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

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1998.04a
• /
• pp.359-364
• /
• 1998

The effects of boundary conditions on natural frequencies for the ring stiffened composite cylindrical shells are investigated by theoretical method. The Love's thin shell theory and the discrete stiffener theory with beam functions in the Ritz procedure are used to derive the frequency equation. Five different boundary conditions such as clamped-clamped, simply supported-simply supported, free-free, clamped-free, clamped-simply supported are considered in this study. Also, the experimental investigation is presented to validate the theoretical results.

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

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.21 no.4
• /
• pp.384-391
• /
• 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 of Mechanical Engineers A
• /
• v.29 no.5 s.236
• /
• pp.716-725
• /
• 2005

The method of substructure synthesis o. component mode synthesis(CMS) provides an effective means of dynamic analysis of very large and/or complex structures. In this study, residual dynamic flexibility attachment modes in hybrid component mode synthesis are considered for the purpose of exactly compensating the effect of higher order truncated modes. Following this way, the analysis accuracy of the synthesized structure can be improved effectively with less computational effort. In order to show the accuracy and effectiveness of the proposed hybrid component mode synthesis(HCMS), numerical experiments were carried out for the models of a clamped-clamped beam. The results verified the effectiveness of the proposed method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.05a
• /
• pp.423-428
• /
• 2002

A numerical method is presented to obtain natural frequencies and mode shapes of tapered beams with static deflections due to self-weight. The differential equation governing the free vibrations of beam taken into account the static deflection due to self-weight is derived and solved numerically. The hinged-hinged, clamped-clamped and clamped-hinged and clamped-free end constraints are applied in the numerical examples. As the numerical results, the lowest three natural frequencies versus distributed slenderness ratio and section ratio are reported in figures. And for the comparison purpose, the typical mode shapes with the effects of static deflection are presented in figures.

• Journal of the Korean Society for Precision Engineering
• /
• v.27 no.6
• /
• pp.47-54
• /
• 2010

In this paper, the purpose is to study a method for detection of crack in clamped-clamped beams using the vibration characteristics. The natural frequency of beam is obtained by FEM and experiment. The governing differential equations of a Timoshenko beam are derived via Hamilton's principle. The two coupled governing differential equations are reduced to one fourth order ordinary differential equation in terms of the flexural displacement. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The differences between the actual and predicted crack positions and sizes are less than 9.8% and 28%, respectively.

• Journal of KSNVE
• /
• v.8 no.3
• /
• pp.524-532
• /
• 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
• /
• v.21 no.6
• /
• pp.570-579
• /
• 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.

• International Journal of Precision Engineering and Manufacturing
• /
• v.5 no.2
• /
• pp.53-59
• /
• 2004

The pseudospectral method is applied to the analysis of out-of$.$plane free vibration of circularly curved Timoshenko beams. The analysis is based on the Chebyshev polynomials and the basis functions are chosen to satisfy the boundary conditions. Natural frequencies are calculated for curved beams of circular cross sections under hinged-hinged, clamped-clamped and hinged-clamped end conditions. The present method gives good accuracy with only a limited number of collocation points.