• 한국기계연구소 소보
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• 통권18호
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• pp.131-136
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• 1988

A small-deflected beam can be easily solved by assuming a linear system. But a large-deflected beam can not be solved by superposition of the displacements, because the system is nonlinear. The solutions for the large-deflection problems can not be obtained directly from elementary beam theory for linearized systems since the basic assumptions are no longer valid. Specifically, elementary theory neglects the square of the first derivative in the beam curvature formula and provides no correction for the shortening of the moment-arm cause by transverse deflection. These two effects must be considered to analyze the large deflection. Through the correction of deflected geometry and internal axial force, the proposed new approach is developed from the linearized beam theory. The solutions from the proposed approach are compared with exact solutions.

• Wind and Structures
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• 제23권1호
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• pp.59-73
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• 2016

In this paper, a hyperbolic shear deformation beam theory is developed for free vibration analysis of functionally graded (FG) sandwich beams. The theory account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The material properties of the functionally graded sandwich beam are assumed to vary according to power law distribution of the volume fraction of the constituents. The core layer is still homogeneous and made of an isotropic material. Based on the present refined beam theory, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain frequencies. Illustrative examples are given to show the effects of varying gradients and thickness to length ratios on free vibration of functionally graded sandwich beams.

• Advances in nano research
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• 제13권1호
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• pp.63-75
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• 2022

The nonlinear dynamic behavior of a nonuniform small-scale nonlocal beam is investigated in this work. The nanobeam is theoretically modeled using the nonlocal Eringen theory, as well as a few of Von-nonlinear Kármán's theories and the classical beam theory. The Hamilton principle extracts partial differential equations (PDE) of an axially functionally graded (AFG) nano-scale beam consisting of SUS304 and Si₃N₄ throughout its length, and an elastic Winkler-Pasternak substrate supports the tapered AFG nanobeam. The beam thickness is a function of beam length, and it constantly varies throughout the length of the beam. The numerical solution strategy employs an iteration methodology connected with the generalized differential quadratic method (GDQM) to calculate the nonlinear outcomes. The nonlinear numerical results are presented in detail to examine the impact of various parameters such as nonlinear amplitude, nonlocal parameter, the component of the elastic foundation, rate of cross-section change, and volume fraction parameter on the linear and nonlinear free vibration characteristics of AFG nanobeam.

• 대한기계학회논문집A
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• 제37권12호
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• pp.1547-1557
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• 2013

시간변화 이동자기력이 작용하는 레일의 변형을 티모센코 보 이론(Timoshenko beam theory)로 가정하였으며, 보의 진동특성에 영향을 미치는 탄성체기초의 감쇠효과 및 강성을 고려하였다. 푸리에 급수와 수치해석을 이용해 강제진동모델의 동적응답과 임계속도를 구하였다. 레일의 진동모델을 유한요소 해석 및 오일러 보 이론(Euler beam theory)과 비교 검증하였다. 강제진동모델을 이용하여 레일의 영구변형을 예측하였으며, 실험결과 레일표면의 영구변형 및 마모를 확인하였다. 보의 설계변수인 레일의 형상, 재료, 탄성체 기초의 감쇠효과 및 강성이 레일의 임계속도 및 레일의 처짐, 축 방향 응력, 전단 응력에 미치는 영향에 대한 매개변수적 연구를 진행하였으며, 보의 설계방향을 얻을 수 있었다.

• Advances in nano research
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• 제7권6호
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• pp.443-457
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• 2019

In this investigation, dynamic and bending behaviors of isolated protein microtubules are analyzed. Microtubules (MTs) can be considered as bio-composite structures that are elements of the cytoskeleton in eukaryotic cells and posses considerable roles in cellular activities. They have higher mechanical characteristics such as superior flexibility and stiffness. In the modeling purpose of microtubules according to a hollow beam element, a novel single variable sinusoidal beam model is proposed with the conjunction of modified strain gradient theory. The advantage of this model is found in its new displacement field involving only one unknown as the Euler-Bernoulli beam theory, which is even less than the Timoshenko beam theory. The equations of motion are constructed by considering Hamilton's principle. The obtained results are validated by comparing them with those given based on higher shear deformation beam theory containing a higher number of variables. A parametric investigation is established to examine the impacts of shear deformation, length scale coefficient, aspect ratio and shear modulus ratio on dynamic and bending behaviors of microtubules. It is remarked that when length scale coefficients are almost identical of the outer diameter of MTs, microstructure-dependent behavior becomes more important.

