• Advances in aircraft and spacecraft science
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• 제4권5호
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• pp.585-611
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• 2017

This article covenants with the post buckling witticism of carbon nanotube reinforced composite (CNTRC) beam supported with an elastic foundation in thermal atmospheres with arbitrary assumed random system properties. The arbitrary assumed random system properties are be modeled as uncorrelated Gaussian random input variables. Unvaryingly distributed (UD) and functionally graded (FG) distributions of the carbon nanotube are deliberated. The material belongings of CNTRC beam are presumed to be graded in the beam depth way and appraised through a micromechanical exemplary. The basic equations of a CNTRC beam are imitative constructed on a higher order shear deformation beam (HSDT) theory with von-Karman type nonlinearity. The beam is supported by two parameters Pasternak elastic foundation with Winkler cubic nonlinearity. The thermal dominance is involved in the material properties of CNTRC beam is foreseen to be temperature dependent (TD). The first and second order perturbation method (SOPT) and Monte Carlo sampling (MCS) by way of CO nonlinear finite element method (FEM) through direct iterative way are offered to observe the mean, coefficient of variation (COV) and probability distribution function (PDF) of critical post buckling load. Archetypal outcomes are presented for the volume fraction of CNTRC, slenderness ratios, boundary conditions, underpinning parameters, amplitude ratios, temperature reliant and sovereign random material properties with arbitrary system properties. The present defined tactic is corroborated with the results available in the literature and by employing MCS.

• 한국정밀공학회지
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• 제21권8호
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• pp.129-135
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• 2004

This paper discussed on the effect of an intermediate support on the stability of elastic material subjected to dry friction force. It is assumed in this paper that the dry frictional force between a tool stand and an elastic material can be modeled as a distributed follower force. The elastic material on the friction material is modeled for simplicity into an elastic beam on Winkler-type elastic foundation. The stability of beams on the elastic foundation subjected to distributed follower force is formulated by using finite element method to have a standard eigenvalue problem. The first two eigen-frequencies are obtained to investigate the dynamics of the beam. The eigen-frequencies yield the stability bound and the corresponding unstable mode. The considered beams lose its stability by flutter or divergence, depending on the location of intermediate support.

• 한국농공학회지
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• 제45권4호
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• pp.115-125
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• 2003

Shell structures are widely used in a variety of engineering application, and mathematical solution of shell structures are available only for a few special cases. The solution of shell structure is more complicated when it has such condition as winkler foundation, other problems. In this study many simplified methods (analogy of beam on elastic foudation, finite element method and transfer matrix method) are applied to analyze a hemisphere-cylindrical shell structures on elastic foundation. And the transfer matrix method is extensively used for the structural analysis because of its merit in the theoretical backgroud and applicability. Therefore, this paper presents the analysis of hemisphere-cylindrical shell structure base on the transfer matrix method. The technique is attractive for implementation on a numerical solution by means of a computer program coded in FORTRAN language with a few elements. To demonstrate this fact, it gives good results which compare well with finite element method.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.1005-1009
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• 2001

This paper deals with the free vibration analysis of beam-columns on elastic foundation using Differential Quadrature Method. Based on the dynamic equilibrium equation of a beam element acting the stress resultants and the inertia force, the governing differential equation is derived for the in-plane free vibration of such beam-columns. For calculating the natural frequencies, this equation is solved by the Differential Quadrature Method. It is expected that the results obtained herein can be used in application of Differential Quadrature Method to the field of civil engineering and practically in the structural engineering, the foundation engineering and the vibration control fields.

• Structural Engineering and Mechanics
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• 제62권2호
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• pp.171-178
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• 2017

Nonlinear vibrations of an Euler-Bernoulli beam resting on a nonlinear elastic foundation are discussed. In search of approximate analytical solutions, the classical multiple scales (MS) and the multiple scales Lindstedt Poincare (MSLP) methods are used. The case of primary resonance is investigated. Amplitude and phase modulation equations are obtained. Steady state solutions are considered. Frequency response curves obtained by both methods are contrasted with each other with respect to the effect of various physical parameters. For weakly nonlinear systems, MS and MSLP solutions are in good agreement. For strong hardening nonlinearities, MSLP solutions exhibit the usual jump phenomena whereas MS solutions are not reliable producing backward curves which are unphysical.

