• Structural Engineering and Mechanics
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• 제16권2호
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• pp.195-217
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• 2003

This paper, which is an extension of a previous work by Viola et al. (2002), deals with the dynamic stability of beams under a triangularly distributed sub-tangential forces when the effect of an elastically restrained end is taken into account. The sub-tangential forces can be realised by a combination of axial and tangential follower forces, that are conservative and non-conservative forces, respectively. The studied beams become unstable in the form of either flutter or divergence, depending on the degree of non-conservativeness of the distributed sub-tangential forces and the stiffness of the elastically restrained end. A non-conservative parameter ${\alpha}$ is introduced to provide all possible combinations of these forces. Problems of this kind are usually, at least in the first approximation, reduced to the analysis of beams according to the Bernoulli-Euler theory if shear deformability and rotational inertia are negligible. The equation governing the system may be derived from the extended form of Hamilton's principle. The stability maps will be obtained from the eigenvalue analysis in order to define the divergence and flutter domain. The passage from divergence to flutter is associated with a noticeable lowering of the critical load. A number of particular cases can be immediately recovered.

• Coupled systems mechanics
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• 제6권3호
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• pp.251-272
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• 2017

In this paper, the thermo-mechanical vibration characteristics of functionally graded (FG) nanobeams subjected to three types of thermal loading including uniform, linear and non-linear temperature change are investigated in the framework of third-order shear deformation beam theory which captures both the microstructural and shear deformation effects without the need for any shear correction factors. Material properties of FG nanobeam are assumed to be temperature-dependent and vary gradually along the thickness according to the power-law form. Hence, applying a third-order shear deformation beam theory (TSDBT) with more rigorous kinetics of displacements to anticipate the behaviors of FG nanobeams is more appropriate than using other theories. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton's principle and they are solved applying analytical solution. The obtained results are compared with those predicted by the nonlocal Euler-Bernoulli beam theory and nonlocal Timoshenko beam theory and it is revealed that the proposed modeling can accurately predict the vibration responses of FG nanobeams. The obtained results are presented for the thermo-mechanical vibration analysis of the FG nanobeams such as the effects of material graduation, nonlocal parameter, mode number, slenderness ratio and thermal loading in detail. The present study is associated to aerospace, mechanical and nuclear engineering structures which are under thermal loads.

• Steel and Composite Structures
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• 제36권3호
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• pp.293-305
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• 2020

This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.

• Smart Structures and Systems
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• 제26권2호
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• pp.213-226
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• 2020

In this manuscript, static and dynamic behaviors of geometrically imperfect carbon nanotubes (CNTs) subject to different types of end conditions are investigated. The Doublet Mechanics (DM) theory, which is length scale dependent theory, is used in the analysis. The Euler-Bernoulli kinematic and nonlinear mid-plane stretching effect are considered through analysis. The governing equation of imperfect CNTs is a sixth order nonlinear integro-partial-differential equation. The buckling problem is discretized via the differential-integral-quadrature method (DIQM) and then it is solved using Newton's method. The equation of linear vibration problem is discretized using DIQM and then solved as a linear eigenvalue problem to get natural frequencies and corresponding mode shapes. The DIQM results are compared with analytical ones available in the literature and excellent agreement is obtained. The numerical results are depicted to illustrate the influence of length scale parameter, imperfection amplitude and shear foundation constant on critical buckling load, post-buckling configuration and linear vibration behavior. The current model is effective in designing of NEMS, nano-sensor and nano-actuator manufactured by CNTs.

• 한국전산구조공학회논문집
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• 제19권1호
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• pp.85-92
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• 2006

이 논문은 일단고정 타단스프링으로 지지된 변단면 Beck 기둥의 임계하중에 관한 연구이다. 기둥의 변단면을 중실 직사각형 단면을 갖는 선형 변단면으로 채택하고, Bernoulli-Euler보 이론을 이용하여 경사종동력이 작용하는 소위 Beck 기둥의 자유진동을 지배하는 상미분방정식과 경계조건을 유도하였다. 이 미분방정식을 수치해석하여 하중-고유진동수 곡선을 얻고 이로부터 발산임계하중 및 동요임계하중을 산출하였다. 수치해석의 결과로부터 변단면 형태, 경사변수 및 스프링 강성이 임계하중에 미치는 영향을 고찰하였다

