective function is to maximize the thickness-shear component of strain energy density at the thickness-shear mode. Constraints are the allowable volume and area of masking plate. Numerical examples show that the optimal design yields an improved mode shape and thickness-shear energy.