• 제목/요약/키워드: Boundary mode method

검색결과 525건 처리시간 0.022초

Vibrational characteristic of FG porous conical shells using Donnell's shell theory

  • Yan, Kai;Zhang, Yao;Cai, Hao;Tahouneh, Vahid
    • Steel and Composite Structures
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    • 제35권2호
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    • pp.249-260
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    • 2020
  • The main purpose of this research work is to investigate the free vibration of conical shell structures reinforced by graphene platelets (GPLs) and the elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. To this end, a shell model is developed based on Donnell's theory. To solve the problem, the analytical Galerkin method is employed together with beam mode shapes as weighting functions. Due to importance of boundary conditions upon mechanical behavior of nanostructures, the analysis is carried out for different boundary conditions. The effects of boundary conditions, semi vertex angle, porosity distribution and graphene platelets on the response of conical shell structures are explored. The correctness of the obtained results is checked via comparing with existing data in the literature and good agreement is eventuated. The effectiveness and the accuracy of the present approach have been demonstrated and it is shown that the Donnell's shell theory is efficient, robust and accurate in terms of nanocomposite problems.

Natural vibrations and hydroelastic stability of laminated composite circular cylindrical shells

  • Bochkareva, Sergey A.;Lekomtsev, Sergey V.
    • Structural Engineering and Mechanics
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    • 제81권6호
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    • pp.769-780
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    • 2022
  • This paper studies the dynamic behavior of laminated composite circular cylindrical shells interacting with a fluid. The mathematical formulation of the dynamic problem for an elastic body is developed based on the variational principle of virtual displacements and the relations of linear elasticity theory. The behavior of an ideal compressible fluid is described by the potential theory, the equations of which together with boundary conditions are transformed to a weak form. The hydrodynamic pressure exerted by the fluid on the internal surface of the shell is calculated according to the linearized Bernoulli equation. The numerical implementation of the mathematical formulation has been done using the semi-analytical finite element method. The influence of the ply angle and lay-up configurations of laminated composites on the natural vibration frequencies and the hydroelastic stability boundary have been analyzed for shells with different geometrical dimensions and under different kinematic boundary conditions set at their edges. It has been found that the optimal value of the ply angle depends on the level of filling of the shell with a fluid. The obtained results support the view that by choosing the optimal configuration of the layered composite material it is possible to change upwards or downwards the frequency and mode shape, as well as the critical velocity for stability loss over a wide range.

Thermal post-buckling analysis of graphene platelets reinforced metal foams beams with initial geometric imperfection

  • Gui-Lin She;Yin-Ping Li;Yujie He;Jin-Peng Song
    • Computers and Concrete
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    • 제33권3호
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    • pp.241-250
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    • 2024
  • This article investigates the thermal and post-buckling problems of graphene platelets reinforced metal foams (GPLRMF) beams with initial geometric imperfection. Three distribution forms of graphene platelet (GPLs) and foam are employed. This article utilizes the mixing law Halpin Tsai model to estimate the physical parameters of materials. Considering three different boundary conditions, we used the Euler beam theory to establish the governing equations. Afterwards, the Galerkin method is applied to discretize these equations. The correctness of this article is verified through data analysis and comparison with the existing articles. The influences of geometric imperfection, GPL distribution modes, boundary conditions, GPLs weight fraction, foam distribution pattern and foam coefficient on thermal post-buckling are analyzed. The results indicate that, perfect GPLRMF beams do not undergo bifurcation buckling before reaching a certain temperature, and the critical buckling temperature is the highest when both ends are fixed. At the same time, the structural stiffness of the beam under the GPL-A model is the highest, and the buckling response of the beam under the Foam-II mode is the lowest, and the presence of GPLs can effectively improve the buckling strength.

