• Structural Engineering and Mechanics
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• v.78 no.1
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• pp.103-116
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• 2021

In this work, a model of a functionally graded (FG) nanotube conveying fluid embedded in an elastic medium is developed based on the nonlocal strain gradient theory (NSGT) in conjunction with Euler-Bernoulli beam theory (EBT). The main objective of this research is to investigate the nonlinear vibration and stability analysis of fluid-conveying nanotubes. The governing equations of motion are derived by means of Hamiltonian principle. The analytical expressions of nonlinear frequencies and critical flow velocities for two different types of boundary conditions including pinned-pinned (P-P) and clamped-clamped (C-C) conditions are obtained by employing Galerkin method as well as Hamiltonian Approach (HA). Comparison of the obtained results with the published works show the acceptable accuracy of the current solutions. The effects of the power-law index, the nonlocal and material length scale parameters and the elastic medium on the stability and nonlinear responses of FG nanotubes are thoroughly investigated and discussed.

• 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.

• Computers and Concrete
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• v.33 no.3
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• pp.251-264
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• 2024

The present study pertains to the effects of variations in the location and size of drilled web openings on the behavior of fixed-fixed reinforced concrete (RC) beams. For this purpose, a reference bending beam with a transverse opening in each half span was tested to failure. Later, the same beam was modeled and analyzed with the help of finite element software using ABAQUS. Upon achieving close agreement between the experimental and numerical results, the location and size of the web opening were altered to uncover the effects of these factors on the shear strength and load-deflection behavior of RC beams. The experimental failure mode of the tested beam and the numerical results were also verified by theoretical calculations. In numerical analysis, when compared to the reference (D0) specimen, if the distance of the opening center from the support is 0 or h or 2h, reduction in load-bearing capacity of 1.5%-22.8% or 2.0%-11.3% or is 4.1%-40.7%. In other words, both the numerical analyses and theoretical calculations indicated that the beam behavior shifted from shear-controlled to flexure-controlled as the openings approached the supports. Furthermore, the deformation capacities, energy absorption values, and the ductilities of the beams with different opening diameters also increased with the decreasing distance of the opening from supports. Web compression failure was shown to be the predominant mode of failure of beams with large diameters due to the lack of sufficient material in the diagonal compression strut of the beam. The present study indicated that transverse openings with diameters, not exceeding about 1/3 of the entire beam depth, do not cause the premature shear failure of RC beams. Finally, shear damage should be prevented by placing special reinforcements in the areas where such gaps are opened.

• Journal of KSNVE
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• v.8 no.2
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• pp.313-323
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• 1998

This paper addresses a sliding mode control of vibration in a flexible structure using ER(electro-rheological) dampers. A clamped-clamped flexible structure system supported by two short columns is considered. Three ER dampers to be operated in shear mode are designed on the basis of Bingham model of the arabic gum-based ER fluid, and attached to the flexible beam structure. After deriving the governing equation of motion and associated boundary conditions, a sliding mode controller is formulated to effectively suppress the vibration of the beam structure caused by sinusoidal and random excitations. In the formulation of the controller, parameter variations such as natural frequency deviation are treated to take into account the robustness of control system. The effectiveness of the proposed control system is confirmed by both simulation and experimental results.

• Structural Engineering and Mechanics
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• v.61 no.2
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• pp.209-220
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• 2017

The purpose of this paper is to study the geometrically nonlinear free vibration of functionally graded nano/micro beams (FGNBs) based on the modified couple stress theory. For practical applications, some analytical expressions of nonlinear frequencies for FGNBs on a nonlinear Pasternak foundation are developed. Hamilton's principle is employed to obtain nonlinear governing differential equations in the context of both Euler-Bernoulli and Timoshenko beam theories for a comprehensive investigation. The modified continuum theory contains one material length scale parameter to capture the size effect. The variation of two-constituent material along the thickness is modeled using Reddy's power-law. Also, the Mori-Tanaka method as an accurate homogenization technique is implemented to estimate the effective material properties of the FGNBs. The results are presented for both hinged-hinged and clamped-clamped boundary conditions. The nonlinear partial differential equations are reduced to ordinary differential equations using Galerkin method and then the powerful method of homotopy analysis is utilized to obtain the semi-analytical solutions. Eventually, the presented analytical expressions are used to examine the influences of the length scale parameter, material gradient index, and elastic foundation on the nonlinear free vibration of FGNBs.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.4
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• pp.427-436
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• 2000

