• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.4
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• pp.763-774
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• 2014

A simple and efficient vibration analysis procedure for stiffened panels with openings and arbitrary boundary conditions based on the assumed mode method is presented. Natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion, where Mindlin theory is applied for plate and Timoshenko beam theory for stiffeners. The effect of stiffeners on vibration response is taken into account by adding their strain and kinetic energies to the corresponding plate energies whereas the strain and kinetic energies of openings are subtracted from the plate energies. Different stiffened panels with various opening shapes and dispositions for several combinations of boundary conditions are analyzed and the results show good agreement with those obtained by the finite element analysis. Hence, the proposed procedure is especially appropriate for use in the preliminary design stage of stiffened panels with openings.

• Steel and Composite Structures
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• v.25 no.1
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• pp.67-78
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• 2017

In this study, free vibration of functionally graded (FG) micro/nanobeams based on nonlocal third-order shear deformation theory and under different boundary conditions is investigated by applying the differential quadrature method. Third-order shear deformation theory can consider the both small-scale effects and quadratic variation of shear strain and hence shear stress along the FG nanobeam thickness. The governing equations are obtained by using the Hamilton's principle, based on third-order shear deformation beam theory. The differential quadrature (DQ) method is used to discretize the model and attain the natural frequencies and mode shapes. The properties of FG micro/nanobeam are assumed to be chanfged along the thickness direction based on the simple power law distribution. The effects of various parameters such as the nonlocal parameter, gradient index, boundary conditions and mode number on the vibration characteristics of FG micro/nanobeams are discussed in detail.

• Journal of the Earthquake Engineering Society of Korea
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• v.10 no.4 s.50
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• pp.15-24
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• 2006

This work reports the results of our study on the dynamic response of various buried pipelines depending on their boundary conditions. We have studied behavior of the buried pipelines both along the axial and the transverse direction. The buried pipelines are modeled as beams on elastic foundation while the seismic wave as a ground displacement in the form of a sinusoidal wave. The natural frequency, its mode, and the effect of parameters have been interpreted in terms of free vibration. In order to investigate the response on the ground wave, the resulting frequency and the mode shape obtained from the free vibration have been utilized to derive the mathematical formula for the forced vibration. The natural frequency varies most significantly by the soil stiffness and the length of the buried pipelines in the case of free vibration. The effects of the propagation direction and velocity and the frequency of ground wave on the dynamic responses of concrete, steel, and FRP pipes have been analyzed and then dynamic responses depending on the type of pipes have been compared. Through performing dynamic analyser for various boundary conditions and estimation of the location of maximum strain has been estimated for the type of pipes and boundary conditions.

• Advances in nano research
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• v.6 no.2
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• pp.135-145
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• 2018

This work represents the study of the vibration response of the double walled carbon nanotubes (DWCNT) for various boundary conditions. The inner and outer carbon nanotubes are modeled as two individual Euler-Bernoulli's elastic beams interacting each other by Van der waals force. Differential transform method (DTM) is used as a numerical method to solve the governing differential equations and associated boundary conditions. The influence of Winkler elastic medium on vibration frequency is also examined and results are interpreted. MATLAB is used as a tool for solving the governing differential equations. The fundamental natural frequencies are validating with those available in literature and observed a good agreement between them.

• Steel and Composite Structures
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• v.21 no.5
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• pp.999-1016
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• 2016

This study presents free vibration of beam made of porous material. The mechanical properties of the beam is variable in the thickness direction and the beam is investigated in three situations: poro/nonlinear nonsymmetric distribution, poro/nonlinear symmetric distribution, and poro/monotonous distribution. First, the governing equations of porous beam are derived using principle of virtual work based on Euler-Bernoulli theory. Then, the effect of pores compressibility on natural frequencies of the beam is studied by considering clamped-clamped, clamped-free and hinged-hinged boundary conditions. Moreover, the results are compared with homogeneous beam with the same boundary conditions. Finally, the effects of poroelastic parameters such as pores compressibility, coefficients of porosity and mass on natural frequencies has been considered separately and simultaneously.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.4
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• pp.317-323
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• 2014

This study is concerned with the free vibration analysis of an inextensible uniform rope with a spring-mass system at the tip. The rope is hanged vertically in a gravitational field. This problem is related to the free vibration of an elevator rope connected to an elevator cage. The equation of motion and the corresponding boundary conditions are derived by using the Hamilton's principle. The general solution of the governing equation of motion is expressed in terms of Bessel functions. The characteristic equation was derived by applying the boundary conditions. The characteristic values which are in fact non-dimensionalized natural frequencies were obtained numerically. The effects of mass and spring constant were investigated. The numerical results show how the tip mass and spring affect the natural frequencies of the rope.

• Journal of Ocean Engineering and Technology
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• v.16 no.6
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• pp.37-43
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• 2002

The calculation of earthwork plays a major role in the plan or design phase of many civil engineering projects, such as seashore reclamation; and thus, it has become very important to improve upon its accuracy. There have been common drawbacks to earlier methods of ground profiling, such as dialing with sharp corners or the grid points of any tow straight lines. In this paper, we prepose an algorithm for finding a terrain surface using the natural boundary conditions and the both direction spline method, which interpolates the given three-dimensional data by using spline. As a result of this study, the algorithm of the proposed two methods to estimate pit excavation volume should provide a better accuracy than Spot height, Chambers, Chen, or Lin method. Also, the mathematical model mentioned offers maximum accuracy in estimating the volume of a pit excavation.

• Journal of KSNVE
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• v.6 no.6
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• pp.771-779
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• 1996

In this paper, double Fourier sine series is used as a modal displacement functions of a rectangular plate and applied to the free vibration analysis of a rectangular plate under various boundary conditions. The method of stationary potential energy is used to obtain the modal displacements of a plate. To enhance the flexibility of the double Fourier sine series, Lagrangian multipliers are utilized to match the geometric boundary conditions, and Stokes' transformation is used to handle the displacements that are not satisfied by the double Fourier sine series. The frequency parameters and mode shapes obtained by the present method are compared with those obtained by MSC/NASTRAN and other analysis.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.164-168
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• 2004

The vibration analysis of an axially moving membrane are investigated when the membrane has the two sets of in-plane boundary conditions, which are free and fixed constraints in the lateral direction. Since the in-plane stiffness is much higher than the out-of-plane stiffness, it is assumed during deriving the equations of motion that the in-plane motion is in a steady state. Under this assumption. the equation of out-of\ulcornerplane motion is derived, which is a linear partial differential equation influenced by the in-plane stress distributions. After discretizing the equation by using the Galerkin method, the natural frequencies and mode shapes are computed. In particular, we put a focus on analyzing the effects of the in-plane boundary conditions on the natural frequencies and mode shapes of the moving membrane.

• Journal of Industrial Technology
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• v.15
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• pp.169-174
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• 1995

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 D. H. Kim in 1974. IN this paper, the result of application of this method to the laminated plates with axial forces and with attached point mass/masses is presented. Both $N_x$ and $N_y$ forces are considered. The solution for the laminated plates with arbitrary boundary conditions and irregular section can be obtained by simply obtaining the deflection influence coefficients by any method. The effect of neglecting the mass of the plates on the natural frequency, as the ratio of the point mass/masses to the plate mass increases, is thoroughly studied. The influence of $N_x$ and $N_y$ is also carefully investigated.