• Computers and Concrete
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• 제22권6호
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• pp.501-514
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• 2018

The paper presents the thermo-mechanically induced non-linear response of multiwall carbon nanotube reinforced laminated composite beam (MWCNTRCB) supported by elastic foundation using higher order shear deformation theory and von-Karman non-linear kinematics. The elastic properties of MWCNT reinforced composites are evaluated using Halpin-Tsai model by considering MWCNT reinforced polymer matrix as new matrix by dispersing in it and then reinforced with E-glass fiber in an orthotropic manner. The laminated beam is supported by Pasternak elastic foundation with Winkler cubic nonlinearity. A generalized static analysis is formulated using finite element method (FEM) through principle of minimum potential energy approach.

• 한국해양공학회지
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• 제6권1호
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• pp.69-77
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• 1992

The natural frequencies of a beam on elastic foundation are investigated in the present paper. The inhomogeneous elastic foundation can be modelled as a combination of distributed translational spring, rotational spring, intermediate supports and dampers. The natural frequencies and mode shapes of the system are obtained by using the Galerkin's method, and also compared with the results in the literature. Furthermore, the natural frequencies of the beam with elastically mounted masses, which can be used as vibration absorbers, are obtained by an efficient numerical scheme suggested in the present paper.

• 대한토목학회논문집
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• 제13권4호
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• pp.251-258
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• 1993

이 논문은 Winkler형 지반위에 놓인 보-기둥의 자유진동 및 좌굴하중 해석에 관한 연구이다. 축하중을 받는 탄성지반위에 놓인 보-기둥이 자유진동할 때 보-기둥 미소요소에 작용하는 힘들의 동적평형방정식으로부터 지배 미분방정식을 유도하였으며, 물리적인 특성관계를 이용하여 탄성지반위에 놓인 보-기둥의 좌굴을 지배하는 미분방정식을 직접 유동하였다. 유도된 미분방정식은 수치해석기법인 Runge-Kutta method와 행렬값 탐사법을 이용하여 해석하였다. 실제의 수치예에서는 양단회전 및 양단고정의 단부조건에 대하여 수치해석하였다. 수치해석의 결과로 무차원 고유진동수와 지반탄성계수 관계, 무차원 좌굴하중과 지반탄성계수 관계 및 축하중과 무차원 고유진동수 관계를 그림에 나타내었으며, 탄성지지구간의 변화에 따른 고유진동수 및 좌굴하중 변화를 고찰하였다. 또한 3구간으로 나누어지는 비균질 지반위에 놓인 보-기둥의 축하중과 고유진동수 관계를 고찰하였으며 이에 대한 진동형을 그림에 나타내었다.

• 대한기계학회논문집A
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• 제28권2호
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• pp.143-148
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• 2004

This paper discussed on the stability of elastic material subjected to dry friction force for low boundary conditions: clamped free, clamped-simply supported, simply supported-simply supported, clamped-clamped. It is assumed in this paper that the dry frictional force between a tool stand and an elastic material can be modeled as a distributed follower force. The friction material is modeled for simplicity into a Winkler-type elastic foundation. The stability of beams on the elastic foundation subjected to distribute follower force is formulated by using finite element method to have a standard eigenvalue problem. It is found that the clamped-free beam loses its stability in the flutter type instability, the simply supported-simply supported beam loses its stability in the divergence type instability and the other two boundary conditions the beams lose their stability in the divergence-flutter type instability.

• International Journal of Precision Engineering and Manufacturing
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• 제3권4호
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• pp.54-63
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• 2002

In recent years, mechanical systems such as high speed vehicles and railway trains moving on elastic beam structures have become a very important issue to consider. In this paper, a general approach, which can predict the dynamic behavior of a constrained mechanical system moving on a flexible beam structure, is proposed. Various supporting conditions for the foundation support are considered for the elastic beam structure. The elastic structure is assumed to be a non-uniform and linear Bernoulli-Euler beam with a proportional damping effect. Combined differential-algebraic equation of motion is derived using the multi-body dynamics theory and the finite element method. The proposed equations of motion can be solved numerically using the generalized coordinate partitioning method and predictor-corrector algorithm, which is an implicit multi-step integration method.