Vibration Analysis of Circular Arch Element Using Curvature

Saffari, Hamed; Tabatabaei, R.; Mansouri, S. H.

doi:10.1155/2008/149393

Cited by 8 publications

(5 citation statements)

References 15 publications

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“…The convergence and efficiency of the curved beam elements is verified by numerical examples. It is shown that for the approximate for- 15 The angular velocity of the rigid hub mulation using straight beam elements, two times the number of elements is needed to obtain accurate results compared with the present formulation using curved beam elements. Newmark and Newton-Raphson iteration methods are used for solving the differential equations of the rigidflexible coupling system.…”

Section: Discussionmentioning

confidence: 88%

“…By adding the shear and torsion degree of freedom, Wu et al [14] extended this method to solve the out-of-plane problem. Saffari et al [15] and Yang et al [16] presented the three-node beam element based on the curvature by the transformation matrix between nodal curvatures and nodal displacements, the final finite element equilibrium equation were written in terms of the displacement components of the two edge nodes. Leung et al [17] presented Fourier p-elements for in-plane vibration of thin and thick curved beams by introducing additional internal degrees of freedom which are sine functions to Fourier trigonometric functions to avoid membrane and shear locking and to increase the convergence and stability of the curved element.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Geometric nonlinear dynamic analysis of curved beams using curved beam element

Pan

Liu

2011

Acta Mech Sin

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Instead of using the previous straight beam element to approximate the curved beam, in this paper, a curvilinear coordinate is employed to describe the deformations, and a new curved beam element is proposed to model the curved beam. Based on exact nonlinear strain-displacement relation, virtual work principle is used to derive dynamic equations for a rotating curved beam, with the effects of axial extensibility, shear deformation and rotary inertia taken into account. The constant matrices are solved numerically utilizing the Gauss quadrature integration method. Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system. The present results are compared with those obtained by commercial programs to validate the present finite method. In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation, comparison of the results of the present formulation with those of the ADAMS software are made. Furthermore, the present results obtained from linear formulation are compared with those from nonlinear formulation, and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.

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Section: Discussionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Geometric nonlinear dynamic analysis of curved beams using curved beam element

Pan

Liu

2011

Acta Mech Sin

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“…The proposed method is directly applied to third mode shape, crack locations are shadowed by two false peaks induced by two inflexions of the third mode shape, as showed in Figure 4(b). As mentioned above, a linear mapping as shown in (7) was applied to solve the inflexion problem. The parameter is selected as −89 ∘ .…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…The vibration-based crack detection methods are developed to overcome these difficulties [3,4]. The fundamental idea of vibration-based crack identification is to detect the crack-induced changes in the physical properties, which will lead to detectable changes in mode properties [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Identification of Crack Location in Beam Structures Using Wavelet Transform and Fractal Dimension

Jiang

Zhang

et al. 2015

Shock and Vibration

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Identification of structural crack location has become an intensely investigated subject due to its practical importance. In this paper, a hybrid method is presented to detect crack locations using wavelet transform and fractal dimension (FD) for beam structures. Wavelet transform is employed to decompose the mode shape of the cracked beam. In many cases, small crack location cannot be identified from approximation signal and detailed signals. And FD estimation method is applied to calculate FD parameters of detailed signals. The crack locations will be detected accurately by FD singularity of the detailed signals. The effectiveness of the proposed method is validated by numerical simulations and experimental investigations for a cantilever beam. The results indicate that the proposed method is feasible and can been extended to more complex structures.

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“…Cannarozzi and Molari [16] proposed a stress-mixed element based on the improved Hellinger-Reissner function and proved that the element can be used to calculate arbitrary geometrical curved beam structures through calculation examples. Saffari et al [17] regard the curved beam structure as a combination of arch elements, each basic arch element introduces shear and axial deformation energy, and the elements are connected by a transformation matrix constructed by curvature. Kim et al [18] introduced additional node-independent degrees of freedom in the displacement interpolation function, which significantly improved the numerical accuracy of the displacement-stress hybrid element, making it more suitable for predicting higher-order modes.…”

Section: Introductionmentioning

confidence: 99%

A General Fourier Formulation for In-Plane and Out-of-Plane Vibration Analysis of Curved Beams

Nie

Zhu

et al. 2021

Shock and Vibration

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Based on the principle of energy variation, an improved Fourier series is introduced as an allowable displacement function. This paper constructs a calculation model that can study the in-plane and out-of-plane free and forced vibrations of curved beam structures under different boundary conditions. Firstly, based on the generalized shell theory, considering the shear and inertial effects of curved beam structures, as well as the coupling effects of displacement components, the kinetic energy and strain potential energy of the curved beam are obtained. Subsequently, an artificial spring system is introduced to satisfy the constraint condition of the displacement at the boundary of the curved beam, obtain its elastic potential energy, and add it to the system energy functional. Any concentrated mass point or concentrated external load can also be added to the energy function of the entire system with a corresponding energy term. In various situations including classical boundary conditions, the accuracy and efficiency of the method in this paper are proved by comparing with the calculation results of FEM. Besides, by accurately calculating the vibration characteristics of common engineering structures like slow curvature (whirl line), the wide application prospects of this method are shown.

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Vibration Analysis of Circular Arch Element Using Curvature

Cited by 8 publications

References 15 publications

Geometric nonlinear dynamic analysis of curved beams using curved beam element

Geometric nonlinear dynamic analysis of curved beams using curved beam element

Identification of Crack Location in Beam Structures Using Wavelet Transform and Fractal Dimension

A General Fourier Formulation for In-Plane and Out-of-Plane Vibration Analysis of Curved Beams

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