• Proceedings of the KSR Conference
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• 2007.11a
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• pp.923-926
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• 2007

In this paper, the vibration of a rotating shaft with a thin rigid disk is considered. It is assumed that the shaft has uniform, circular cross-section. Based on the Timoshenko-beam theory, the transverse displacements and slops in two lateral directions, the axial displacement, and the torsional deformation are considered. A spectral element model is developed by using the variation method for the vibration analysis of the rotating shaft with a thin rigid disk, which is modeled by two shaft elements and a thin rigid disk element. The result of vibration analysis by finite element method is compared to the result of this research.

• Proceedings of the KSR Conference
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• 2008.06a
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• pp.826-830
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• 2008

In this paper, the vibration of a rotating shaft with a thin rigid disk on bearing supports is considered. It is assumed that the shaft has uniform, circular cross-section. Based on the Timoshenko-beam theory, the transverse displacements and slops in two lateral directions, the axial displacement, and the torsional deformation are considered. And flexible supports are used to analyse the bearings. A spectral element model is developed for the vibration analysis of the rotating shaft with a thin rigid disk, which is modeled by two shaft elements and a thin rigid disk element. The result of vibration analysis by finite element method is compared to the result of this research.

• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.221-238
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• 2016

One of the objectives of this study is to implement the direct calculation of the torsional moment of inertia for non-circular cross-sections, which is based on the St. Venant torsion formulation and the finite element method. Recently the proposed method provides a unique calculation of the torsional rigidity of simply and multiply connected cross-sections. Next, free vibration analyses of cylindrical and non-cylindrical helices with non-circular cross-sections are solved by a curved two-nodded mixed finite element based on the Timoshenko beam theory. Some thin-thick closed or open sections are handled and the natural frequencies of cylindrical and non-cylindrical helices are compared with the literature and the commercial finite element program SAP2000.

• Structural Engineering and Mechanics
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• v.51 no.1
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• pp.111-130
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• 2014

The aim of this study is to investigate the effects of the beam aspect ratio(L/h), hole diameter, hole location and stacking layer sequence ($[0/45/-45/90]_s$, $[45/0/-45/90]_s$ and $[90/45/-45/0]_s$) on natural frequencies of glass/epoxy perforated beams under room and high (40, 60, 80, and $100^{\circ}C$) temperatures for the common clamped-free boundary conditions (cantilever beam). The first three out of plane bending free vibration of symmetric laminated beams is studied by Timoshenko's first order shear deformation theory. For the numerical analyses, ANSYS 13.0 software package is utilized. The results show that the hole diameter, stacking layer sequence and hole location have important effect especially on the second and third mode natural frequency values for the short beams and the high temperatures affects the natural frequency values significantly. The results are presented in tabular and graphical form.

• Structural Engineering and Mechanics
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• v.56 no.6
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• pp.1003-1020
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• 2015

In this study, free vibration analysis of an edge cracked multilayered symmetric sandwich beams made of functionally graded materials are investigated. Modelling of the cracked structure is based on the linear elastic fracture mechanics theory. Material properties of the functionally graded beams change in the thickness direction according to the power and exponential laws. To represent functionally graded symmetric sandwich beams more realistic, fifty layered beam is considered. Composition of each layer is different although each layer is isotropic and homogeneous. The considered problem is carried out within the Timoshenko first order shear deformation beam theory by using finite element method. A MATLAB code developed to calculate natural frequencies for clamped and simply supported conditions. The obtained results are compared with published studies and excellent agreement is observed. In the study, the effects of crack location, depth of the crack, power law index and slenderness ratio on the natural frequencies are investigated.

