• 한국소음진동공학회논문집
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• 제26권3호
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• pp.281-289
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• 2016

In this paper, a new dynamic model for modal analysis of a rotating cantilever beam with a tip-mass is developed. The nonlinear strain such as von Karman type and the corresponding linearized stress are used to consider the geometric nonlinearity, and Euler-Bernoulli beam theory is applied in the present model. The nonlinear equations of motion and the associated boundary conditions which include the inertia of the tip-mass are derived through Hamilton's principle. In order to investigate modal characteristics of the present model, the linearized equations of motion in the neighborhood of the equilibrium position are obtained by using perturbation technique to the nonlinear equations. Since the effect of the tip-mass is considered to the boundary condition of the flexible beam, weak forms are used to discretize the linearized equations. Compared with equations related to stiffening effect due to centrifugal force of the present and the previous model, the present model predicts the dynamic characteristic more precisely than the another model. As a result, the difference of natural frequencies loci between two models become larger as the rotating speed increases. In addition, we observed that the mode veering phenomenon occurs at the certain rotating speed.

• Structural Engineering and Mechanics
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• 제82권4호
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• pp.477-490
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• 2022

This article investigates the nonlinear behavior of two-directional functionally graded materials (TDFGM) doubly curved panels with porosities for the first time. An improved and effectual approach is established based on the improved first-order shear deformation shell theory (IFSDST) and von Karman's type nonlinearity. The IFSDST considers the effects of shear deformation without the need for a shear correction factor. The composition of TDFGM constitutes four different materials, and the modified power-law function is employed to vary the material properties continuously in both thickness and longitudinal directions. A nonlinear finite element method in conjunction with Hamilton's principle is used to obtain the governing equations. Then, the direct iterative method is incorporated to accomplish the numerical results using the frequency-amplitude, nonlinear central deflection relations. Finally, the influence of volume fraction grading indices, porosity distributions, porosity volume, curvature ratio, thickness ratio, and aspect ratio provides a thorough insight into the linear and nonlinear responses of the porous curved panels. Meanwhile, this study emphasizes the influence of the volume fraction gradation profiles in conjunction with the various material and geometrical parameters on the linear frequency, nonlinear frequency, and deflection of the TDFGM porous shells. The numerical analysis reveals that the frequencies and nonlinear deformations can be significantly regulated by changing the volume fraction gradation profiles in a specified direction with an appropriate combination of materials. Hence, TDFGM panels can overcome the drawbacks of the functionally graded materials with a gradation of properties in a single direction.

• 소음진동
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• 제9권4호
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• pp.806-812
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• 1999

Dynamic behaviors are analyzed for a flexble spinning disk with angular acceleration, considering geometric nonlinearity. Based upon the Kirchhoff plate theory and the von Karman strain theory, the nonlinear governing equations are derived which are coupled equations with the in-plane and out-of-planedisplacements. The governing equations are discretized by using the Galerkin approximation. With the discretized nonlinear equations, the time responses are computed by using the generalized-$\alpha$ method and the Newton-Raphson method. The analysis shows that the existence of angular acceleration increases the displacements of the spinning disk and makes the disk unstable.

• 한국구조물진단유지관리공학회 논문집
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• 제6권3호
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• pp.139-149
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• 2002

Explicit 직접적분법을 사용하여 충격하중을 받는 박판의 후좌굴거동을 해석할 수 있는 알고리즘을 제안하였다. von Karman의 대변위 판 이론과 Marquerre의 쉘 이론을 이용하여 유도한 직사각형 평판 유한요소는 박판의 초기처짐과 기하학적 비선형 거동을 고려할 수 있다. 중앙차분법을 바탕으로 해석 알고리즘을 개발하였고 이를 프로그램화 시켜, 하중형상과 재하시간이 다른 충격하중에 대하여 박판의 동적 좌굴거동을 해석 하였다. 수치해석 예제를 통하여 Explicit 직접적분법의 특성을 평가하였다.

• Smart Structures and Systems
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• 제18권1호
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• pp.155-181
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• 2016

In the present paper we discuss the stability and the post-buckling behaviour of thin piezoelastic plates. The first part of the paper is concerned with the modelling of such plates. We discuss the constitutive modelling, starting with the three-dimensional constitutive relations within Voigt's linearized theory of piezoelasticity. Assuming a plane state of stress and a linear distribution of the strains with respect to the thickness of the thin plate, two-dimensional constitutive relations are obtained. The specific form of the linear thickness distribution of the strain is first derived within a fully geometrically nonlinear formulation, for which a Finite Element implementation is introduced. Then, a simplified theory based on the von Karman and Tsien kinematic assumption and the Berger approximation is introduced for simply supported plates with polygonal planform. The governing equations of this theory are solved using a Galerkin procedure and cast into a non-dimensional formulation. In the second part of the paper we discuss the stability and the post-buckling behaviour for single term and multi term solutions of the non-dimensional equations. Finally, numerical results are presented using the Finite Element implementation for the fully geometrically nonlinear theory. The results from the simplified von Karman and Tsien theory are then verified by a comparison with the numerical solutions.