• Steel and Composite Structures
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• 제30권6호
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• pp.603-615
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• 2019

In the present work, free vibration of beams made of imperfect functionally graded materials (FGMs) including porosities is investigated. Because of faults during process of manufacture, micro voids or porosities may arise in the FGMs, and this situation causes imperfection in the structure. Therefore, material properties of the beams are assumed to vary continuously through the thickness direction according to the volume fraction of constituents described with the modified rule of mixture including porosity volume fraction which covers two types of porosity distribution over the cross section, i.e., even and uneven distributions. The governing equations of power law FGM (P-FGM) and sigmoid law FGM (S-FGM) beams are derived within the frame works of classical beam theory (CBT) and first order shear deformation beam theory (FSDBT). The resulting equations are solved using separation of variables technique and assuming FG beams are simply supported at both ends. To validate the results numerous comparisons are carried out with available results of open literature. The effects of types of volume fraction function, beam theory and porosity volume fraction, as well as the variations of volume fraction index, span to depth ratio and porosity volume fraction, on the first three non-dimensional frequencies are examined in detail.

• Structural Engineering and Mechanics
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• 제19권5호
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• pp.477-501
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• 2005

In this study, a new smart beam finite element is proposed for the finite element modeling of beam-type smart structures that are equipped with bonded plate-type piezoelectric sensors and actuators. Constitutive equations for the direct piezoelectric effect and converse piezoelectric effect of piezoelectric materials are considered in the formulation. By using a variational principle, the equations of motion for the smart beam finite element are derived. The proposed 2-node beam finite element is an isoparametric element based on Timoshenko beam theory. The proposed smart beam finite element is applied to the free vibration control adopting a constant gain feedback scheme. The electrical force vector, which is obtained in deriving an equation of motion, is the control force equivalent to that in existing literature. Validity of the proposed element is shown through comparing the analytical results of the verification examples with those of other previous researchers. With the use of smart beam finite elements, simulation of free vibration control is demonstrated by sensing the voltage of the piezoelectric sensors and by applying the voltages to the piezoelectric actuators.

• 복합신소재구조학회 논문집
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• 제1권4호
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• pp.13-17
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• 2010

A post-tensioned slab bridge is analyzed by the specially orthotropic theory. Each longitudinal and transverse steel layer is regarded as a lamina, and material constants of each lamina is calculated by the use of rule of mixture. This slab bridge with simple support is under uniformly distributed vertical and axial loads. In this paper, the finite difference method and the beam theory are used for analysis. The result of beam analysis is modified to obtain the solution of the plate analysis. The result of this paper can be used for post-tensioned slab bridge analysis by the engineers with undergraduate study in near future.

• Structural Engineering and Mechanics
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• 제73권2호
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• pp.109-121
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• 2020

This study aims to estimate crack location and crack length in damaged beam structures using transfer matrix formulations, which are based on analytical solutions of governing equations of motion. A single variable shear deformation theory (SVSDT) that considers parabolic shear stress distribution along beam cross-section is used, as well as, Timoshenko beam theory (TBT). The cracks are modelled using massless rotational springs that divide beams into segments. In the forward problem, natural frequencies of intact and cracked beam models are calculated for different crack length and location combinations. In the inverse approach, which is the main concern of this paper, the natural frequency values obtained from experimental studies, finite element simulations and analytical solutions are used for crack identification via plots of rotational spring flexibilities against crack location. The estimated crack length and crack location values are tabulated with actual data. Three different beam models that have free-free, fixed-free and simple-simple boundary conditions are considered in the numerical analyses.

• Structural Engineering and Mechanics
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• 제66권6호
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• pp.703-711
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• 2018

In this paper is studied the effect of considering the theory of Timoshenko in the vibration of AFG beams that support ground masses. As it is known, Timoshenko theory takes into account the shear deformation and the rotational inertia, provides more accurate results in the general study of beams and is mandatory in the case of high frequencies or non-slender beams. The Rayleigh-Ritz Method is employed to obtain approximated solutions of the problem. The accuracy of the procedure is verified through results available in the literature that can be represented by the model under study. The incidence of the Timoshenko theory is analyzed for different cases of beam slenderness, variation of its cross section and compositions of its constituent material, as well as different amounts and positions of the attached masses.