• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.357-364
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• 2008

This paper deals with the free vibrations of arches with rectangular hollow section having constant area. The differential equations governing free vibrations of arches are derived in polar coordinates, in which the effect of rotatory inertia is included. Natural frequencies is computed numerically for parabolic arches with clamped-clamped, clamped-hinged and hinged-hinged ends. Comparisons of natural frequencies between this study and reference are made to validate theories and numerical methods developed herein. The lowest four natural frequency parameters are reported, with the rotatory inertia, as functions of three non-dimensional system parameters: the breadth ratio, the thickness ratio and the shape ratio

• Structural Engineering and Mechanics
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• v.72 no.2
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• pp.229-244
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• 2019

Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.

• Magazine of the Korean Society of Agricultural Engineers
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• v.42 no.1
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• pp.105-112
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• 2000

This paper deals with the free vibrations of columns immersed in fluid. The column model is based on the classical Bernoulli-euler theory which neblects the effects of rotatory inerital and shear deformation. The eccentricity and rotatory inertial of the concentrated mass at the top are taken into accuont. In the governing equation for the free vibration of column, thedensity of immersed part was midified to account for theadded fluid mass. The govering differential equations are solved numerically using the corresponding boundary conditions. The lowest four natural frequencies and corresponding mode shapes are calculated over a range of non-dimensional system parameters ; the mas density ration of fluid to column, the ratio of fluid depth to span length, the ratio of tip mass to total column mass, the dimensionless mass moment of inertia, and the eccentricity.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.3 no.4
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• pp.109-122
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• 1983

An accurate thick beam element (TB4) which includes the effects of the shear deformation and rotatory inertia has been degenerated from the three dimensional continuum by employing the Timoshenko beam assumptions. The proposed TB4 element has four nodes and two degrees of freedom at each node, totally eight degrees of freedom. The transverse deflection W and plane rotation ${\theta}$ with the cubic interpolation functions are selected as nodal variables. The element characteristics are formulated by discretizing the beam equations of motion, using the Galerkin weighted residual method, and are numerically integrated by the reduced shear integration technique, using the three-point Gauss quadrature with the various shear coefficients. Several numerical examples are analyzed to demonstrate the accuracy and the monotonic convergence behavior of the proposed TB4 beam element. The result indicates that the TB4 element shows the more excellent performance and the monotonic convergence behavior than the other existing Timoshenko beam type elements for the whole range of the beam aspect ratios, in both static and free vibration analyses.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.10
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• pp.300-309
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• 2016

Curved beams are increasingly used in buildings, vehicles, ships, and aircraft, which has resulted in considerable effort towards developing an accurate method for analyzing the dynamic behavior of such structures. The stability behavior of elastic curved beams has been the subject of many investigations. Solutions to the relevant differential equations have traditionally been obtained by the standard finite difference or finite element methods. However, these techniques require a great deal of computer time for a large number of discrete nodes with conditions of complex geometry and loading. One efficient procedure for the solution of partial differential equations is the differential quadrature method (DQM). This method has been applied to many cases to overcome the difficulties of complex algorithms and high storage requirements for complex geometry and loading conditions. Out-of-plane buckling of curved beams with rotatory inertia were analyzed using DQM under uniformly distributed radial loads. Critical loads were calculated for the member with various parameter ratios, boundary conditions, and opening angles. The results were compared with exact results from other methods for available cases. The DQM used only a limited number of grid points and shows very good agreement with the exact results (less than 0.3% error). New results according to diverse variation are also suggested, which show important roles in the buckling behavior of curved beams and can be used for comparisons with other numerical solutions or experimental test data.

• Structural Engineering and Mechanics
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• v.45 no.4
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• pp.569-594
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• 2013

The free vibration of axially functionally graded tapered arches including shear deformation and rotatory inertia are studied through solving the governing differential equation of motion. Numerical results are presented for circular, parabolic, catenary, elliptic and sinusoidal arches with hinged-hinged, hinged-clamped and clamped-clamped end restraints. In this study Differential Quadrature element of lowest order (DQEL) or Lagrangian Interpolation technique is applied to solve the problems. Three general taper types for rectangular section are considered. The lowest four natural frequencies are calculated and compared with the published results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.402.1-402
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• 2002

A linearly tapered beam immersed partially in other material is considered and is modelled as a linearly tapered Bernoulli-Euler beam fixed at the bottom with a concentrated mass at the top. Its governing equations is derived and its free vibration analysis is performed for various boundary conditions. And the rotatory inertia of the eccentric lumped tip mass is considered. (omitted)

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.429-434
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• 2002

The differential equations governing in-plane free vibrations of stepped circular arcs, including the effects of axial deformation, rotatory inertia and shear deformation, are derived and solved numerically to obtain frequencies and mode shapes. Numerical results are calculated for the clamped-clamped symmetric and unsymmetric circular arcs with thickness varying in a discontinuous fashion. The lowest four natural frequencies and mode shapes are presented over a range of non-dimensional system parameters: the subtended angle, the slenderness ratio, the section ratio and the ratio of discontinuous section.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.989-993
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• 2001

This paper deals with the free vibrations of horizontally curved beams supported by non-homogeneous elastic foundation. 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 linear elastic foundation is considered as the non-homogeneous foundation. Differential equations are solved numerically to calculate natural frequencies. In numerical examples, the parabolic curved member is considered. The parametric studies are conducted and the lowest four frequency parameters are reported in tables and figures as the non-dimensional forms.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.697-702
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• 2006

This paper deals with the free vibrations of immersed columns with soft base. The support condition of the column is represented by using a translational spring and a rotational spring. The eccentricity and rotatory inertia of the concentrated mass at the top are taken into account. In the governing equation for the free vibration of column, the density of immersed part was modified to account for the added fluid mass. The governing differential equations are solved numerically using the corresponding boundary conditions. Numerical results are presented to show the effects on the natural frequencies of non-dimensional system parameters: the mass density ratio of fluid to column, the ratio of fluid depth to span length, the ratio of tip mass to total column mass, the dimensionless mass moment of inertia, the eccentricity, the translation spring parameter, and the rotational spring parameter.