• Advances in nano research
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• 제17권1호
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• pp.61-73
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• 2024

This paper presents nonlinear vibration analysis of a composite cylindrical shell. The core of the shell is made of functionally graded (FG) porous materials and layers is fabricated of carbon nanotubes (CNTs) reinforced nanocomposites. To increase the accuracy of results, neutral surface position is considered. First-order shear deformation theory is used as displacement field to derive the basic relations of equation motions. In addition, von-Karman nonlinear strains are employed to account geometric nonlinearity and to enhance the results' precision, the exact position of the neutral surface is considered. To governing the partial equations of motion, the Hamilton's principle is used. To reduce the equation motions into a nonlinear motion equation, the Galerkin's approach is employed. After that the nonlinear motion equation is solved by multiple scales method. Effect of various parameters such as volume fraction and distribution of CNTs along the thickness directions, different patterns and efficiency coefficients of porous materials, geometric characteristics and initial conditions on nonlinear to linear ratio of frequency is investigated.

• Structural Engineering and Mechanics
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• 제86권4호
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• pp.443-459
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• 2023

This study investigates the theoretical thermal buckling analyses of thick porous rectangular functionally graded (FG) plates with different geometrical boundary conditions resting on a Winkler-Pasternak elastic foundation using a new higher-order shear deformation theory (HSDT). This new theory has only four unknowns and involves indeterminate integral variables in which no shear correction factor is required. The variation of material properties across the plate's thickness is considered continuous and varied following a simple power law as a function of volume fractions of the constituents. The effect of porosity with two different types of distribution is also included. The current formulation considers the Von Karman nonlinearity, and the stability equations are developed using the virtual works principle. The thermal gradients are involved and assumed to change across the FG plate's thickness according to nonlinear, linear, and uniform distributions. The accuracy of the newly proposed theory has been validated by comparing the present results with the results obtained from the previously published theories. The effects of porosity, boundary conditions, foundation parameters, power index, plate aspect ratio, and side-to-thickness ratio on the critical buckling temperature are studied and discussed in detail.

• Structural Engineering and Mechanics
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• 제66권5호
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• pp.557-568
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• 2018

An investigation is made in the present work on the post-buckling and geometrically nonlinear behaviors of moderately thick perfect and imperfect rectangular plates made-up of functionally graded materials. Spectral collocation approach based on Legendre basis functions is developed to analyze the functionally graded plates while they are subjected to end-shortening strain. The material properties in this study are varied through the thickness according to the simple power law distribution. The fundamental equations for moderately thick rectangular plates are derived using first order shear deformation plate theory and taking into account both geometric nonlinearity and initial geometric imperfections. In the current study, the domain of interest is discretized with Legendre-Gauss-Lobatto nodes. The equilibrium equations will be obtained by discretizing the Von-Karman's equilibrium equations and also boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Due to effect of geometric nonlinearity, the final set of equilibrium equations is nonlinear and therefore the quadratic extrapolation technique is used to solve them. Since the number of equations in this approach will always be more than the number of unknown coefficients, the least squares technique will be used. Finally, the effects of boundary conditions, initial geometric imperfection and material properties are investigated and discussed to demonstrate the validity and capability of proposed method.

• Nuclear Engineering and Technology
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• 제55권11호
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• pp.4295-4306
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• 2023

The vibration of fuel rods in axial flow is a universally recognized issue within both engineering and academic communities due to its significant importance in ensuring structural safety. This paper aims to thoroughly investigate the stability and nonlinear vibration of a fuel rod subjected to axial flow in a newly designed high temperature gas cooled reactor. Considering the possible presence of thermal expansion and large deformation in practical scenarios, the thermal effect and geometric nonlinearity are modeled using the von Karman equation. By applying Hamilton's principle, we derive the comprehensive governing equation for this fluid-structure interaction system, which incorporates the quadratic nonlinear stiffness. To establish a connection between the fluid and structure aspects, we utilize the Galerkin method to solve the perturbation potential function, while employing mode expansion techniques associated with the structural analysis. Following convergence and validation analyses, we examine the stability of the structure under various conditions in detail, and also investigate the bifurcation behavior concerning the buckling amplitude and flow velocity. The findings from this research enhance the understanding of the underlying physics governing fuel rod behavior in axial flow under severe yet practical conditions, while providing valuable guidance for reactor design.

• 대한토목학회논문집
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• 제11권1호
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• pp.79-87
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• 1991

본 논문에서는 단조증가하중을 받는 철근콘크리트 쉘구조의 탄성, 비탄성, 극한영역등 모든 응력상태에 대한 재료적(材料的), 기하학적(幾何學的) 비선형(非線形) 해석(解析)을 위해서 유한요소법에 의한 수치해법(數値解法)을 개발하였다. 유한요소로서는 면회전단변형을 고려하여 Degeneration 방법에 의해 유도된 8절점 Serendipity 등매개변수 요소를 사용하였으며, 두께방향에 대한 철근과 콘크리트의 재료성질을 고려하기 위하여 층상화기법(層狀化技法)을 도입하였다. 기하학적(幾何學的) 비선형성(非線形性)은 Von Karman의 가정에 기본을 둔 total Lagrangian formulation에 의해 고려하였으며, 재료적(材料的) 비선형성(非線形性)에 대해서는 균열콘크리트에 대한 인장, 압축, 전단모델과 콘크리트 중에 있는 철근모델을 조합하여 고려하였다. 이에 대한 콘크리트의 균열모델로서는 분산균열모델을 사용했으며, 철근에 대해서는 1축 응력상태로 가정하여 등가의 분산분포된 철근량으로 모델화하였다. 차후 논문( )의 수치예제를 통하여 본 논문의 해석방법이 기하학적(幾何學的), 재료적(材料的) 비선형성(非線形性)을 고려한 임의형상의 철근콘크리트 쉘구조의 해석에 적합한 방법임을 입증하고자 한다.