• Smart Structures and Systems
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• v.13 no.4
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• pp.659-683
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• 2014

The static analysis of structures with arbitrary cross-section geometry and material lamination via a refined one-dimensional (1D) approach is presented in this paper. Higher-order 1D models with a variable order of expansion for the displacement field are developed on the basis of Carrera Unified Formulation (CUF). Classical Euler-Bernoulli and Timoshenko beam theories are obtained as particular cases of the first-order model. Numerical results of displacement, strain and stress are provided by using the finite element method (FEM) along the longitudinal direction for different configurations in excellent agreement with three-dimensional (3D) finite element solutions. In particular, a layered thin-walled cylinder is considered as first assessment with a laminated conventional cross-section. An atherosclerotic plaque is introduced as a typical structure with arbitrary cross-section geometry and studied for both the homogeneous and nonhomogeneous material cases through the 1D variable kinematic models. The analyses highlight limitations of classical beam theories and the importance of higher-order terms in accurately detecting in-plane cross-section deformation without introducing additional numerical problems. Comparisons with 3D finite element solutions prove that 1D CUF provides remarkable three-dimensional accuracy in the analysis of even short and nonhomogeneous structures with arbitrary geometry through a significant reduction in computational cost.

• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.145-153
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• 2017

In this article, a novel simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) beams is proposed. The beauty of this theory relies on its 2-unknowns displacement field as the Euler-Bernoulli beam theory, which is even less than the Timoshenko beam theory. A shear correction factor is, therefore, not needed. Equations of motion are obtained via Hamilton's principle. Analytical solutions for the bending and free vibration analysis are given for simply supported beams. Efficacy of the proposed model is shown through illustrative examples for bending and dynamic of FG beams. The numerical results obtained are compared with those of other higher-order shear deformation beam theory results. The results obtained are found to be accurate.

• Smart Structures and Systems
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• v.26 no.2
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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.

• Smart Structures and Systems
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• v.21 no.5
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• pp.677-686
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• 2018

The structural responses are often used to identify the structural local damages. However, it is usually difficult to gain the responses of the track, as the sensors cannot be installed on the track directly. The vehicles running on a track excite track vibration and can also serve as response receivers because the vehicle dynamic response contains the vibration information of the track. A damage identification method using the vehicle responses and sensitivity analysis is proposed for the vehicle-track coupling system in this paper. Different from most damage identification methods of vehicle-track coupling system, which require the structural responses, only the vehicle responses are required in the proposed method. The local damages are identified by a sensitivity-based model updating process. In the vehicle-track coupling system, the track is modeled as a discrete point supported Euler-Bernoulli beam, and two vehicle models are proposed to investigate the accuracy and efficiency of damage identification. The measured track irregularity is considered in the calculation of vehicle dynamic responses. The measurement noises are also considered to study their effects to the damage identification results. The identified results demonstrate that the proposed method is capable to identify the local damages of the track accurately in different noise levels with only the vehicle responses.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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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.

• International Journal of Precision Engineering and Manufacturing
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• v.5 no.4
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• pp.50-60
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• 2004

A very flexible beam can be used to model various types of continuous mechanical parts such as cables and wires. In this paper, the dynamic properties of a very flexible beam, included in a multibody system, are analyzed using absolute nodal coordinates formulation, which is based on finite element procedures, and the general continuum mechanics theory to represent the elastic forces. In order to consider the dynamic interaction between a continuous large deformable beam and a rigid multibody system, a combined system equations of motion is derived by adopting absolute nodal coordinates and rigid body coordinates. Using the derived system equation, a computation method for the dynamic stress during flexible multibody simulation is presented based on Euler-Bernoulli beam theory, and its reliability is verified by a commercial program NASTRAN. This method is significant in that the structural and multibody dynamics models can be unified into one numerical system. In addition, to analyze a multibody system including a very flexible beam, formulations for the sliding joint between a very deformable beam and a rigid body are derived using a non-generalized coordinate, which has no inertia or forces associated with it. In particular, a very flexible catenary cable on which a multibody system moves along its length is presented as a numerical example.

• Journal of KSNVE
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• v.5 no.2
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• pp.169-181
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• 1995

A theoretical model has been studied to describe the sound radiation analysis for structural vibration noise control of tire under the action of random moving line forces. When a tire is analyzed, it has been modeled as a curved beam with distributed springs and dash-pots which represent the radial, tangential stiffness and damping of tire, respectively. The reaction due to fluid loading on the vibratory response of the curved beam is taken into account. The curved beam is assumed to occupy the plane y = 0 and to be axially infinite. The material of curved beam and elastic foundation are assumed to be lossless, and governed by the law of Bernoulli-Euler beam theory. The expression for sound power is integrated numerically and its results examined as a function of Mach number(M), wavenumber ratio(.gamma.) and stiffness factor(.PSI.). The experimental investigation for structural vibration noise of tire under the action of random moving line forces has been made. Based on the STSF(Spatial Transformation of Sound Field) techniques, the sound power and sound radiation are measured. The experimental results show that operating condition, material properties and design factors of the tire have a great effect on the sound power and sound radiation characteristics.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.11
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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.

• Steel and Composite Structures
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• v.24 no.6
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• pp.727-740
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• 2017

The present paper studies the stability analysis of the continuously graded CNT-Reinforced Composite (CNTRC) panel stiffened by rings and stringers. The Stiffened Panel (SP) subjected to axial and lateral loads is reinforced by agglomerated CNTs smoothly graded through the thickness. A two-parameter Eshelby-Mori-Tanaka (EMT) model is adopted to derive the effective material moduli of the CNTRC. The stability equations of the CNRTC SP are obtained by means of the adjacent equilibrium criterion. Notwithstanding most available literature in which the stiffener effects were smeared out over the respective stiffener spacing, in the present work, the stiffeners are modeled as Euler-Bernoulli beams. The Generalized Differential Quadrature Method (GDQM) is employed to discretize the stability equations. A numerical study is performed to investigate the influences of different types of parameters involved on the critical buckling of the SP reinforced by agglomerated CNTs. The results achieved reveal that continuously distributing of CNTs adjacent to the inner and outer panel's surface results in improving the stiffness of the SP and, as a consequence, inclining the critical buckling load. Furthermore, it has been concluded that the decline rate of buckling load intensity factor owing to the increase of the panel angle is significantly more sensible for the smaller values of panel angle.

• Advances in nano research
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• v.4 no.1
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• pp.51-64
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• 2016

This paper investigates the effects of thermal load and shear force on the buckling of nanobeams. Higher-order shear deformation beam theories are implemented and their predictions of the critical buckling load and post-buckled configurations are compared to those of Euler-Bernoulli and Timoshenko beam theories. The nonlocal Eringen elasticity model is adopted to account a size-dependence at the nano-scale. Analytical closed form solutions for critical buckling loads and post-buckling configurations are derived for proposed beam theories. This would be helpful for those who work in the mechanical analysis of nanobeams especially experimentalists working in the field. Results show that thermal load has a more significant impact on the buckling behavior of simply-supported beams (S-S) than it has on clamped-clamped (C-C) beams. However, the nonlocal effect has more impact on C-C beams that it does on S-S beams. Moreover, it was found that the predictions obtained from Timoshenko beam theory are identical to those obtained using all higher-order shear deformation theories, suggesting that Timoshenko beam theory is sufficient to analyze buckling in nanobeams.