• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.677-697
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• 2010

This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.

• International Journal of Precision Engineering and Manufacturing
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• v.7 no.1
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• pp.24-29
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• 2006

In this paper, the effect of open crack on the dynamic behavior of simply supported Timoshenko beam with a moving mass was studied. The influences of the depth and the position of the crack on the beam were studied on the dynamic behavior of the simply supported beam system by numerical methods. The equation of motion is derived by using Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is modeled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces on the crack section and is derived by applying fundamental fracture mechanics theory. As the depth of the crack increases, the mid-span deflection of the Timoshenko beam with a moving mass is increased.

• Structural Engineering and Mechanics
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• v.25 no.6
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• pp.691-716
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• 2007

The purpose of the present work is to establish a method for predicting the location and depth of a crack in a circular cross section beam by only considering the frequencies of the cracked beam. An accurate knowledge of the material properties is not required. The crack location and size is identified by finding the point of intersection of pulsation ratio contour lines of lower vertical and horizontal modes. This process is presented and numerically validated in the case of a simply supported beam with various crack locations and sizes. If the beam has structural symmetry, the identification of crack location is performed by adding an off-center placed mass to the simply supported beam. In order to avoid worse diagnostic, it was demonstrated that a robust identification of crack size and location is possible if two tests are undertaken by adding the mass at the left and then right end of the simply supported beam. Finally, the pulsation ratio contour lines method is generalized in order to be extended to the case of rectangular cross section beams or more complex structures.

• Structural Engineering and Mechanics
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• v.52 no.4
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• pp.687-699
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• 2014

Based on the energy method considering the second order effects, the natural frequencies of externally prestressed simply supported beam and the compression softening effect of external prestress force were analyzed. It is concluded that the compression softening effect depends on the loss of external tendon eccentricity. As the number of deviators increases from zero to a large number, the compression softening effect of external prestress force decreases from the effect of axial compression to almost zero, which is consistent with the conclusion mathematically rigorously proven. The frequencies calculated by the energy method conform well to the frequencies by FEM which can simulate the frictionless slide between the external tendon and deviator, the accuracy of the energy method is validated. The calculation results show that the compression softening effect of external prestress force is negligible for the beam with 2 or more deviators due to slight loss of external tendon eccentricity. As the eccentricity and area of tendon increase, the first natural frequency of the simply supported beams noticeably increases, however the effect of the external tendon on other frequencies is negligible.

• Journal of KSNVE
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• v.8 no.4
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• pp.616-622
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• 1998

An analytical method has been developed to estimate the dynamic contact force between wheel and rail when trains are running on rail with vertical irregularities. In this method, the effect of Hertzian deformation at the contact point is considered as a linearized spring and the wheel is considered as an sprung mass. The rail is modelled as a discretely-supported Timoshenko beam, and the periodic structure theory was adopted to obtain the driving-point receptance. As an example, the dynamic contact force for a typical wheel/rail system was analysed by the method developed in this research and the dynamic characteristics of the system was also discussed. It is revealed that discretely-supported Timoshenko beam model should be used instead of the previously used continuously-supported model or discretelysupported Euler beam model, for the frequency range above several hundred hertz.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.7
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• pp.555-561
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• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported Euler-Bernoulli beams with the moving masses. The influences of the velocities of moving masses, the distance between the moving masses and a crack have been studied on the dynamic behavior of a simply supported beam system by numerical method. The Presence of crack results In large deflection of beam. 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 theory. Totally, as the velocity of the moving masses and the distance between the moving masses are increased, the mid-span deflection of simply supported beam with the crack is decreased.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.1
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• pp.27-38
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• 2016

The purpose of this study is to investigate the influence of moving mass on the vibration characteristics and the dynamic response of the simply supported beam. The three types of the moving mass(moving load, unsprung mass, and sprung mass) are applied to the vehicle-bridge interaction analysis. The numerical analyses are then conducted to evaluate the effect of the mass, spring and damper properties of the moving mass on natural frequencies and dynamic responses of the simply supported beam. Particularly, in the case of the sprung mass, variations of the natural frequency of simply supported beam are explored depending on the position of the moving mass and the frequency ratio of the moving mass and the beam. Finally the parametric studies on the resonance phenomena are performed with changing mass, spring and damper parameters through the dynamic interaction analyses.

• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.259-270
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• 2017

The stochastic vibration response of the sandwich beam with the nonlinear adjustable visco-elastomer core and supported mass under stochastic support motion excitations is studied. The nonlinear dynamic properties of the visco-elastomer core are considered. The nonlinear partial differential equations for the horizontal and vertical coupling motions of the sandwich beam are derived. An analytical solution method for the stochastic vibration response of the nonlinear sandwich beam is developed. The nonlinear partial differential equations are converted into the nonlinear ordinary differential equations representing the nonlinear stochastic multi-degree-of-freedom system by using the Galerkin method. The nonlinear stochastic system is converted further into the equivalent quasi-linear system by using the statistic linearization method. The frequency-response function, response spectral density and mean square response expressions of the nonlinear sandwich beam are obtained. Numerical results are given to illustrate new stochastic vibration response characteristics and response reduction capability of the sandwich beam with the nonlinear visco-elastomer core and supported mass under stochastic support motion excitations. The influences of geometric and physical parameters on the stochastic response of the nonlinear sandwich beam are discussed, and the numerical results of the nonlinear sandwich beam are compared with those of the sandwich beam with linear visco-elastomer core.

• Advances in aircraft and spacecraft science
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• v.4 no.5
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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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.534-537
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• 2004

In this paper, a dynamic behavior of spring supported cantilever beam with a crack and a moving mass is presented. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by using the Lagrange's eauation. 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 theory. And the crack is assumed to be in the first mode of fracture. As the depth of the crack is increased the tip displacement of the cantilever beam is increased.