• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.7
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• pp.265-274
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• 2018

The increasing use of curved beams in buildings, vehicles, ships, and aircraft has prompted studies directed toward the development of an accurate method for analyzing the dynamic behavior of such structures. The stability behavior of elastic curved beams has been the subject of a large number of investigations. Solutions of the relevant differential equations have been obtained traditionally using standard finite difference or finite element methods. These techniques require a great deal of computer time as the number of discrete nodes becomes relatively large under the conditions of complex geometry and loading. One of the efficient procedures for the solution of partial differential equations is the method of differential quadrature. The differential quadrature method (DQM) has been applied to a large number of cases to overcome the difficulties of the complex algorithms of programming for the computer, as well as the excessive use of storage due to the conditions of complex geometry and loading. The in-plane buckling of curved beams considering the extensibility of the arch axis was analyzed under uniformly distributed radial loads using the DQM. The critical loads were calculated for the member with various parameter ratios, boundary conditions, and opening angles. The results were compared with the precise results by other methods for cases, in which they were available. The DQM, using only a limited number of grid points, provided results that agreed very well (less than 0.3%) with the exact ones. New results according to diverse variations were obtained, showing the important roles in the buckling behavior of curved beams, and can be used in comparisons with other numerical solutions or with experimental test data.

• 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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.3
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• pp.321-328
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• 2000

An improved formulation of thin-wailed curved beams with variable curvatures based on displacement field considering the second order terms of finite semitangential rotations is presented. From linearized virtual work principle by Vlasov's assumptions, the total potential energy is derived and all displacement parameters and the warping functions are defined at cendtroid axis. In developing the thin-walled curved beam element having eight degrees of freedom per a node, the cubic Hermitian polynomials are used as shape functions. In order to verify the accuracy and practical usefulness of this study, free vibrations and buckling analyses of parabolic and elliptic arche shapes with mono-symmetric sections are carried out and compared with the results analyzed by ABAQUS' shell element.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.7
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• pp.2858-2864
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• 2012

The differential quadrature method (DQM) is applied to computation of the eigenvalues of in-plane buckling of the curved beams. Critical moments and loads are calculated for the beam subjected to equal and opposite bending moments and uniformly distributed radial loads with various end conditions and opening angles. Results are compared with existing exact solutions where available. The DQM gives good accuracy even when only a limited number of grid points is used. More results are given for two sets of boundary conditions not considered by previous investigators for in-plane buckling: clamped-clamped and simply supported-clamped ends.

• Journal of Korean Society of Steel Construction
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• v.13 no.6
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• pp.651-659
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• 2001

The main purpose of this paper is to present an analytical method for free vibration of stepped horizontally curved members on two-parameter elastic foundation. The ordinary differential equations governing the free vibration of such beams are derived as non-dimensional forms including the effects of rotatory inertia and shear deformation. The governing equations are solved numerically for the circular, parabolic, sinusoidal and elliptic curved beams with hinged-hinged, hinged-clamped and clamped-clamped end constraints. As the numerical results, the lowest four natural frequency parameters are presented as the functions of various non-dimensional system parameters. Also the typical mode shapes are presented.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.4
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• pp.417-425
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• 2007

The differential quadrature method(DQM) is applied to computation of eigenvalues of the equations of motion governing the free out-of-plane vibration for circular curved beams including the effects of rotatory inertia and transverse shearing deformation. Fundamental frequencies are calculated for the members with clamped-clamped end conditions and various opening angles. The results are compared with exact solutions or numerical solutions by other methods for cases in which they are available. The DQM provides good accuracy even when only a limited number of grid points is used.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.7 no.5
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• pp.793-800
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• 2006

DQM(differential quadrature method) is applied to computation of eigenvalues of the equations of motion governing the free in-plane vibration fur circular curved beams including both rotatory inertia and shear deformation. Fundamental frequencies are calculated for the members with clamped-clamped end conditions and various opening angles. The results are compared with numerical solutions by other methods for cases in which they are available. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.

• Coupled systems mechanics
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• v.5 no.3
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• pp.255-267
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• 2016

To investigate the surface effects on vibration of embedded circular curved nanosize beams, nonlocal elasticity model is used in combination with surface properties including surface elasticity, surface tension and surface density for modeling the nano scale effect. The governing equations are determined via the energy method. Analytically Navier method is utilized to solve the governing equations for simply supported at both ends. Solving these equations enables us to estimate the natural frequency for circular curved nanobeam including Winkler and Pasternak elastic foundations. The results determined are verified by comparing the results by available ones in literature. The effects of various parameters such as nonlocal parameter, surface properties, Winkler and Pasternak elastic foundations and opening angle of circular curved nanobeam on the natural frequency are successfully studied. The results reveal that the natural frequency of circular curved nanobeam is significantly influenced by these effects.

• Journal of Korean Association for Spatial Structures
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• v.7 no.1 s.23
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• pp.55-62
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• 2007

The Paper presents three methods for calculating the natural frequencies of cantilevered curved Beams. A summary is given of the development of two techniques: theoretic value and the result of the experiment. Theoretic value of curved beam vibration analysis are derived from complementary variational principles assuming as unknown stress-displacement result fields. In order to perform free vibration analysis of curved beam, Aluminum-made cantilevered curved beam is used in experiment. Experimental input and output signals are derived from the impact hammer and the one accelemeter are amplificated by an amplifier. The validity of the modal analysis method

• Structural Engineering and Mechanics
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• v.64 no.1
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• pp.121-133
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• 2017

This paper proposes an analytical solution method for free vibration of curved functionally graded (FG) nonlocal beam supposed to different thermal loadings, by considering porosity distribution via nonlocal elasticity theory for the first time. Material properties of curved FG beam are assumed to be temperature-dependent. Thermo-mechanical properties of porous FG curved beam are supposed to vary through the thickness direction of beam and are assumed to be temperature-dependent. Since variation of pores along the thickness direction influences the mechanical and physical properties, porosity play a key role in the mechanical response of curved FG structures. The rule of power-law is modified to consider influence of porosity according to even distribution. The governing equations of curved FG porous nanobeam under temperature field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is used to achieve the natural frequencies of porous FG curved nanobeam supposed to thermal loadings with simply supported boundary condition. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality, porosity volume fractions, type of temperature rising, gradient index, opening angle and aspect ratio of curved FG porous nanobeam on the natural frequency are successfully discussed. It is concluded that these parameters play key roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.