This study presents the nonlinear responses of a hinged-clamped beam under broadband random excitation. By using Galerkin's method the governing equation is reduced to a system or nonautonomous nonlinear ordinary differential equations. The Fokker-Planck equation is used to generate a general first-order differential equation in the joint moments of response coordinates. Gaussian and non-Gaussian closure schemes are used to close the infinite coupled moment equations. The closed equations are then solved for response statistics in terms of system and excitation parameters. The case of two mode interaction is considered in order to compare it with the case of three mode interaction. Monte Carlo simulation is used for numerical verification.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.4
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• pp.417-425
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• 2007

The differential quadrature method(DQM) is applied to computation of eigenvalues of the equations of motion governing the free out-of-plane vibration for circular curved beams including the effects of rotatory inertia and transverse shearing deformation. Fundamental frequencies are calculated for the members with clamped-clamped end conditions and various opening angles. The results are compared with exact solutions or numerical solutions by other methods for cases in which they are available. The DQM provides good accuracy even when only a limited number of grid points is used.

• Structural Engineering and Mechanics
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• v.36 no.5
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• pp.545-560
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• 2010

Two or more distinct materials are combined into a single functionally graded material (FGM) where the microstructural composition and properties change gradually. Thermal post-buckling behavior of uniform slender FGM beams is investigated independently using the classical Rayleigh-Ritz (RR) formulation and the versatile Finite Element Analysis (FEA) formulation developed in this paper. The von-Karman strain-displacement relations are used to account for moderately large deflections of FGM beams. Bending-extension coupling arising due to heterogeneity of material through the thickness is included. Simply supported and clamped beams with axially immovable ends are considered in the present study. Post-buckling load versus deflection curves and buckled mode shapes obtained from both the RR and FEA formulations for different volume fraction exponents show an excellent agreement with the available literature results for simply supported ends. Response of the FGM beam with clamped ends is studied for the first time and the results from both the RR and FEA formulations show a very good agreement. Though the response of the FGM beam could have been studied more accurately by FEA formulation alone, the authors aim to apply the RR formulation is to find an approximate closed form post-buckling solutions for the FGM beams. Further, the use of the RR formulation clearly demonstrates the effect of bending-extension coupling on the post-buckling response of the FGM beams.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.7 no.5
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• pp.793-800
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• 2006

DQM(differential quadrature method) is applied to computation of eigenvalues of the equations of motion governing the free in-plane vibration fur circular curved beams including both rotatory inertia and shear deformation. Fundamental frequencies are calculated for the members with clamped-clamped end conditions and various opening angles. The results are compared with numerical solutions by other methods for cases in which they are available. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.

• Coupled systems mechanics
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• v.13 no.2
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• pp.153-170
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• 2024

The problem considered in this theoretical paper is the delamination of a multilayered inhomogeneous beam structure that has viscoelastic behaviour under angle of twist, horizontal and vertical displacements which vary smoothly with time according to prescribed laws. The cross-section of the beam is a rectangle. The layers are made of different materials which are smoothly inhomogeneous along the length of the beam. The beam under consideration represents statically undetermined structure since it is clamped in its two ends. The problem of the strain energy release rate is solved. For this purpose, the strain energy stored in the beam structure is analyzed. In order to verify the solution obtained, the strain energy release rate is found also analyzing the time-dependent compliances of the beam under prescribed angle of twist and displacements. A parametric investigation is carried-out by applying the solution obtained. Special attention is paid to the effect of the parameters which control the variation of the angle of twist and the displacements with time on the strain energy release rate.