• Steel and Composite Structures
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• v.25 no.3
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• pp.347-360
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• 2017

The goal of this study is to fill this apparent gap in the area about vibration analysis of multiwalled carbon nanotubes (MWCNTs) curved panels by providing 3-D vibration analysis results for functionally graded multiwalled carbon nanotubes (FG-MWCNTs) sandwich structure with power-law distribution of nanotube. The effective material properties of the FG-MWCNT structures are estimated using a modified Halpin-Tsai equation. Modified Halpin-Tsai equation was used to evaluate the Young's modulus of MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. Also, the mass density and Poisson's ratio of the MWCNT/phenolic composite are considered based on the rule of mixtures. Parametric studies are carried out to highlight the influence of MWCNT volume fraction in the thickness, different types of CNT distribution, boundary conditions and geometrical parameters on vibrational behavior of FG-MWCNT thick curved panels. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including Free, Simply supported and Clamped at the curved edges. For an overall comprehension on 3-D vibration analysis of sandwich panel, some mode shape contour plots are reported in this research work.

• Steel and Composite Structures
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• v.28 no.5
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• pp.541-557
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• 2018

This paper presents the influence of carbon nanotubes (CNTs) waviness and aspect ratio on the vibrational behavior of functionally graded nanocomposite sandwich annular sector plates resting on two-parameter elastic foundations. The carbon nanotube-reinforced (CNTR) sandwich plate has smooth variation of CNT fraction along the thickness direction. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak's elastic foundation coefficients, sandwich plate thickness, face sheets thickness and plate aspect ratio are investigated on the free vibration of the sandwich plates with wavy CNT-reinforced face sheets. The study is carried out based on three-dimensional theory of elasticity and in contrary to two-dimensional theories, such as classical, the first- and the higher-order shear deformation plate theories, this approach does not neglect transverse normal deformations. The sandwich annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free.

• Smart Structures and Systems
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• v.21 no.1
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• pp.65-74
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• 2018

In this article, an analytic non-classical model for the free vibrations of nanobeams accounting for surface stress effects is developed. The classical continuum mechanics fails to capture the surface energy effects and hence is not directly applicable at nanoscale. A general beam model based on Gurtin-Murdoch continuum surface elasticity theory is developed for the analysis of thin and thick beams. Thus, surface energy has a significant effect on the response of nanoscale structures, and is associated with their size-dependent behavior. To check the validity of the present analytic solution, the numerical results are compared with those obtained in the scientific literature. The influences of beam thickness, surface density, surface residual stress and surface elastic constants on the natural frequencies of nanobeams are also investigated. It is indicated that the effect of surface stress on the vibrational response of a nanobeam is dependent on its aspect ratio and thickness.

• Advances in nano research
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• v.8 no.4
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• pp.265-276
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• 2020

A study that primarily focuses on nonlocal strain gradient plate model for the sole purpose of vibration examination, for graphene sheets under linearly variable in-plane mechanical loads. To study a better or more precise examination on graphene sheets, a new advance model was conducted which carries two scale parameters that happen to be related to the nonlocal as well as the strain gradient influences. Through the usage of two-variable shear deformation plate approach, that does not require the inclusion of shear correction factors, the graphene sheet is designed. Based on Hamilton's principle, fundamental expressions in regard to a nonlocal strain gradient graphene sheet on elastic half-space is originated. A Galerkin's technique is applied to resolve the fundamental expressions for distinct boundary conditions. Influence of distinct factors which can be in-plane loading, length scale parameter, load factor, elastic foundation, boundary conditions, and nonlocal parameter on vibration properties of the graphene sheets then undergo investigation.

• Journal of the Korean Society for Railway
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• v.2 no.3
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• pp.36-45
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• 1999

The basic idea of cable-stayed girder bridges is the utilization of high strength cables to provide intermediate supports for the bridge girder so that the girder can span a much longer distance. In the cable-stayed bridge, the cables exhibit nonlinear behavior because of the change in sag, due to the dead weight of the cable, which occurs with changing tension in the cable resulting from the movement of the end points of the cable as the bridge is loaded. Techniques required for the static analysis of cable-stayed bridges has been developed by many researchers. However, little work has been done on the dynamic analysis of such structures. To investigate the characteristics of the dynamic response of long-span cable-stayed bridges due to various dynamic loadings likes moving traffic loads. two different 3-D cable-stayed bridge models are considered in this study. Two models are exactly the same in structural configurations but different in finite element discretization. Modal analysis is conducted using the deformed dead-load tangent stiffness matrix. A new concept was presented by using divided a cable into several elements in order to study the effect of the cable vibration (both in-plane and swinging) on the overall bridge dynamics. The result of this study demonstrates the importance of cable vibration on the overall bridge dynamics.

