• Journal of Industrial Technology
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• v.15
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• pp.71-75
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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. This method has been developed for two-dimensional problems including the laminated composite plates and was proved to be very effective for the plates with arbitrary boundary conditions and irregular sections. In this paper, the result of application of this method to the clamped composite plates with non-uniform cross-section and with attached point mass/masses is presented.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.977-983
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• 2003

Free vibration analysis of helical springs was performed by the use of the commercial finite element analysis program, ANSYS. The investigation of national frequency was focused on the effect of various parameters such as boundary conditions, spring indices, number of coil turns and helix angles which are considered to affect the free vibration of a spring. The finite element method was validated by comparison with the result of a previouosly published literature. The similarity of frequency trend was shown among three boundary conditions: clamped-clamped, free-free, simpliy supported-simply supported but there was no similarity in light of mode shapes among them. Several modes showed similar frequencies on and near the frequencies identified by the natural frequency formula of Wahl. Natural frequencies increased with spring indices and number of turns decreasing and with helix angles increasing. The results investigated by finiete element method were compared with the experemental result and theoretical result and showed a good agreement among them.

• Structural Engineering and Mechanics
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• v.32 no.6
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• pp.811-833
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• 2009

In the present article bending, buckling and vibration analyses of tapered beams using Eringen non-local elasticity theory are being carried out. The associated governing differential equations are solved employing Rayleigh-Ritz method. Both Euler-Bernoulli and Timoshenko beam theories are considered in the analyses. Present results are in good agreement with those reported in literature. Beam material is considered to be made up of functionally graded materials (fgms). Non-local analyses for tapered beam with simply supported - simply supported, clamped - simply supported and clamped - free boundary conditions are carried out and discussed. Further, effect of length to height ratio on maximum deflections, vibration frequencies and critical buckling loads are studied.

• Journal of the Korean Society of Safety
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• v.12 no.2
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• pp.37-44
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• 1997

Composite materials have various complicated characteristics depending on the ply materials, ply orientations, ply stacking sequences and boundary conditions. Therefore, it is difficult to analyze composite materials. For efficient use of composite materials in engineering applications, the dynamic behavior such as natural frequencies and nodal patterns should be identified. This study presents FEM results for the free vibration of symmetrically and antisymmetrically laminated composite and hybrid composite rectangular plates. The natural frequencies of laminated composite rectangular plates having the various boundary conditions (completely clamped, 2-edge clamped, cantilevered) are experimentally obtained. In order to demonstrate the validity of the experiment, FEM analysis using ANSYS was performed and natural frequencies experimentally obtained is compared with that calculated by FEM analysis. The results obtained from both experiment and FEM analysis show a good agreement.

• Computers and Concrete
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• v.32 no.3
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• pp.303-311
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• 2023

An analysis of the Poisson's ratios influence of single walled carbon nanotubes (SWCNTs) based on Sander's shell theory is carried out. The effect of Poisson's ratio, boundary conditions and different armchairs SWCNTs is discussed and studied. The Galerkin's method is applied to get the eigen values in matrix form. The obtained results shows that, the decrease in ratios of Poisson, the frequency increases. Poisson's ratio directly measures the deformation in the material. A high Poisson's ratio denotes that the material exhibits large elastic deformation. Due to these deformation frequencies of carbon nanotubes increases. The frequency value increases with the increase of indices of single walled carbon nanotubes. The prescribe boundary conditions used are simply supported and clamped simply supported. The Timoshenko beam model is used to compare the results. The present method should serve as bench mark results for agreeing the results of other models, with slightly different value of the natural frequencies.

• Smart Structures and Systems
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• v.19 no.3
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• pp.299-307
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• 2017

The magneto-electro-elastic (MEE) material under thermal environment exhibits pyroelectric and pyromagnetic coefficients resulting in pyroelectric and pyromagnetic effects. The pyroelectric and pyromagnetic effects on the behavior of multiphase MEE sensors bonded on top surface of a mild steel beam under thermal environment is presented in this paper. The aim of the study is to find out how samples having different volume fractions of the multiphase MEE composite behave in sensor applications. This is studied at optimal location on the beam, where the maximum electric and magnetic potentials are induced due to pyroelectric and pyromagnetic effects under clamped-free and clamped-clamped boundary conditions. The sensor which is bonded on the top surface of the beam is modeled using 8-node brick element. The MEE sensor bonded on mild steel beam is subjected to uniform temperature rise of 50K. It is assumed that beam and sensor is perfectly bonded to each other. The maximum pyroelectric and pyromagnetic effects on electric and magnetic potentials are observed when volume fraction is ${\nu}_f=0.2$. The boundary conditions significantly influence the pyroelectric and pyromagnetic effects on electric and magnetic potentials.