A method to evaluate the frequencies of free transversal vibrations in self-anchored cable-stayed bridges

  • Monaco, Pietro;Fiore, Alessandra
    • Computers and Concrete
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    • 제2권2호
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    • pp.125-146
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    • 2005
  • The objective of this paper is setting out, for a cable-stayed bridge with a curtain suspension, a method to determine the modes of vibration of the structure. The system of differential equations governing the vibrations of the bridge, derived by means of a variational formulation in a nonlinear field, is reported in Appendix C. The whole analysis results from the application of Hamilton's principle, using the expressions of potential and kinetic energies and of the virtual work made by viscous damping forces of the various parts of the bridge (Monaco and Fiore 2003). This paper focuses on the equation concerning the transversal motion of the girder of the cable-stayed bridge and in particular on its final form obtained, restrictedly to the linear case, neglecting some quantities affecting the solution in a non-remarkable way. In the hypotheses of normal mode of vibration and of steady-state, we propose the resolution of this equation by a particular method based on a numerical approach. Respecting the boundary conditions, we derive, for each mode of vibration, the corresponding frequency, both natural and damped, the shape-function of the girder axis and the exponential function governing the variability of motion amplitude in time. Finally the results so obtained are compared with those deriving from the dynamic analysis performed by a finite elements calculation program.

수직면에서 작동하는 탄성 매니퓰레이터의 효율적인 제어에 관한 연구 (A Study on the efficient control of an elastic manipulator moving in a vertical plane)

  • 강준원;이중섭;권혁조;오재윤;정재욱
    • 한국정밀공학회:학술대회논문집
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    • 한국정밀공학회 1996년도 추계학술대회 논문집
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    • pp.318-322
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    • 1996
  • This paper presents a technique to control a robot which has a flexible manipulator moving in a vertical plane. The flexible manipulator is modeled as an Euler-Bernoulli beam. Elastic deformation is represented using the assumed modes method. A comparison function which satisfies all geometric and natural boundary conditions of a cantilever beam with an end mass is used as an assumed mode shape. Lagrange's equation is utilized for the development of a discretized model. A control algorithm is developed using a simple PID control technique. The proportional, integral and derivative control gains are determined based on the dominant pole placement method and tuned to show no overshoot and having a short settling time. The effectiveness of the developed control scheme is showed experimentally. In the position control experiment, three different end masses are used. The experimental results shows little overshoot, no steady state error, and less than 2.5 second settling time in case of having an end mass which is equivalent to 45% of the total system weight. Also the residual vibration of the end point is effectively controlled.

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단층 래티스돔의 안정해석기법 및 좌굴특성에 관한 연구 (A Study on the Analytical Technique of Stability and Buckling Characteristics of the Single Layer Latticed Domes)

  • 한상을
    • 전산구조공학
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    • 제9권3호
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    • pp.209-216
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    • 1996
  • 본 논문의 목적은 단층래티스 돔의 안정해석 기법을 제안하고, 다양한 조건하에서 단층 래티스 돔이 갖는 좌굴특성을 규명하는데 있다. 기하학적 비선형 평형경로의 탐색 및 좌굴점 그리고 분기경로의 방향 등을 수직적으로 계산하기 위하여 호장법(Arc-Length Method)을 이용하였으며, 부재의 좌굴가능성을 판단하기 위하여 에너지밀도함수를 제안하였다. 강절점을 갖는 구조물의 거동 특성을 규명하기 위하여 3종류의 비선형 강성행렬을 유도하여 해석하였으며, semi-rigid절점을 갖는 구조물을 해석하기 위하여 스프링모델을 제안하고, 부재의 세장비, 반개각, 경계조건 및 다양한 하중조건을 파라메터로하여 좌굴특성을 규명하였다.

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Bi-stability in a vertically excited rectangular tank with finite liquid depth

  • Spandonidis, Christos C.;Spyrou, Kostas J.
    • Ocean Systems Engineering
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    • 제2권3호
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    • pp.229-238
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    • 2012
  • We discuss the bi - stability that is possibly exhibited by a liquid free surface in a parametrically - driven two-dimensional (2D) rectangular tank with finite liquid depth. Following the method of adaptive mode ordering, assuming two dominant modes and retaining polynomial nonlinearities up to third-order, a nonlinear finite-dimensional nonlinear modal system approximation is obtained. A "continuation method" of nonlinear dynamics is then used in order to elicit efficiently the instability boundary in parameters' space and to predict how steady surface elevation changes as the frequency and/or the amplitude of excitation are varied. Results are compared against those of the linear version of the system (that is a Mathieu-type model) and furthermore, against an intermediate model also derived with formal mode ordering, that is based on a second - order ordinary differential equation having nonlinearities due to products of elevation with elevation velocity or acceleration. The investigation verifies that, in parameters space, there must be a region, inside the quiescent region, where liquid surface instability is exhibited. There, behaviour depends on initial conditions and a wave form would be realised only if the free surface was substantially disturbed initially.

