• Structural Engineering and Mechanics
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• v.14 no.5
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• pp.611-624
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• 2002

In this paper, a complete solution is presented for dynamic plastic response of a rigid, perfectly plastic hinged-free beam, of which one end is simply supported or hinged and the other end free, subjected to a transverse strike by a travelling mass at an arbitrary location along its span. The governing differential equations are expressed in non-dimensional forms and solved numerically to obtain the instantaneous deflection of the beam and the plastic dissipated energy in the beam. The dynamic behavior for a hinged-free beam is more complicated than that of a free-free beam. It transpires that the mass ratio and impact position have significant influence on the final deformation. In the aspect of energy dissipation, unlike simply supported or clamped beams for which the plastic deformation consumes almost the total input energy, a considerable portion of the input energy would be transferred as rigid-body motion of hinged-free beam, and the energy dissipated in its plastic deformation is greatly reduced.

• Structural Engineering and Mechanics
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• v.26 no.5
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• pp.483-498
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• 2007

In case of considering the shear effect, the complete solutions are obtained for dynamic plastic response of a rigid, perfectly plastic hinged-free beam, of which one end is hinged and the other end free, subjected to a transverse strike by a travelling rigid mass at an arbitrary location along its span. Special attention is paid to new deformation mechanisms due to shear sliding on both sides of the rigid mass and the plastic energy dissipation. The dimensionless numerical results demonstrate that three parameters, i.e., mass ratio, impact position of mass, as well as the non-dimensional fully plastic shear force, have significant influence on the partitioning of dissipated energy and failure mode of the hingedfree beam. The shear effect can never be negligible when the mass ratio is comparatively small and the impact location of mass is close to the hinged end.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.4
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• pp.384-391
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• 2011

This paper deals with free vibrations of the parabolic hollowed beam-columns with constant volume. The cross sections of beam-column taper are the hollowed regular polygons whose depths are varied with the parabolic functional fashion. Volumes of the objective beam-columns are always held constant regardless given geometrical conditions. Ordinary differential equation governing free vibrations of such beam-columns are derived and solved numerically for determining the natural frequencies. In the numerical examples, hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, the relationships between non-dimensional frequency parameters and various beam-column parameters such as end constraints, side number, section ratio, thickness ratio and axial load are reported in tables and figures.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.6
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• pp.570-579
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• 2011

This paper deals with free vibrations of the circular curved beams with constant volume, whose cross sectional shapes are the circular solid cross-sections. Volumes of the objective beam are always held in constant regardless shape functions of the cross-sectional radius. The shape functions are chosen as the linear, parabolic and sinusoidal ones. Ordinary differential equations governing free vibrations of such beam are derived and solved numerically for determining the natural frequencies. In numerical examples, the hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, relationships between frequency parameters and various beam parameters such as rise ratio, section ratio, elasticity ratio, volume ratio, slenderness ratio and taper type are reported in tables and figures.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.709-712
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• 2004

A study of the coupled flexural-torsional vibrations of thin-walled beams with monosymmetric cross-section is presented. The governing differential equations for free vibration of such beams are solved numerically to obtain natural frequencies and their corresponding mode shapes. The beam model is based on the Bernoulli-Euler beam theory and the effect of warping is taken into consideration. Numerical results are given for two specific examples of beams with free-free, clamped-free, hinged-hinged, clamped-hinged and clamped-clamped end constraints both including and excluding the effect of warping stiffness. The effect of warping stiffness on the natural frequencies and mode shapes is discussed and it is concluded that substantial error can be incurred if the effect is ignored.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.3
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• pp.223-233
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• 2012

This paper deals with free vibrations of the tapered Timoshenko beam with constant volume, in which both the rotatory inertia and shear deformation are included. The cross section of the tapered beam is chosen as the regular polygon cross section whose depth is varied with the parabolic function. The ordinary differential equations governing free vibrations of such beam are derived based on the Timoshenko beam theory by decomposing the displacements. Governing equations are solved for determining the natural frequencies corresponding with their mode shapes. In the numerical examples, three end constraints of the hinged-hinged, hinged-clamped and clamped-clamped ends are considered. The effects of various beam parameters on natural frequencies are extensively discussed. The mode shapes of both the deflections and stress resultants are presented, in which the composing rates due to bending rotation and shear deformation are determined.

• Journal of KSNVE
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• v.8 no.3
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• pp.524-532
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• 1998

The purpose of this paper is to investigate the free vibrations of horizontally curved beams resting on Winkler-type foundations. Based on the classical Bernoulli-Euler beam theory, the governing differential equations for circular curved beams are derived and solved numerically. Hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered in numerical examples. The free vibration frequencies calculated using the present analysis have been compared with the finite element's results computed by the software ADINA. Numerical results are presented to show the effects on the natural frequencies of curved beams of the horizontal rise to span length ratio, the foundation parameter, and the width ratio of contact area between the beam and foundation.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.1
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• pp.66-73
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• 2011

This paper deals with free vibrations of the tapered beams with the constant surface area. The surface area of the objective beams are always held constant regardless shape functions of the cross-sectional depth. The shape functions are chosen as the linear and parabolic ones. Ordinary differential equations governing free vibrations of such beams are derived and solved numerically for determining the natural frequencies. In the numerical examples, hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, the relationships between non-dimensional frequency parameters and various beam parameters such as section ratio, surface area ratio, end constraint and taper type are reported in tables and figures. Especially, section ratios of the strongest beam are calculated, under which the maximum frequencies are achieved.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.29-36
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• 2003

This paper deals with the free vibration analysis of horizontally circular mea beams with variable cross sectional width on elastic foundations. Taking into account the effects of rotatory inertia and shear deformation differential equations governing the free vibrations of such beams are derived, in which the Whlkler foundation model is considered as the elastic foundation. The variable width of beam is chosen as the linear equation. The differential equations are solved numerically to calculate natural frequencies. In numerical examples, the curved beam with the hinged-hinged, hinged-clamped, clamped-hinged and damped-clamped end constraints are considered The parametric studies are conducted and the lowest four frequency parameters are reported in figures as the non-dimensional forms.

• Steel and Composite Structures
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• v.21 no.5
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• pp.999-1016
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• 2016

This study presents free vibration of beam made of porous material. The mechanical properties of the beam is variable in the thickness direction and the beam is investigated in three situations: poro/nonlinear nonsymmetric distribution, poro/nonlinear symmetric distribution, and poro/monotonous distribution. First, the governing equations of porous beam are derived using principle of virtual work based on Euler-Bernoulli theory. Then, the effect of pores compressibility on natural frequencies of the beam is studied by considering clamped-clamped, clamped-free and hinged-hinged boundary conditions. Moreover, the results are compared with homogeneous beam with the same boundary conditions. Finally, the effects of poroelastic parameters such as pores compressibility, coefficients of porosity and mass on natural frequencies has been considered separately and simultaneously.