• Structural Engineering and Mechanics
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• v.48 no.4
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• pp.519-545
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• 2013

An outline of the Timoshenko beam theory is presented. Two differential equations of motion in terms of deflection and rotation are comprised into single equation with deflection and analytical solutions of natural vibrations for different boundary conditions are given. Double frequency phenomenon for simply supported beam is investigated. The Timoshenko beam theory is modified by decomposition of total deflection into pure bending deflection and shear deflection, and total rotation into bending rotation and axial shear angle. The governing equations are condensed into two independent equations of motion, one for flexural and another for axial shear vibrations. Flexural vibrations of a simply supported, clamped and free beam are analysed by both theories and the same natural frequencies are obtained. That fact is proved in an analytical way. Axial shear vibrations are analogous to stretching vibrations on an axial elastic support, resulting in an additional response spectrum, as a novelty. Relationship between parameters in beam response functions of all type of vibrations is analysed.

• Journal of Mechanical Science and Technology
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• v.20 no.9
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• pp.1371-1381
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• 2006

This paper deals with the active vibration control of a simply-supported beam traversed by a moving mass using fuzzy control. Governing equations for dynamic responses of a beam under a moving mass are derived by Galerkin's mode summation method, and the effect of forces (gravity force, Coliolis force, inertia force caused by the slope of the beam, transverse inertia force of the beam) due to the moving mass on the dynamic response of a beam is discussed. For the active control of dynamic deflection and vibration of a beam under the moving mass, the controller based on fuzzy logic is used and the experiments are conducted by VCM (voice coil motor) actuator to suppress the vibration of a beam. Through the numerical and experimental studies, the following conclusions were obtained. With increasing mass ratio y at a fixed velocity of the moving mass under the critical velocity, the position of moving mass at the maximum dynamic deflection moves to the right end of the beam. With increasing velocity of the moving mass at a fixed mass ratio ${\gamma}$, the position of moving mass at the maximum dynamic deflection moves to the right end of the beam too. The numerical predictions of dynamic deflection of the beam have a good agreement with the experimental results. With the fuzzy control, more than 50% reductions of dynamic deflection and residual vibration of the tested beam under the moving mass are obtained.

• Computers and Concrete
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• v.5 no.1
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• pp.37-60
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• 2008

Structural health monitoring of existing infrastructure is currently an important field of research, where elaborate experimental programs and advanced analytical methods are used in identifying the current state of health of critical and important structures. The paper outlines two methods of system identification of beam-like reinforced concrete structures representing bridges, through static measurements, in a distributed damage scenario. The first one is similar to the stiffness method, re-cast and the second one to flexibility method. A least square error (LSE) based solution method is used for the estimation of flexural rigidities and damages of simply supported, cantilever and propped cantilever beam from the measured deformation values. The performance of both methods in the presence of measurement errors is demonstrated. An experiment on an un-symmetrically damaged simply supported reinforced concrete beam is used to validate the developed method. A method for damage prognosis is demonstrated using a generalized, indeterminate, propped cantilever beam.

• Journal of Mechanical Science and Technology
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• v.20 no.9
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• pp.1382-1389
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• 2006

Dynamic responses of a simply supported beam with a translational spring carrying a moving mass are studied. Governing equations of motion including all the inertia effects of a moving mass are derived by employing the Galerkin's mode summation method, and solved by using the Runge-Kutta integral method. Numerical solutions for dynamic responses of a beam are obtained for various cases by changing parameters of the spring stiffness, the spring position, the mass ratio and the velocity ratio of a moving mass. Some experiments are conducted to verify the numerical results obtained. Experimental results for the dynamic responses of the test beam have a good agreement with numerical ones.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.4
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• pp.64-71
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• 2002

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

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.799-804
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• 2004

In this paper a dynamic behavior of simply supported cracked simply supported beam with the moving masses is presented. Based on the Timoshenko beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics the of. And the crack is assumed to be in th first mode of fracture. As the depth of the crack and velocity of fluid are increased the mid-span deflection of the pipe conveying fluid with the moving mass is increased. As depth of the crack is increased, the effect that the velocity of the fluid on the mid-span deflection appeals more greatly.

• Structural Engineering and Mechanics
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• v.34 no.5
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• pp.549-561
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• 2010

In this paper, free vibration analyses of a parallel placed twin pipe system simulated by simply supported-simply supported and fixed-fixed Euler-Bernoulli beams resting on Winkler elastic soil are presented. The motion of the system is described by a homogenous set of two partial differential equations, which is solved by a simulation method called the Differential Transform Method (DTM). Free vibrations of an elastically connected twin pipe system are realized by synchronous and asynchronous deflections. The results of the presented theoretical analyses for simply supported Euler-Bernoulli beams are compared with existing ones in open literature and very good agreement is demonstrated.

• Steel and Composite Structures
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• v.31 no.6
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• pp.591-600
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• 2019

Based on the energy-variational principle, a coupling vibration analysis model of high-speed railway simply supported beam bridge-track structure system (HSRBTS) was established by considering the effect of shear deformation. The vibration differential equation and natural boundary conditions of HSRBTS were derived by considering the interlayer slip effect. Then, an analytic calculation method for the natural vibration frequency of this system was obtained. By taking two simply supported beam bridges of high-speed railway of 24 m and 32 m in span as examples, ANSYS and MIDAS finite-element numerical calculation methods were compared with the analytic method established in this paper. The calculation results show that two of them agree well with each other, validating the analytic method reported in this paper. The analytic method established in this study was used to evaluate the natural vibration characteristics of HSRBTS under different interlayer stiffness and length of rails at different subgrade sections. The results show that the vertical interlayer compressive stiffness had a great influence on the high-order natural vibration frequency of HSRBTS, and the effect of longitudinal interlayer slip stiffness on the natural vibration frequency of HSRBTS could be ignored. Under different vertical interlayer stiffness conditions, the subgrade section of HSRBTS has a critical rail length, and the critical length of rail at subgrade section decreases with the increase in vertical interlayer compressive stiffness.

• Structural Engineering and Mechanics
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• v.37 no.4
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• pp.415-425
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• 2011

In this study, the homotopy perturbation method (HPM) is applied to free vibration analysis of beam on elastic foundation. This numerical method is applied on three different axially loaded cases, namely: 1) one end fixed, the other end simply supported; 2) both ends fixed and 3) both ends simply supported cases. Analytical solutions and frequency factors are evaluated for different ratios of axial load N acting on the beam to Euler buckling load, $N_r$. The application of HPM for the particular problem in this study gives results which are in excellent agreement with both analytical solutions and the variational iteration method (VIM) solutions for all the cases considered in this study and the differential transform method (DTM) results available in the literature for the fixed-pinned case.

• Steel and Composite Structures
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• v.19 no.4
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• pp.897-916
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• 2015

A procedure for critical buckling moment of a tapered beam is proposed with the application of potential energy calculations using Ritz method. Respective solution allows to obtain critical moments initiating lateral buckling of the simply supported, modestly tapered steel I-beams. In particular, lateral-torsional buckling of beams with simultaneously tapered flanges and the web are considered. Detailed, numerical, parametric analyses are carried out. Typical engineering, uniformly distributed design loads are considered for three cases of the load, applied to the top flange, shear centre, as well as to the bottom flange. In addition simply supported beam under gradient moments is investigated. The parametric analysis of simultaneously tapered beam flanges and the web, demonstrates that tapering of flanges influences much more the critical moments than tapering of the web.