• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.239-246
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• 1997

The general formulation of free vibration and stability analysis of unsymmetric thin-walled space frames and beam-columns is presented. The kinetic and total potential energy is derived by applying the extended virtual work principle, introducing displacement parameters defined at the arbitrarily chosen axis and including second order terms of finite semitangential rotations. In formulating the finite element procedure, cubic Hermitian polynomials are utilized as shape functions of the two node space frame element. Mass, elastic stiffness, and geometric stiffness matrices for the unsymmetric thin-walled section are evaluated. In order to illustrate the accuracy and practical usefulness of this formulation, finite element solutions for the free vibration and stability problems of thin-walled beam-columns and space frames are presented and compared with available solutions.

• Computers and Concrete
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• v.3 no.5
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• pp.285-299
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• 2006

The free vibration of stiffened and damaged coupled shear walls is investigated using the mixed finite element method. The anisotropic damage model is adopted to describe the damage extent of the reinforced concrete shear wall element. The internal energy of a locally damaged shear wall element is derived. Polynomial shape functions established by Kwan are used to present the component of displacements vector on each point within the wall element. The principle of virtual work is employed to deduce the stiffness matrix of a damaged shear wall element. The stiffened system is reinforced by an additional stiffening beam at some level of the structure. This induces additional axial forces, and thus reduces the bending moments in the walls and the lateral deflection, and increases the natural frequencies. The effects of the damage extent and the stiffening beam on the free vibration characteristics of the structure are studied. The optimal location of the stiffening beam for increasing as far as possible the first natural frequency of vibration is presented.

• Structural Engineering and Mechanics
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• v.55 no.1
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• pp.79-92
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• 2015

In this study, free vibration analyses of symmetric laminated cantilever and simply supported damaged composite beams are investigated by using finite element method (FEM). Free vibration responses of damaged beams are examined using Euler Bernoulli beam and classical lamination theories. A computer code is developed by using MATLAB software to determine the natural frequencies of a damaged beam. The local damage zone is assumed to be on the surface lamina of the beam by broken fibers after impact. The damaged zone is modeled as a unidirectional discontinuous lamina with $0^{\circ}$ orientations in this study. Fiber volume fraction ($v_f$), fiber aspect ratio ($L_f/d_f$), damage length ($L_D$) and its location (${\lambda}/L$), fiber orientation and stacking sequence parameters effects on natural frequencies are investigated. These parameters are affected the natural frequency values significantly.

• 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.

• Steel and Composite Structures
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• v.33 no.3
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• pp.403-432
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• 2019

Axially functionally graded (AFG) beams are a new class of composite structures that have continuous variations in material and/or geometrical parameters along the axial direction. In this study, the exact analytical solutions for the free vibration of AFG and uniform beams with general elastic supports are obtained by using Euler-Bernoulli beam theory. The elastic supports are modeled with linear rotational and lateral translational springs. Moreover, the material and/or geometrical properties of the AFG beams are assumed to vary continuously and together along the length of the beam according to the power-law forms. Accordingly, the accuracy, efficiency and capability of the proposed formulations are demonstrated by comparing the responses of the numerical examples with the available solutions. In the following, the effects of the elastic end restraints and AFG parameters, namely, gradient index and gradient coefficient, on the values of the first three natural frequencies of the AFG and uniform beams are investigated comprehensively. The analytical solutions are presented in tabular and graphical forms and can be used as the benchmark solutions. Furthermore, the results presented herein can be utilized for design of inhomogeneous beams with various supporting conditions.

• Steel and Composite Structures
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• v.46 no.3
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• pp.335-344
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• 2023

This investigation presents nonlinear free vibration of a carbon nanotube reinforced composite beam based on the Von Kármán nonlinearity and the Euler-Bernoulli beam theory The material properties of the structure is considered as made of a polymeric matrix by reinforced carbon nanotubes according to different material distributions. The governing equations of the nonlinear vibration problem is delivered by using Hamilton's principle and the Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The nonlinear natural frequency and the nonlinear free response of the system is obtained with the effect of different patterns of reinforcement.

• Interaction and multiscale mechanics
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• v.5 no.4
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• pp.385-397
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• 2012

In this paper the dynamic stiffness matrix method was used for the free vibration analysis of axially moving micro beam with constant velocity. The extended Hamilton's principle was employed to derive the governing differential equation of the problem using the modified couple stress theory. The dynamic stiffness matrix of the moving micro beam was evaluated using appropriate expressions of the shear force and bending moment according to the Euler-Bernoulli beam theory. The effects of the beam size and axial velocity on the dynamic characteristic of the moving beam were investigated. The natural frequencies and critical velocity of the axially moving micro beam were also computed for two different end conditions.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.501-508
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• 2001

Free vibration analysis of multi-delaminated composite beam-columns subjected to axial compression load is performed in the present study. In order to investigate the effects of multi-delaminations on the natural frequency and elastic buckling load of multi-delaminated beam-columns, the general kinematic continuity conditions are derived from the assumption of constant slope and curvature at the multi-delamination tip. Characteristic equation of multi-delaminated beam-column is obtained by dividing the global multi-delaminated beam-columns into segments and by imposing recurrence relation from the continuity conditions on each sub-beam-column. The natural frequency and elastic buckling load of multi-delaminated beam-columns according to the incremental load of axial compression, which is limited to the maximum elastic buckling load of sound laminated beam-column, are obtained. It is found that the sizes, locations and numbers of multi-delaminations have significant effect on natural frequency and elastic buckling load, especially the latter ones.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.435-440
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• 2002

The free vibration of partially embedded piles is investigated. The pile model is based on the Bernoulli-Euler beam theory and the soil is idealized as a Winkler model for mathematical simplicity. The governing differential equation for the free vibrations of such members is solved numerically The piles with one typical end constraint (clamped/hinged/free) and the other hinged end with rotational spring are applied in numerical examples. The lowest three natural frequencies are calculated over a range of non-dimensional system parameters: the rotational spring parameter, the relative stiffness and the embedded ratio.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.10
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• pp.6673-6678
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• 2015

Recently, the free form buildings are constructed frequently. Exterior and interior components of these buildings have the free cross-section and a curved shape. So, There are many usages of classical finite element having tapered section and free-style shape. Some general commercial applications like ETABS, SAP2000, MIDAS are usually used for the safety evaluation of the free form structures. However, there are some limits in the accuracy of structural analysis and the length of analysis time because a very complicated finite element mesh have to be used. Therefore, In this study, a pre and post program module was developed to take advantage of general 3-D curved beam element which has a free-style curved shape and mathematical backgrounds. Pre-post processing module has been developed in this study was developed to control the curvature of the curved members by the NURBS control points. As a result, fast geometric modeling than was possible commercial applications. In addition, realistic depiction of the shape and behavior patterns were possible because of the free-form building allows visual check of the free form.