• Journal of Ocean Engineering and Technology
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• v.16 no.6
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• pp.18-24
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• 2002

The vibrational system in this study consists of a cantilever pipe conveying fluid, the moving mass upon it, and an attached tip mass. The equation of motion is derived by using the Lagrange equation. The influences of the velocity and the velocities of fluid flow in the pipe have been studied on the dynamic behavior of a cantilever pipe using a numerical method. While the moving mass moves upon the cantilever pipe, the velocity of fluid flow and the nozzle angle increase; as a result, the tip displacement of the cantilever pipe, conveying fluid, is decreased. After the moving mass passes over the cantilever pipe, the tip displacement of the pipe is influenced by the potential energy of the cantilever pipe and the deflection of the pipe; the effect is the result of the moving mass and gravity. As the velocity of fluid flow and nozzle angle increases, the natural frequency of he system is decreased at the second mode and third mode, but it is increased at the first mode. As the moving mass increases, the natural frequency of the system is decreased at all modes.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.33-41
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• 2018

In this paper, using modified couple stress theory in place of classical continuum theory, and using shell model in place of beam model, vibrational behavior of nanotubes is investigated via the finite element method. Accordingly classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have taken on great appeal. In the present work the mass-stiffness matrix for cylindrical shell element is developed, and by means of size-dependent finite element formulation is extended to more precisely account for nanotube vibration. In addition to modified couple stress cylindrical shell element, the classical cylindrical shell element can also be defined by setting length scale parameter to zero in the equations. The boundary condition were assumed simply supported at both ends and it is shown that the natural frequency of nano-scale shell using the modified coupled stress theory is larger than that using the classical shell theory and the results of Ansys. The results have indicated using the modified couple stress cylindrical shell element, the rigidity of the nano-shell is greater than that in the classical continuum theory, which results in increase in natural frequencies. Besides, in addition to reducing the number of elements required, the use of this type of element also increases convergence speed and accuracy.

• Wind and Structures
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• v.30 no.2
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• pp.211-217
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• 2020

Vibrations of a wind turbine blade have a negative impact on its performance and result in failure of the blade, therefore an approach to effectively control vibration in turbine blades are sought by wind industry. The small domestic horizontal axis wind turbine blades induce flap wise (out-of-plane) vibration, due to varying wind speeds. These flap wise vibrations are transferred to the structure, which even causes catastrophic failure of the system. Shape memory alloys which possess physical property of variable stiffness across different phases are embedded into the composite blades for active vibration control. Previously Shape memory alloys have been used as actuators to change their angles and orientations in fighter jet blades but not used for active vibration control for wind turbine blades. In this work a GFRP blade embedded with Shape Memory Alloy (SMA) and tested for its vibrational and material damping characteristics, under martensitic and austenite conditions. The embedment portrays 47% reduction in displacement of blade, with respect to the conventional blade. An analytical model for the actuated smart blade is also proposed, which validates the harmonic response of the smart blade.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.1
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• pp.169-174
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• 2011

For a double-walled carbon nanotube resonator with a short outer nanotube, the free edge of the short outer wall plays an important role in the vibration of the long inner nanotube. For a double-walled carbon nanotube resonator with a short inner nanotube, the short inner nanotube can be considered as a flexible core, thus, the fundamental frequency is influenced by its length. In this paper, we analysis frequency variation in ultrahigh frequency nanomechanical resonators based on double-walled carbon nanotubes with different wall length. This results will widely apply to the realization of frequency devices controlling the length of the inner or outer nanotube.

• Smart Structures and Systems
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• v.12 no.3_4
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• pp.427-440
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• 2013

A growing need has developed in the United States to obtain more specific knowledge on the structural integrity of infrastructure due to aging service lives, heavier and more frequent loading conditions, and durability issues. This need has spurred extensive research in the area of structural health monitoring over the past few decades. Several structural health monitoring techniques have been developed that are capable of locating damage in structures using modal strain energy of mode shapes. Typically in the past, bending strain energy has been used in these methods since it is a dominant vibrational mode in many structures and is easily measured. Additionally, there may be cases, such as pipes, shafts, or certain bridges, where structures exhibit significant torsional behavior as well. In this research, torsional strain energy is used to locate damage. The damage index method is used on two numerical models; a cantilevered steel pipe and a simply-supported steel plate girder bridge. Torsion damage indices are compared to bending damage indices to assess their effectiveness at locating damage. The torsion strain energy method is capable of accurately locating damage and providing additional valuable information to both of the structures' behaviors.