재해석 기법에 의한 충격 하중을 받는 쉘 구조물의 동적 응답 해석에 관한 연구 (A Study on the Dynamic Response Analysis of Shell Structure with Impulsive Load by Reanalysis Technique)

  • 배동명
    • 수산해양기술연구
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    • 제29권2호
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    • pp.132-151
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    • 1993
  • The proposed method in this paper. termed the substructural reanalysis technique, utilizes the computational merits of the component mode synthesis technique and of reanalysis technique for the design sensitivities of the dynamic characteristics of substructurally combined structure. It is shown that the dynamic characteristics of the entire structure can be obtained by synthesizing the substructural eigensolution and the characteristics of the eigensolution for the design variables of the modifiable substructure. In this paper , the characteristics of the eigenvalue problems obtained by this proposed method are compared to exact eigensolution in terms of accuracy and computational efficiency. and the advantage of this proposed method as compared to the direct application of the whole structure and experimental results is demonstrated through examples of numerical calculation for the dynamic characteristics (natural frequencies and mode shapes) of a flexible vibration of thin cylinderical shell with branch shell under 2-end fixed positions, boundary condition. Thin cylinderical shell of overall length 1280mm, external diameter 360mm, thickness 3mm with branch shell is made of mild steel. The load condition for dynamic response in this paper is impulsive load of which magnitude is 10kgf, which have short duration of 0.1 sec. and time interval applied to calculate. $\Delta$T is 1.0$\times$10 super(-4) seconds.

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수직면에서 회전운동을 하는 탄성로봇의 PID 제어 (PID Control of a flexible robot rotating in vertical plane)

  • 강준원;오재윤;김기호
    • 한국정밀공학회지
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    • 제14권11호
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    • pp.34-41
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    • 1997
  • This paper presents a technique to control a very flexible robot moving in a vertical plane. The flexible robot is modeled as an Euler-Bernoulli beam. Elastic deformation is approximated using the assmed modes method. A comparison function which satisfies all geometric and natural boundary conditions of a cantilever beam with an end mass is used as an assumed mode shape. Lagrange's equation is utilized for the development of a discretized model. A control algorithm is developed using a simple PID cnotrol tech- nique. The proportional, integral and deivative control gains are determined based on the dominant pole placement method and tuned to show no overshoot and no steady state error, and short settling time. The effectiveness of the developed control scheme is showed in the hub angular diaplacement control experiment. Three different end masses are uned in the experiment. The experimental results show that developed control algorithm is very effective showing little overshoot, no steady state error, and less than 2.5 second settl- ing time in case of having an end mass which is equivalent to 45% of the manipulator mass. Also the experimental results show that the residual vibration fo the end point is effectively controlled.

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역대칭 적층쉘의 비선형 동적 특성에 관한 연구 (Nonlinear Dynamic Characteristics of Antisymmetric Laminated Shells)

  • 박승진;삼상륭;김영진
    • 한국강구조학회 논문집
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    • 제10권4호통권37호
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    • pp.691-700
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    • 1998
  • 본 연구에서는 역대칭 또는 비대칭 적층쉘에 대한 Von Karman-Donnell 운동방정식을 기초로 한 다중 모드 접근법을 이용하여 양단이 단순지지 되고 다른 임의지지가 단순 또는 고정지지인 원통 쉘의 비선형 거동에 대해 연구하였다. 방정식은 모든 경계조건에 대해 만족하며, 변위함수는 최저 진동모드와 원주 방향의 변위의 연속성 조건을 만족하는 것으로 한다 비선형 진동 방정식은 Galerkin 법을 이용하여 유도하였고, 비선형 진동수는 조화평균법을 이용하여 적층 매개변수, 재료 상수, 종횡비 및 진동 진폭의 함수로서 표시하였다. 초기 진폭의 영향에 대해서는 4가지 형태의 경계조건에 대한 비선형 진동 결과를 비교 검토하였다.

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