• Steel and Composite Structures
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• v.35 no.3
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• pp.449-462
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• 2020

This work aims to study effects of the crack and the surface energy on the free longitudinal vibration of axially functionally graded nanorods. The surface energy parameters considered are the surface stress, the surface density, and the surface Lamé constants. The cracked nanorod is modelled by dividing it into two parts connected by a linear spring in which its stiffness is related to the crack severity. The surface and bulk material properties are considered to vary in the length direction according to the power law distribution. Hamilton's principle is implemented to derive the governing equation of motion and boundary conditions. Considering the surface stress causes that the derived governing equation of motion becomes non-homogeneous while this was not the case in works that only the surface density and the surface Lamé constants were considered. To extract the frequencies of nanorod, firstly the non-homogeneous governing equation is converted to a homogeneous one using an appropriate change of variable, and then for clamped-clamped and clamped-free boundary conditions the governing equation is solved using the harmonic differential quadrature method. Since the present work considers effects of all the surface energy parameters, it can be claimed that this is a comprehensive work in this regard.

• Advances in nano research
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• v.12 no.1
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• pp.101-115
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• 2022

Some researchers pointed out that the nonlocal cantilever models do not predict the dynamic softening behavior for nanostructures (including nanobeams) with clamped-free (CF) ends. In contrast, some indicate that the nonlocal cantilever models can capture the stiffness softening characteristics. There are substantial differences on this issue between them. The vibration analysis of porosity-dependent functionally graded nanoscale tubes with variable boundary conditions is investigated in this study. Using a modified power-law model, the tube's porosity-dependent material coefficients are graded in the radial direction. The theory of nonlocal strain gradients is used. Hamilton's principle is used to derive the size-dependent governing equations for simply-supported (S), clamped (C) and clamped-simply supported (CS). Following the solution of these equations by the extended differential quadrature technique, the effect of various factors on vibration issues was investigated further. It can be shown that these factors have a considerable effect on the vibration characteristics. It also can be found that our numerical results can capture the unexpected softening phenomena for cantilever tubes.

• Advances in nano research
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• v.16 no.3
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• pp.273-288
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• 2024

The geometrical nonlinear vibrations of the gold nanoscale rod are investigated for the first time by considering the internal modals interactions using different nonlinear beam theories. This phenomenon is usually one of the important features of nonlinear vibration systems. For a more detailed analysis, the von-Karman effects, preserving all the nonlinear terms in the strain-displacement relationships of gold nanoscale rods in three displacement directions, are considered to analyze the nonlinear axial vibrations of gold nanoscale rods. It uses highly accurate analytical-numerical solutions for the clamped-clamped and clamped-free boundary conditions of nanoscale gold rods. Also, with the help of Hamilton's principle, the governing equation and boundary conditions are derived based on Eringen's theory. The influence of nonlinear and nonlocal factors on axial vibrations was investigated separately for all three theories: Simple (ST), Rayleigh (RT) and Bishop (BT). Using different theories, the effects of inertia and shear on the internal resonances of gold nanorods were studied and compared in terms of twoto-one and three-to-one internal resonances. As the nonlocal parameter of the gold nanorod increases, the maximum nonlinear amplitude occurs. So, by adding nonlocal effects in a gold nanorod, the internal modal interactions resulting from the unique structure can be enhanced. It is worth noting that shear and inertial analysis have a significant effect on internal modal interactions in gold nanorods.

• Steel and Composite Structures
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• v.28 no.6
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• pp.655-670
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• 2018

A coupled method, that combines the Ritz method and the finite element (FE) method, is proposed to solve the vibration problem of rectangular thin and thick plates with general boundary conditions. The eigenvalue partial differential equation(s) of the plate is (are) first reduced to a set of eigenvalue ordinary differential equations by the application of the Ritz method. The resulting eigenvalue differential equations are then reduced to an eigenvalue algebraic equation system using the finite element method. The natural boundary conditions of the plate problem including the free edge and free corner boundary conditions are also implemented in a simple and accurate manner. Various boundary conditions including simply supported, clamped and free boundary conditions are considered. Comparisons with existing numerical and analytical solutions show that the proposed mixed method can produce highly accurate results for the problems considered using a small number of Ritz terms and finite elements. The proposed mixed Ritz-FE formulation is also compared with the mixed FE-Ritz formulation which has been recently proposed by the present author and his co-author. It is found that the proposed mixed Ritz-FE formulation is more efficient than the mixed FE-Ritz formulation for free vibration analysis of rectangular plates with Levy-type boundary conditions.