• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.341-348
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• 1998

A method of calculating the natural frequency corresponding to the first mode of vibration of beams and tower structures, with irregular cross sections and with arbitrary boundary conditions was developed and reported by Kim, D. H. in 1974. In this paper, the result of application of this method to the subject problem is presented. The structure considered for this report is two span continuous special orthotropic plates with elastic intermediate support. The use of elastic support as one of the passive control means is common. Any method may be used to obtain the deflection influence surfaces needed for this vibration analysis. Finite difference method is used for this purposa in this paper. The influence of the modulus of the foundation, and $D_{ij}$ stiffnesses on the natural frequency is thoroughly studied.

• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.419-432
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• 2015

The free vibration of rotating Euler-Bernoulli beams with the thickness and/or width of the cross-section vary linearly along the length is investigated by using the Adomian modified decomposition method (AMDM). Based on the AMDM, the governing differential equation for the rotating tapered beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and the closed form series solution of the corresponding mode shapes can be easily obtained simultaneously. The computed results for different taper ratios as well as different offset length and rotational speeds are presented in several tables and figures. The accuracy is assured from the convergence and comparison with the previous published results. It is shown that the AMDM provides an accurate and straightforward method of free vibration analysis of rotating tapered beams.

• 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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.6
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• pp.423-429
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• 2003

On this study. we improved the efficiency applying algorithm that is repeatedly using table of orthogonal array in discrete design space and filling a defect of gradient method in continuous design space. we showed optimal ply angle that maximized 1st natural frequency of CFRP laminated composite plate without a hole and with a hole by each aspect ratio. In the case of CFRP laminated composite plate without a hole, we confirmed the reliance and efficiency of algorithm in comparison with the result of optimization achievement repeatedly using statistical table of orthogonal array of experimental design and the BFGS optimal design method.

• Advances in aircraft and spacecraft science
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• v.3 no.1
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• pp.45-59
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• 2016

In this paper, the condensation method which is based on the Rayleigh-Ritz method, is described for the free vibration analysis of axially loaded slightly curved beams subject to partial axial restraints. If the longitudinal inertia is neglected, some of the Rayleigh-Ritz minimization equations are independent of the frequency. These equations can be used to formulate a relationship between the weighting coefficients associated with the lateral and longitudinal displacements, which leads to "connection coefficient matrix". Once this matrix is formed, it is then substituted into the remaining Rayleigh-Ritz equations to obtain an eigenvalue equation with a reduced matrix size. This method has been applied to simply supported and partially clamped beams with three different shapes of imperfection. The results indicate that for small imperfections resembling the fundamental vibration mode, the sum of the square of the fundamental natural and a non-dimensional axial load ratio normalized with respect to the fundamental critical load is approximately proportional to the square of the central displacement.

• Steel and Composite Structures
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• v.21 no.6
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• pp.1211-1226
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• 2016

In this study, free vibration and damping characteristics of composite beams with holes are investigated, experimentally and numerically. Two types of samples with different fabrics are used: unidirectional and woven. The effects of diameter, number and location of circular holes on the vibration characteristics of composite beams are examined. The effects of rotation angle and minor to major diameter ratio of the elliptical hole are also investigated numerically. Moreover, the mode shapes of all types of beams are obtained numerically. According to the results, the natural frequency decreases with increasing hole diameter but increases very little with increasing the distance between the hole center and the clamped end. Damping ratio decreases by increasing the diameter of hole. But it fluctuates by increasing the diameters of holes of beam having three holes. Furthermore it decreases by increasing the distance between hole center and clamped end except for the range 50 mm to 100 mm.

• Steel and Composite Structures
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• v.50 no.2
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• pp.135-148
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• 2024

This paper analytically investigates the free vibration analysis of functionally graded-carbon nanotube reinforced composite (FG-CNTRC) plates by dynamic stiffness method (DSM). The properties of CNTRC are determined with the extended rule of mixture. The governing differential equations of motion based on the first-order shear deformation theory of CNTRC plate are derived using Hamilton's principle. The FG-CNTRC plates are studied for a uniform and two different distributions of carbon nanotubes (CNTs). The accuracy and performance of the DSM are compared with the results obtained from closed closed-form and semi-analytical solution methods in previous studies. In this study, the effects of boundary condition, distribution type of CNTs, plate aspect ratio, plate length to thickness ratio, and different values of CNTs volume fraction on the natural frequencies of the FG-CNTRC plates are investigated. Finally, various natural frequencies of the plates in different conditions are provided as a benchmark for comparing the accuracy and precision of the other analytical and numerical methods.

• Journal of the Society of Naval Architects of Korea
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• v.35 no.3
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• pp.54-61
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• 1998

This paper presents a prediction method of natural frequencies of vertical hull girder vibration based on design sensitivity analysis in case of design modification and the variation of loading condition. The resented method premises the vibration analysis by the transfer matrix method. Governing sensitivity equation is derived from the direct differentiation of state vector and transfer matrix to parameters and its transfer over all the hull girder elements. Derivatives of natural frequencies and mode shapes are determined by two trial calculation of the governing equation. Using the derivatives, the changes of natural frequencies and mode shapes can be predicted when mass and stiffness parameter's are changed. As results, it is possible to optimize ship structure as well as to avoid troublesome calculation in hull girder vibration analysis rationally and efficiently. To verify the accuracy and efficiency of the resented method numerical results obtained by both the sensitivity analysis and the ordinary reanalysis far a real ore/bulk carrier in case of the change of mass and stiffness parameters are compared.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.285-287
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• 2014

Equations of motion for the vibration analysis of rotating pre-twisted beams with functionally graded material properties are derived in this paper. Based on Timoshenko beam theory, the effects of shear and rotary inertia are considered. The pre-twisted beam has a rectangular cross-section and is mounted on a rotating rigid hub with a setting angle. Functionally graded material (FGM) properties are considered along the height direction of the beam. The equations of stretching and bending motion are derived by Kane's method employing hybrid deformation variables. To validate the derived equations, natural frequencies of a rotating FGM pre-twisted beam are compared to those obtained by a commercial software ANSYS. The effects of the pre-twisted angle, slenderness ratio, hub radius, volume fraction exponent, and angular speed on the modal characteristics of the system are investigated with the proposed model.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.4
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• pp.338-347
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• 2010

Heunginjimun designated as a Treasure No.1 is a two-story wooden structure with 5 bay and 2 bay in its front and side views, respectively. This paper presents an investigation on vibration characteristics of Heunginjimun through both ambient vibration and impact hammer tests. Ambient vibration test was performed to identify the natural frequency of Heunginjimun from the spectrum analysis of time history. Impact hammer test was undertaken to find the frequency of Heunginjimun which is affected by the surrounding traffics and to verify the reciprocal principle for the wooden structural system. Ambient vibration test results of Heunginjimun showed that the natural frequencies in two principal axes 1.5 Hz and 1.1 Hz, respectively. It was confirmed from impact hammer tests for a ground that the frequency of 4.2 Hz is caused by the traffics surrounding Heunginjimun. It was also observed that from the impact hammer test results between two locations in Heunginjimun that the transfer functions measured from two corresponding locations coincided well with each other. This result shows that the wooden structural system is globally linear, and the reciprocal principle is established.