• Structural Engineering and Mechanics
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• 제54권4호
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• pp.693-710
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• 2015

This paper presents a nonlocal shear deformation beam theory for bending, buckling, and vibration of functionally graded (FG) nanobeams using the nonlocal differential constitutive relations of Eringen. The developed theory account for higher-order variation of transverse shear strain through the depth of the nanobeam, and satisfy the stress-free boundary conditions on the top and bottom surfaces of the nanobeam. A shear correction factor, therefore, is not required. In addition, this nonlocal nanobeam model incorporates the length scale parameter which can capture the small scale effect and it has strong similarities with Euler-Bernoulli beam model in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived from Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam, and the obtained results compare well with those predicted by the nonlocal Timoshenko beam theory.

• 한국정밀공학회지
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• 제17권11호
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• pp.176-184
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• 2000

Recently, it becomes a very important issue to consider the mechanical systems such as high-speed vehicle and railway train moving on a flexible beam structure. Using general approach proposed in the first part of this paper, it tis possible to predict planar motion of constrained mechanical system and elastic structure with various kinds of foundation supporting condition. Combined differential-algebraic equations of motion derived from both multibody dynamics theory and Finite Element Method can be analyzed numerically using generalized coordinate partitioning algorithm. To verify the validity of this approach, results from simply supported elastic beam subjected to a moving load are compared with exact solution from a reference. Finally, parameter study is conducted for a moving vehicle model on a simply supported 3-span bridge.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 추계학술대회논문집
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• pp.306-309
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• 2005

This parer describes the tracking control simulation of 6-DOF shaking table with a bell crank structure, which converts the direction of reciprocating movements. For the Joint coordinate-based control which uses lengths of each actuator, the trajectory conversion process inverse kinematics is performed. Applying the Newton-Euler approach, the dynamic equation of the shaking table is derived. To cope with nonlinear problems, time-delay control(TDC) is considered, which has been noted for its exceptional robustness to parameter uncertainties and disturbance, in addition to steady-state accuracy and computational efficiency. If the nominal model is equal to the real system, joint coordinate-based control can be very efficient. However, manufacturing tolerances installation errors and link offsets contaminate the nominal values of the kinematic parameters used in the kinematic model of the shaking table. To compensate differences between the nominal model and the real system. the joint coordinate-based control using acceleration feedback in the Cartesian coordinate space is proposed.

• Coupled systems mechanics
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• 제4권4호
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• pp.337-364
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• 2015

In this paper we present methodology for parameters identification of constitutive model which is able to present behavior of a connection between two members in a structure. Such a constitutive model for frame connections can be cast in the most general form of the Timoshenko beam, which can present three failure modes. The first failure mode pertains to the bending in connection, which is defined as coupled plasticity-damage model with nonlinear softening. The second failure mode is seeking to capture the shearing of connection, which is defined as plasticity with linear hardening and nonlinear softening. The third failure mode pertains to the diffuse failure in the members; excluding it leads to linear elastic constitutive law. Theoretical formulation of this Timoshenko beam model and its finite element implementation are presented in the second section. The parameter identification procedure that will allow us to define eighteen unknown parameters is given in Section 3. The proposed methodology splits identification in three phases, with all details presented in Section 4 through three different examples. We also present the real experimental results. The conclusions are stated in the last section of the paper.

• Structural Engineering and Mechanics
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• 제76권6호
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• pp.765-779
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• 2020

This article presents a nonclassical size dependent model based on the modified couple stress theory to study and analyze the bending behavior of perforated microbeams under different loading patterns. Modified equivalent material and geometrical parameters for perforated beam are presented. The modified couple stress theory with one material length scale parameter is adopted to incorporate the microstructure effect into the governing equations of perforated beam structure. The governing equilibrium equations of the perforated Timoshenko as well as the perforated Euler Bernoulli are developed based on the potential energy minimization principle. The Poisson's effect is included in the governing equilibrium equations. Regular square perforation configuration is considered. Based on Fourier series expansion, closed forms for the bending deflection and the rotational displacements are obtained for simply supported perforated microbeams. The proposed methodology is validated and compared with the available results in the literature and an excellent agreement is detected. Numerical results demonstrated the applicability of the proposed methodology to investigate the bending behavior of regularly squared perforated beams incorporating microstructure effect under different excitation patterns. The obtained results are significantly important for the design and production of perforated microbeam structures.