• Smart Structures and Systems
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• v.19 no.4
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• pp.441-448
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• 2017

This paper uses the four-variable refined plate theory for the free vibration analysis of functionally graded material (FGM) rectangular plates. The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Equations of motion are derived from the Hamilton's principle. The closed-form solutions of functionally graded plates are obtained using Navier solution. Numerical results of the refined plate theory are presented to show the effect of the material distribution, the aspect and side-to-thickness ratio on the fundamental frequencies. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behavior of functionally graded plates.

• Advances in nano research
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• v.7 no.4
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• pp.277-292
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• 2019

In this present paper, a new two dimensional (2D) and quasi three dimensional (quasi-3D) nonlocal shear deformation theories are formulated for free vibration analysis of size-dependent functionally graded (FG) nanoplates. The developed theories is based on new description of displacement field which includes undetermined integral terms, the issues in using this new proposition are to reduce the number of unknowns and governing equations and exploring the effects of both thickness stretching and size-dependency on free vibration analysis of functionally graded (FG) nanoplates. The nonlocal elasticity theory of Eringen is adopted to study the size effects of FG nanoplates. Governing equations are derived from Hamilton's principle. By using Navier's method, analytical solutions for free vibration analysis are obtained through the results of eigenvalue problem. Several numerical examples are presented and compared with those predicted by other theories, to demonstrate the accuracy and efficiency of developed theories and to investigate the size effects on predicting fundamental frequencies of size-dependent functionally graded (FG) nanoplates.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.10
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• pp.1900-1907
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• 1992

This paper presents the vibration mode, natural frequencies and amplitudes of the circular plate due to the changes of the boundary conditions by varying free arc angles. The vibration mode, amplitudes and natural frequencies of the circular plate are obtained by time-average holographic interferometry and laser doppler vibrometer. The vibration modes of the circular plate with the mixed boundary conditions are found from the 1st mode to the 4th mode. The curve shapes of the natural frequency ratios obtained from this study are in a good agreement with other results obtained by numerical analysis. The displacement curves obtained from time average holographic interferometry and laser doppler vibrometer agree well in case of large amplitude, but show a little difference in case of small amplitude.

• Advances in nano research
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• v.4 no.3
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• pp.197-228
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• 2016

In the present study, thermo-electro-mechanical vibration characteristics of functionally graded piezoelectric (FGP) Timoshenko nanobeams subjected to in-plane thermal loads and applied electric voltage are carried out by presenting a Navier type solution for the first time. Three kinds of thermal loading, namely, uniform, linear and non-linear temperature rises through the thickness direction are considered. Thermo-electro-mechanical properties of FGP nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions based on Timoshenko beam theory are obtained for the free vibration analysis of graded piezoelectric nanobeams including size effect and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FGP nanobeams as compared to some cases in the literature. In following a parametric study is accompanied to examine the effects of several parameters such as various temperature distributions, external electric voltage, power-law index, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams in detail. It is found that the small scale effect and thermo-electrical loading have a significant effect on natural frequencies of FGP nanobeams.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.5A
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• pp.641-647
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• 2008

This paper introduces a new technique that can extract natural frequencies and damping ratios from output-only vibration data. Firstly, the free vibration data is obtained from the cross correlations of the output-only response data using a singular value decomposition process. Secondly, the well-known system identification algorithm is applied to extract the natural frequencies and damping ratios from the extracted free vibration data. Comparing to ERADC technique, the accuracy of the proposed modal parameter identification algorithm has been numerically examined. Furthermore, the practicability of the proposed algorithm has been examined through the output-only acceleration data collected from the Seohae cable-stayed bridge. Using the proposed technique, total 24 modes have been identified for the deck plate motions of the bridge.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.526-529
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• 2004

Arches are one of the most important basic structural units as well as the beams, columns and plates. Most complicated structures consist of only these basic units and therefore it is very attractive research subject to analysis both the static and dynamic behavior of such units including the arches. This study deals with the free vibration of arbitrary shaped arches. In order to obtain the exactly arch shape, which surveyed (x, y) of neutral axis of arbitrary shaped arches are compared to various shape of arch: circular, parabolic, sinusoidal, elliptic, spiral and cartenary. The differential equations governing free vibrations of arches are merely adopted in the open literature rather than deriving the equations in this study. The Taylor series method is used as the numerical differential scheme. The Runge-Kutta method and the Regula-Falsi method, respectively, are used to integrate the governing differential equations and to compute the natural frequencies It is expected that results obtained herein can be practically utilized in the fields of vibration control.

• Advances in aircraft and spacecraft science
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• v.5 no.6
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• pp.671-689
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• 2018

Bending, buckling and free vibration responses of functionally graded (FG) higher-order beams resting on two parameter (Winkler-Pasternak) elastic foundation are studied using a new inverse hyperbolic beam theory. The material properties of the beam are graded along the thickness direction according to the power-law distribution. In the present theory, the axial displacement accounts for an inverse hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the top and bottom surfaces of the beams. Hamilton's principle is employed to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending, bucking and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio and foundation parameter on the displacements, stresses, critical buckling loads and frequencies. Numerical results by using parabolic beam theory of Reddy and first-order beam theory of Timoshenko are specially generated for comparison of present results and found in excellent agreement with each other.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.712-717
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• 2000

The main purpose of this paper is to present both the fundamental and some higher natural frequencies of axially loaded Timoshenko beams resting on the elastic foundation. The non-dimensional differential equation governing the free vibrations of such beam is derived in which the effects of rotatory inertia and shear deformation are included. The Improved Euler method and Determinant Search method are used to perform the integration of the differential equation and to determine the natural frequencies, respectively. The hinged-hinged, hinged-clamped and clamped-clamped end constraints are applied in numerical examples. The relations between frequency parameters and both the foundation parameter and slenderness ratio are presented in figures. The effect of cross-sectional shapes is also investigated.

• Magazine of the Korean Society of Agricultural Engineers
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• v.28 no.1
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• pp.68-74
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• 1986

The governing differential equations and the boundary conditions for the free vibra- tion of the unsymmetric parabolic arch with fixed ends are derived on the basis of the equilibrium equations and the D'Alembert principle. The effect of the rotary inertia as well as the extensional and the flexural deformations is considered in the governing differential equations. A trial eigenvalue method is used for determining the natural frequencies. The Ru- uge-Kutta method is used in this method to perform the integration of the differential equations. The detailed studies are made of the lowest three vibration frequencies for the par- abolic chord length equal to 10m. The effect of the rotary inertia is analyzed and it's numerical data are presented in table. And as the numerical results the frequency versus the rise of arch and the radius of gyration are presented in figures.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.11-16
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• 2002

The differential equations governing free vibrations of the elastic, horizontally curved beams with unsymmetric axis are derived in Cartesian coordinates rather than in polar coordinates, in which the effect of torsional inertia is included. Frequencies are computed numerically for the sinusoidal curved beams with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and SAP 2000 are made to validate theories and numerical methods developed herein. The convergent efficiency is highly improved under the newly derived differential equations in Cartesian coordinates. The lowest four natural frequency parameters are reported, with and without torsional inertia, as functions of three non-dimensional system parameters: the horizontal rise to chord length ratio, the span length to chord length ratio, and the slenderness ratio.