• Structural Engineering and Mechanics
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• v.44 no.3
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• pp.339-361
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• 2012

Large amplitude free vibration and thermal post-buckling of shear flexible Functionally Graded Material (FGM) beams is studied using finite element formulation based on first order Timoshenko beam theory. Classical boundary conditions are considered. The ends are assumed to be axially immovable. The von-Karman type strain-displacement relations are used to account for geometric non-linearity. For all the boundary conditions considered, hardening type of non-linearity is observed. For large amplitude vibration of FGM beams, a comprehensive study has been carried out with various lengths to height ratios, maximum lateral amplitude to radius of gyration ratios, volume fraction exponents and boundary conditions. It is observed that, for FGM beams, the non-linear frequencies are dependent on the sign of the vibration amplitudes. For thermal post-buckling of FGM beams, the effect of shear flexibility on the structural response is discussed in detail for different volume fraction exponents, length to height ratios and boundary conditions. The effect of shear flexibility is observed to be predominant for clamped beam as compared to simply supported beam.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.2
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• pp.151-158
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• 2005

This research analyzes eigenvalue analysis of stiffened plates on the Pasternak foundations using the finite clement method. For analyzing the stiffened plates, both the Mindlin plate theory and Timoshenko beam-column theory were applied. In application of the finite element method, 8-nodes serendipity clement system and 3-nodes finite element system were used for plate and beam elements, respectively. Elastic foundations were modeled as the Pasternak foundations in which the continuity effect of foundations is considered. In order to verify the theory of this study, solutions obtained by this analysis were compared with the classical solutions in reference, experimental solutions and solutions obtained by SAP 2000. The natural frequency of stiffened plates on Pasternak foundations were determined according to changes or foundation parameters and dimensions of stiffener.

• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.625-644
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• 2015

In this paper, a two-layer partial interaction composite beams model considering the higher order shear deformation of sub-elements is built. Then, the governing differential equations and boundary conditions for static analysis of linear elastic higher order composite beams are formulated by means of principle of minimum potential energy. Subsequently, analytical solutions for cantilever composite beams subjected to uniform load are presented by Laplace transform technique. As a comparison, FEM for this problem is also developed, and the results of the proposed FE program are in good agreement with the analytical ones which demonstrates the reliability of the presented exact and finite element methods. Finally, parametric studies are performed to investigate the influences of parameters including rigidity of shear connectors, ratio of shear modulus and slenderness ratio, on deflections of cantilever composite beams, internal forces and stresses. It is revealed that the interfacial slip has a major effect on the deflection, the distribution of internal forces and the stresses.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.794-798
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• 2004

This paper is analysis of stiffened opening thick plate on foundation. This paper has the object of investigating natural frequencies of opening thick plates on Pasternak foundation by means of finite element method and providing Kinematic design data for mat of building structures. In this paper, vibration analysis of rectangular opening thick plate is done by use of Serendipity finite element with 8 nodes by considering shearing strain of plate. And vibration analysis of stiffener is done by used of Timoshenko beam-column element wit 3 nodes. It is shown that natural frequencies depend on not only Winkler foundation parameter but also shear foundation parameter, opening position, opening size, stiffener size.

• Smart Structures and Systems
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• v.13 no.4
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• pp.659-683
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• 2014

The static analysis of structures with arbitrary cross-section geometry and material lamination via a refined one-dimensional (1D) approach is presented in this paper. Higher-order 1D models with a variable order of expansion for the displacement field are developed on the basis of Carrera Unified Formulation (CUF). Classical Euler-Bernoulli and Timoshenko beam theories are obtained as particular cases of the first-order model. Numerical results of displacement, strain and stress are provided by using the finite element method (FEM) along the longitudinal direction for different configurations in excellent agreement with three-dimensional (3D) finite element solutions. In particular, a layered thin-walled cylinder is considered as first assessment with a laminated conventional cross-section. An atherosclerotic plaque is introduced as a typical structure with arbitrary cross-section geometry and studied for both the homogeneous and nonhomogeneous material cases through the 1D variable kinematic models. The analyses highlight limitations of classical beam theories and the importance of higher-order terms in accurately detecting in-plane cross-section deformation without introducing additional numerical problems. Comparisons with 3D finite element solutions prove that 1D CUF provides remarkable three-dimensional accuracy in the analysis of even short and nonhomogeneous structures with arbitrary geometry through a significant reduction in computational cost.